Structure of Neat Liquids Consisting of (Perfect and Nearly

Review pubs.acs.org/CR

Structure of Neat Liquids Consisting of (Perfect and Nearly) Tetrahedral Molecules Szilvia Pothoczki, László Temleitner, and László Pusztai* Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, Konkoly Thege út 29-33, Budapest, H-1121 Hungary 4.1.3. Evolution of Ideas Concerning Orientational Correlations: The Apollo Model and Beyond 4.1.4. Structure of Liquid Carbon TetrachlorideAs We Understand It today 4.2. Liquids of Molecules with a Perfect Tetrahedral Shape: The XY4 Series 4.2.1. Fluid Methane, CH4 4.2.2. Liquid Carbon Tetrahalides: The CX4 Series (X = F, Cl, Br, I) 4.2.3. Liquid Tetrachlorides: The XCl4 Series (X = C, Si, Ge, V, Ti, Sn) 4.2.4. Other Combinations: GeBr4, SnI4, and Neopentane, C(CH3)4 4.3. X4 Types: The Structure of Liquid Phosphorus (P4) 4.4. Connection with the Structure of Crystalline Phases: The Case of Carbon Tetrabromide, CBr4 5. Liquids of Nearly Tetrahedral Molecules 5.1. Five-Atom Molecules with C3v Symmetry: Chloroform, Methyl Iodide, and Their Derivatives 5.1.1. Liquid Chloroform 5.1.2. Analogues: Bromoform (CHBr3), Methyl Iodide (CH3I), Phosphorus Oxychloride (POCl3), and Vanadium Oxychloride (VOCl3) 5.2. Four-Atom Molecules with C3v Symmetry: Phosphorus Halogenides and Ammonia 5.2.1. Liquid PBr3 and Related Materials 5.2.2. Liquid/Fluid Ammonia, NH3 5.3. Tetrahedricity vs Linearity, with C3v Symmetry: Acetonitrile, CH3CN 5.3.1. Diffraction Studies 5.3.2. Integral Equation Theoretical Studies 5.3.3. Computer Simulations 5.4. Molecules with C2v Symmetry: Methylene Chloride and Its Derivatives 5.4.1. Liquid Methylene Chloride, CH2Cl2 5.4.2. Liquid Methylene Halides CH2F2, CH2Br2, CH2I2, and CBr2Cl2 6. Summary and Concluding Remarks Author Information Corresponding Author Notes

CONTENTS 1. Introduction 2. Experimental Techniques: Focus on Diffraction 2.1. Diffraction Phenomenon and Basic Formalism 2.2. X-ray Diffraction 2.3. Neutron Diffraction 2.4. Scattering from Liquids: Correlation Functions 3. Computational Methods 3.1. Computer Simulations 3.1.1. Molecular Dynamics Computer Simulations 3.1.2. Monte Carlo Simulations 3.2. Structural Modeling Based on Diffraction Data: Reverse Monte Carlo 3.2.1. Preparation of Reference Structures: Fused Hard Sphere Monte Carlo Simulations 3.3. Tools for Characterizing the Intermolecular Orientational Structure on the Basis of Large Sets of Particle Coordinates (“Particle Configurations”) 3.3.1. Distance-Dependent Dipole−Dipole Correlation Functions 3.3.2. Special Correlation Functions for Linear Molecules or Dipoles 3.3.3. Perfect Tetrahedral Molecules without Unique Symmetry Axes: Rey Constructions 3.3.4. More Specific Descriptors of Orientations of Tetrahedral Molecules 4. Liquids of Perfect Tetrahedral Molecules 4.1. Prototype: Liquid Carbon Tetrachloride, CCl4 4.1.1. Diffraction Experiments 4.1.2. Computer Simulations and Theoretical Investigations

© XXXX American Chemical Society

B B B E E F G G G H I

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Received: May 22, 2015

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DOI: 10.1021/acs.chemrev.5b00308 Chem. Rev. XXXX, XXX, XXX−XXX

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that has not yet been studied in depth but that may be a potential subject of future investigations.)

AR AR AS

2. EXPERIMENTAL TECHNIQUES: FOCUS ON DIFFRACTION If one wishes to study the atomic level bulk structure of liquids, direct microscopy is not an option due to its resolution limit. In principle, two groups of methods may provide information on the (inter)molecular structure: dif f raction and spectroscopic techniques. Only diffraction may be considered as a direct method for this purpose. Diffraction methods are the workhorses of structure determination, and therefore, they are described in some detail separately below. Diffraction is sensitive to spatial local density variations (of electrons or nuclei, see below): it provides an average (in space and time) of the local density. Spectroscopic methods are able to yield information on the local environment of an atom; however, from the point of view of this review, correlations between neighboring molecules are of primary importance in the liquid state, whereas spectroscopy can focus more on the dynamics (and indirectly on structure) within a molecule via measuring correlation times. As structure studies based solely on spectroscopic measurements are extremely rare for the reviewed liquids, detailed introduction of these methods is omitted. The interested reader may turn to general textbooks, such as that of Atkins,89 and/or to texts specialized on NMR90 and vibrational91 spectroscopies. For those interested in the theoretical background of spectroscopic methods in terms of intermolecular interaction, the work, e.g., of Torii92 may also be recommended. In this section, a short introduction to X-ray and neutron diffraction is given. More detailed description can be found in textbooks93−97 and specialized review articles.98,99 Note that although, in principle, electron diffraction is also able to provide the kind of correlation functions applicable for describing disordered structures, for technical reasons, this technique has not been applied for the systems of interest here.

1. INTRODUCTION The liquid structure of carbon tetrachloride, a molecular liquid consisting of molecules with perfect tetrahedral shape (Td symmetry), has been continuously investigated for more than 80 years (see refs 1 and 2). The reason for such outstanding interest is that, arguably, without adequate knowledge of this “simple” prototype structure there would be no appropriate basis for studying more complex molecular materials. Although it has been claimed that the intermolecular structure had been understood, these claims have, until recently, always been refuted: unfortunately, plausible and attractive ideas (such as that of the “Apollo model”3) have proved to be inadequate. As a result of concentrated efforts during the past decade, it is now possible to draw a consistent picture ofeven fine details ofthe orientational structure in liquid CCl4, as well as in many related molecular liquids. It is the primary aim of the present review to reveal this consistent picture, including the structure of individual liquids and, perhaps more importantly, to find connections between the individual structures and observable tendencies as the nature of atoms involved changes. Many of the stages of the 80 year long quest are mentioned. Following this short introduction, approaches that finally have led to the present consensus are presented in more detail; among these, liquid diffraction and molecular dynamics simulations have appeared to be the most valuable. The most successful strategy has been found to be the creation of large sets of atomic coordinates that are fully consistent with experimental (mostly diffraction) data. The structure then is presented as it is calculable from these large particle configurations, containing thousands of molecules. The bulkiest part of this review is devoted to the description, at different levels, of the intermolecular structure of liquids consisting of molecules with a perfect tetrahedral shape, starting from partial radial distribution functions to an extensive introduction of mutual, distance-dependent orientations of molecular pairs. Next, a similaralthough, necessarily, more complicated treatise for liquids consisting of slightly distorted (i.e., nearly) tetrahedral molecules is provided. Perhaps the best known example of such materials is chloroform, CHCl3. Also, structural properties of individual liquids are related to each other (and, in some cases, also to the appropriate crystalline phases) by following trends that may be revealed on changing the size and/or nature of atoms involved, as well as on gradually changing the symmetry of the molecules. Having understood these particulars, we will be able to rightfully venture into the realm of genuine complex liquids, and as a bonus, we may realize that complex molecules do contain lots of tetrahedral fragments, that is, the 80 year long voyage has, indeed, provided practical means for treating complexity in the future. As a general introduction of our subjects, basic properties (melting and boiling points, densities) of each material to be discussed can be found in Tables 1−3. An overview of the crystalline phases (most frequently, of the ones that melt into the liquid phases reviewed) is also provided for each system considered in Table 4. (Note that the tables contain material

2.1. Diffraction Phenomenon and Basic Formalism

It is well known that when we place objects in the way of incoming monochromatic (particle) waves, whose wavelength is comparable to the size of the objects, a diffraction pattern can be observed. This phenomenon is based on the fact that the objects behave as sources of spherical waves, whose amplitudes should be summed up to yield the picture of interference, taking into account the differences in phases. A similar phenomenon can be observed during the process of scattering of X-rays and thermal neutrons from condensed matter, because their wavelength is comparable to the distance between atoms. In order to be able to provide a mathematical formulation of the scattering process and then connect that to the structure of the liquids under study, we need an observable, intensity-like (even if the phase information is lost) quantity with a dimension length squared. This quantity gives the number of scattered particles into dΩ solid angle during the time of 1 s, if the incoming flux of particles is 1 particle/(cm2s) for one scattering object. The desired quantity is the so-called dif ferential cross section (dσ/dΩ). Before we can connect this quantity to the interference of scattered particles/waves on the atoms of material, it is necessary to make several consideration related to the process of scattering. During the scattering process, the energy and momentum of the scattering particle may change. The momentum transfer ( p ⃗ ) B


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Table 1. Physical Properties of XY4-Type Molecular Liquids name and synonyms tetrachloromethane/carbon tetrachloride tetrachlorosilane/silicium(IV)chloride germanium(IV) chloride tin(IV) chloride titanium(IV) chloride vanadium(IV) chloride tin(IV) iodide methane tetrafluoromethane/carbon tetrafluoride tetrabromomethane/carbon tetrabromide germanium(IV) bromide tetrafluorosilane neopentane/2,2-dimethylpropane tetramethylsilane a

molecular formula

ref

Mw (g)

CAS RN

ρ (Å−3)

a

ρ (g/cm3)

mp (°C)

bp (°C)

CCl4

4

56-23-5

153.823

1.59402

0.0312

−22.62

76.8

colorless

other properties

SiCl4 GeCl4 SnCl4 TiCl4 VCl4 SnI4 CH4 CF4 CBr4

4 4 4 4 4 4 4 4 4

10026-04-7 10038-98-9 7646-78-8 7550-45-0 7632-51-1 7790-47-8 74-82-8 75-73-0 558-13-4

169.897 214.42 260.521 189.678 192.753 626.328 16.043 88.005 331.627

1.5 1.88 2.234 1.73 1.816 4.46 0.4228b 3.03425 2.96081c

0.0266 0.0264 0.0258 0.0275 0.0284 0.0214 0.0794 0.1038 0.0269

−68.74 −51.50 −34.07 −24.12 −25.7 143 −182.47 −183.60 92.3

57.65 86.55 114.15 136.45 148 364.35 −161.48 −128.0 189.5

colorless, fuming colorless colorless, fuming colorless or yellow red, unstable yellow-brown colorless colorless colorless

GeBr4 SiF4 C(CH3)4 Si(CH3)4

4 4 4 4

13450-92-5 7783-61-1 463-82-1 75-76-3

392.23 104.080 72.149 88.224

3.132 0.4254 0.585225d 0.64819

0.0240 0.0123 0.0830 0.0752

26.1 −90.2 −16.4 −99.06

186.35 −86 9.48 26.6

white colorless colorless volatile

At 20 °C. bAt −162 °C. cAt 100 °C. dAbove a pressure of 1.013 bar.

Table 2. Physical Properties of CXY3- and (A)BX3-Type Molecular Liquids name and synonyms fluoromethane/methyl fluoride trifluoromethane/fluoroform trichlorofluoromethane/refrigerant 11 chlorotrifluoromethane/refrigerant 13 bromotrifluoromethane tribromomethane/bromoform bromomethane/methyl bromide bromotrichloromethane chloromethane/methyl chloride trichloromethane/chloroform iodomethane/methyl iodide ammonia phosphorus(III) chloride phosphorus(III) bromide phosphorus(III) iodide antimony(III) chloride arsenic(III) chloride phosphorus(III) fluoride arsenic(III) fluoride acetonitrile/methyl cyanide a

molecular formula

ref

CAS RN

Mw (g)

ρ (g/cm3)

ρ (Å−3)

mp (°C)

bp (°C)

other properties

CH3F CHF3 CCl3F

4 4 5

593-53-3 75-46-7 75-69-4

34.033 70.014 137.368

0.55725 0.67325a 1.479328b

0.0493 0.0290 0.0324

−141.8 −155.2 −111.11

−78.4 −82.1 23.71

colorless colorless volatile

CClF3

5

75-72-9

104.459

1.521437b

0.0439

−181

81.48

colorless

CBrF3 CHBr3 CH3Br CBrCl3 CH3Cl CHCl3 CH3I NH3 PCl3 PBr3 PI3

4 4 4 4 5 4 4 5 4 4 4

75-63-8 75-25-2 74-83-9 75-62-7 74-87-3 67-66-3 74-88-4 7664-41-7 7719-12-2 7789-60-8 13455-01-1

148.910 252.731 94.939 198.274 50.488 119.378 141.939 17.03 137.332 270.686 411.687

1.58002 2.878825 1.675520 2.01225 1.0043b 1.478825 2.278920 0.68197b 1.574 2.8 4.18

0.0319 0.0343 0.0531 0.0306 0.0599b 0.0373 0.0483 0.0965 0.0276 0.0249 0.0245

−172 8.69 −93.68 −5.65 −97.72 −63.41 −66.4 −77.74 −93.6 −41.5 61.2

−57.8 149.1 3.5 105 −24.2 61.17 42.43 −33.33 76.1 173.2 227c

colorless colorless or yellow colorless

SbCl3 AsCl3 PF3 AsF3 CH3CN

4 4 5 4 4

10025-91-9 7784-34-1 7783-55-3 7784-35-2 75-05-8

228.118 181.280 87.969 131.917 41.052

3.14 2.150 1.574 2.7 0.785720

0.0332 0.0286 0.0431 0.0493 0.0692

73.4 −16 −152 −5.9 −43.82

220.3 130 −101 57.8 81.65

a

colorless

colorless colorless colorless red-orange, hygroscopic colorless, hygroscopic colorless colorless colorless

Above a pressure of 1.013 bar. bAt a pressure of 1.013 bar at boiling point. cDecomposes.

from the incoming (particle) wave to the atom is related to the → ⎯ scattering vector (Q⃗ ) as follows, if k 0 is the wavenumber vector → ⎯ of the incoming and k1 of the (scattered) outgoing (particle) wave → ⎯ → ⎯ p ⃗ = ℏQ⃗ = ℏ( k 0 − k1) (1)

If the energy exchange is small in comparison with the energy of the incoming (particle) wave or the elastic scattering condition can be approached well via integrating the doubledifferential cross-section over all values of the energy exchange, it is usually sufficient to measure the differential cross-section. This is called as static approximation, and eq 1 is simplified to → ⎯ → ⎯ the elastic case (| k 0| = | k1| = 2π /λ )

If there is also energy change during the (inelastic) scattering process, a new quantity should be introduced, which is the double-dif ferential cross-section related to the differential crosssection as

4π |Q⃗ | = sin Θ λ

where λ is the wavelength of the incoming particle wave and 2Θ is the scattering angle between the k ⃗ vectors.

2

∫ dEd dσΩ dE = ddΩσ

(3)

(2) C


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Table 3. Physical Properties of CX2Y2- and CX2YZ-Type Molecular Liquids name and synonyms difluoromethane/methylene fluoride dichlorofluoromethane/(refrigerant 21)-freon F21 dichlorodifluoromethane/refrigerant 12 dibromomethane/methylene bromide dichloromethane/methylene chloride diiodoomethane/methylene iodide dibromodichloromethane a

molecular formula

ref

CAS RN

Mw (g)

ρ (g/cm3)

ρ (Å−3)

mp (°C)

bp (°C)

other properties

CH2F2 CHCl2F

4 5

75-10-5 75-43-4

52.024 102.923

1.2139 1.40545a

0.0703 0.0411

−136.8a −135

−51.6 8.86

colorless colorless

CCl2F2 CH2Br2 CH2Cl2 CH2I2 CBr2Cl2

5 4 4 4 4

75-71-8 74-95-3 75-09-2 75-11-6 594-18-3

120.914 173.835 84.933 267.836 242.725

1.487004a 2.49692 1.32662 3.321120 2.4225

0.0370 0.0432 0.0470 0.0373 0.0301

−158 −52.5 −97.2 6.1 38

−29.75 97 40 182 150.2

colorless

yellow

At a pressure of 1.013 bar at boiling point. aTriple point temperature.

Table 4. Crystal Structure Corresponding to the Liquids in This Reviewa molecular formula

ref RN

space group of phases b 6,8,9 Fm3m ̅ ; , rhombohedral;b,7 C2/c; P21/c; Pa3̅ P21/cd P21/c P21/c P21/c

CCl4

6,7

SiCl4 GeCl4 SnCl4 TiCl4 VCl4 SnI4

10 11 12 13 14 15

CH4

16,17

CF4

18,19

CBr4

20,21

CI4 GeBr4 SiF4 SiH4 P4 As4 C(CH3)4 Si(CH3)4 C(CH3)3Cl

22 24,25 26 27 28 30,31 32,33 34 35

Pa3;̅ unknown; fcc; 2 amorphous fcc;b,17 Fm3c;b,16 Cmca; R3̅; others rhombohedral;b,18,19 C2/c; P21/c Fm3̅m;b C2/c; rhombohedral I4̅2m;e,23 Pa3̅; P21/c I4̅3m tetragonal; P21/c cubic;b,29 P1̅ 2(3) phases fcc;b tetragonal unknown;b Pnma; Pa3̅ fcc;b P4/nmm; P21/m

CH3F

36

P21/c

CHF3

37

P21/c

CCl3F

38

Pbca

CBr3F

39

Pnmae

CClF3

40

Cmc21

CBrF3

41

P21/c

CF3I

42

Cmca; unknown

CHBr3

43,44

P63/m;b P1̅; P3̅; P63

CH3Br

45

Cmc21; Pnma

CHI3

46

P63/m;b P63

molecular formula

molecular geometryg CCl: 1.76 Å6 SiCl: 2.01 Å GeCl: 2.10 Å SnCl: 2.28 Å TiCl: 2.22 Å VCl:2.13 Å SnI: 2.65 Å

ref RN

space group of phases

molecular geometryg

CBrCl3

47,48

CH3Cl CHCl3 CH3I POF3

49 44,50 51 52

fcc;b,47 rhombohedral;b,47 C2/cc,47 Cmc21 Pnma; P63c,44 Pnma P3m ̅ 1

POCl3

53

Pna21

POBr3

54

Pnma

VOCl3

55

Pnma

NH3

56−59

PF3 PCl3

61 62

P213;e,60 P63/mmc;b,57 b 59 Fm3m ̅ ; , P212121 unknown;b 2 unknowns Pnma

CCl: 1.75 Å; CBr: 1.91 Å47 CCl: 1.80 Å CCl: 1.75 Å50 CI: 2.13 Å PO: 1.43 Å; PF: 1.51 Å; OPF: 116° PO: 1.46 Å; PCl: 1.98 Å; OPCl: 111° PO: 1.47 Å; PBr: 2.14 Å; OPBr: 112° VO: 1.56 Å; VCl: 2.12 Å; OVCl: 107° NH: 1.06 Å; HNH: 108°56

PBr3

63

Pnma

PI3 SbF3 SbCl3

64 65 66

P63 C2cm Pnma

SbBr3

67,68

P212121; Pnma

SbI3

69,70

R3̅; P21/c

AsF3

71

Pna21

AsCl3

72

P212121

AsBr3

73

P212121

AsI3

70,73

R3̅; P3112/P3212; P21/c

CH3CN

74

P21/c; Cmc21

CH: 1.04 Å17 CF: 1.31 Å18 CBr: 1.91 Å21 CI: 2.16 Å GeBr: 2.26 Å24 SiF: 1.56 Å SiH: 1.49 Å PP: 2.21 Å AsAs: 2.42 Åf30 CC: 1.58 Å33 SiC: 1.86 Å CC: 1.53 Å; CCl: 1.81 Å CH: 1.07 Å; CF: 1.40 Å CF: 1.32 Å; CH: 1.11 Å CCl: 1.76 Å; CF: 1.36 Å CBr: 1.93 Å; CF: 1.33 Å CF: 1.50 Å; CCl: 2.04 Å CF: 1.32 Å; CBr: 1.92 Å CF: 1.26 Å; CI: 2.11 Å CH: 1.09 Å; CBr: 1.92 Å43 CH: 1.03 Å; CBr: 1.93 Å CI: 2.14 Å

PCl: 2.03 Å; ClPCl: 100° PBr: 2.21 Å; BrPBr: 100° PI: 2.46 Å; IPI: 102° SF: 1.92 Å SbCl: 2.36 Å; ClSbCl: 93° SbBr: 2.50 Å; BrSbBr: 95°68 SbI: 2.69 Å; ISbI: 96°69 AsF: 1.71 Å; FAsF: 93° AsCl: 2.17 Å; ClAsCl: 98° AsBr: 2.36 Å; BrAsBr: 98° AsI: 2.59 Å; IAsI: 100°73 CN: 1.17 Å; CC: 1.43 Å; CH: 1.08 Å

a

Out of the available references, the most recent paper(s) is(are) selected that reports the structure of the molecule and provides an overview about known crystalline phases (table continues as Table 5). b Orientationally disordered/plastic crystalline phase. cPartially/substitutionally disordered phase. dPhase II data. eDiffuse scattering reported/can be observed. fData from amorphous phase. gAveraged data sets.

1 dσ = N dΩ

We may now connect the differential cross-section to the interference caused by the scattering of incoming particles on N

∑ ⟨fi (Q , E)f *j (Q , E)e−iQ⃗ (r ⃗− r ⃗)⟩ i

i,j

j

(4)

scatterer atoms, averaged over time as follows D


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where f(Q, E) is the atomic form factor (units of length) and indices i and j go over scatterer atoms of the material. As the atomic form factor accounts for the microscopic process of scattering by a given atom, we should look at the properties of the radiation scattered: X-rays and thermal neutrons.

101). Finally, we have to note that as the photon has a spin of 1, it possesses polarization that affects the measurable intensity. Nowadays, X-rays (for the purposes of diffraction experiments) are produced via two ways: by laboratory X-ray machines and by synchrotron sources. In the lab-based instruments, accelerated electrons hit the target anode and remove lower shell electrons that are replaced by electrons from outer shells; during this process, unpolarized X-ray photons, with a characteristic energy, are emitted. Moreover, the accelerated electrons produce, throughout their deceleration process, radiation with a continuous energy distribution. At a synchrotron, electrons are accelerated to the energy of several GeV. Where this high-energy beam changes its direction by the effect of the magnetic field [of a bending magnet or insertion device (wiggler, undulator)], a highly polarized (into the radial direction of the storage ring), pinlike beam of X-rays is produced due to the relativistic speed of the electrons.102 The energy spectra of synchrotron radiation is continuous (bending magnet, wiggler) with resonances (undulator). There are two kinds of diffraction setups: the energy- and angular-dispersive ones. In the former, the continuous characteristics of the X-ray beam are exploited so that after being scattered by the sample the energy spectrum is detected by a detector. The latter one usually makes use of a monochromator or filter to select the Kα radiation from the monochromatic or a prespecified wavelength from the continuous radiation and scattered photons are detected by counters placed so that they cover (a fraction as large as possible of) the space around the sample.

Table 5. Crystal Structure Corresponding to the Liquids in This Review molecular formula

ref RN

CHClF2

75

P42/n; P2/c

CHCl2F

76

Pbca

CHBrCl2

77,78

P1;̅ c,77 Pnmac,78

CHBr2Cl

77,78

P1;̅ c,77 P63;c,78 Pnmac,78

CH2F2 CH2Br2 CH2Cl2 CH2I2 CBr2Cl2

79 80 81 80 47,82

CCl2F2 CH2BrCl CH2BrI CH2ClF

83 84 85 86

1 unknown;b 3 unknowns C2/c Pbcn C2/c; Fmm2 fcc;b,47 C2/c;c,47 rhombohedralb,82 Fdd2 C2/c;c Pbcnc C2/cc P21

CH2ClI

87,88

space group of phases

unknown;b,87 other unknown; Pnma; Pna21

molecular geometryg CH: 1.09 Å; CF: 1.34 Å; CCl: 1.75 Å CH: 1.06 Å; CF: 1.33 Å; CCl: 1.76 Å CH: 1.14 Å; CX: 1.83 Å77 CH: 1.10 Å; CX: 1.88 Å77 CH: 1.06 Å; CBr: 1.94 Å CH: 0.99 Å; CCl: 1.77 Å CH: 1.10 Å; CI: 2.15 Å CBr: 1.91 Å; CCl: 1.75 Å47 CF: 1.33 Å; CCl: 1.77 Å CH: 0.97 Å; CX: 1.85 Å CX: 2.02 Å CH: 1.09 Å; CCl: 1.79 Å; CF: 1.37 Å CH: 1.06 Å; CCl: 1.74 Å; CI: 2.15 Å87

2.3. Neutron Diffraction

a

Out of the available references, the most recent paper(s) is(are) selected that reports the structure of the molecule and provides an overview about known crystalline phases (Table 4 continued). b Orientationally disordered/plastic crystalline phase. cPartially/substitutionally disordered phase. dPhase II data. eDiffuse scattering reported/can be observed. fData from amorphous phase. gAveraged data sets.

The thermal neutron is an electrically neutral particle with a spin of 1/2, whose kinetic energy spreads from a few hundreds to a few tens of meV (wavelength 0.5−2 Å). As this particle is neutral, it can only participate in nuclear processes and via electric dipole−dipole interaction with the unpaired electron of the material. As a consequence, the scattering is relatively weak and its strength depends on the kind of scattering nucleus and on the coupling of the nuclear spin (if it were other than zero) and the neutron spin. Because there is a difference of 5 orders of magnitude between the diameter of the nucleus (several fm) and the wavelength of the thermal neutron (order of Angstroms), the atomic form factor does not depend on the momentum transfer. Thus, the name form factor is simplified to (bound) scattering length for neutrons (b), which are tabulated in units of fm.103 From these properties it follows that if the sample contains a single isotope (with nonzero nuclear spin), only the average (over individual scattering processes) of the scattering lengths would contribute to the coherent scattering part and their root mean squared differences to the incoherent scattering. The name of the former average is coherent scattering length, whereas this kind of incoherency (that may depend only on the spins of the neutron and the nucleus that take part in the scattering process) is called by spin incoherency. (The two types of scattered intensities might be separated each other by polarization analysis, see, e.g., ref 104.) If the sample contains different isotopes of the same element (with possibly different coherent scattering lengths), the coherent scattering length of the element would be the average of the coherent scattering lengths of each isotope. Also, the appearance of the so-called isotope incoherency is originated from this effect. The diversity of the coherent scattering lengths of different isotopes belonging

2.2. X-ray Diffraction

The X-ray photon is an electromagnetic particle whose energy is in the range of a few keV to several hundreds keV (wavelength, some Angstroms to 0.05 Å). In this energy range, the X-ray photon interacts with electrons of atoms by photovoltaic absorption, Thompson (elastic), and Compton (inelastic) scattering processes. Thus, the atomic form factor will be proportional to the number of electrons of the atom. Because electrons have a properly defined radial distribution around the nucleus and the size of the electronic cloud is comparable to the wavelength of X-rays, the X-ray atomic form factors depend on the modulus of the momentum transfer. As a result, tabulated atomic form factors are available for atoms and ions in electron units100 (f 0(Q)). Moreover, as the excitation of atomic electrons to higher energy levels is a resonance process, the energy dependence can be approximated by Q-independent anomalous dispersion correction terms (Δf ′(E) and Δf ″(E) in electron units), providing the final form of atomic form factors f (Q , E) = re(f0 (Q ) + Δf ′(E) + iΔf ″(E))

(5)

where re is the classical electron radius. This weak energy dependency can be exploited to alter the form factor of some chemical elements close to one of their absorption edge energies (anomalous X-ray scattering, see, e.g., refs 99 and E


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further, it is important to define the (partial) radial distribution f unction (gab(r), (P)RDF) which can be calculated, according to its simplest definition, as the ratio of the local and the average (bulk) density of atoms of type b in an infinitesimally thin spherical shell located at distance r from a central atom of type a. gab(r) at large distances tends to be 1, since the local density approaches the bulk density. At small distances, gab(r) tends to zero, because atoms possess a finite volume, thus preventing nearby particles to approach each other closer than the sum of atomic radii. The PRDF can be obtained from the corresponding Faber−Ziman partial structure factor by a onedimensional Fourier transform, exploiting that liquids are disordered and therefore isotropic beyond length scales of the order of a few atomic diameters

to the same element allows one to vary the coherent scattering length of the element without changing the sample chemically: the name of this technique is isotopic substitution (NDIS), frequently used to yield stronger contrast. In practice, neutrons can be generated via two ways: (1) In reactor sources, where nuclear fission provides approximately 2.3 fast neutrons/fission process on average, fast neutrons are thermalized in a moderator. One of the neutrons should be able to continue the regulated chain reaction, while nonabsorbed extra neutrons can be exploited for performing experiments. (2) At spallation sources protons are accelerated to energies of the order of GeV, and when they hit the target (made of heavy elements, like tungsten or mercury), they explode the nuclei, thus producing large numbers of fast neutrons that may be also thermalized in moderators. In the moderator, neutrons are slowed down by a series of collisions with nuclei of the moderator, yielding thermal neutrons with a Maxwell− Boltzmann energy distribution (around the moderator temperature). Similarly to X-ray photons, there are also two basic techniques to detect scattered neutrons: (1) In the constant wavelength technique, a monochromator selects a monochromatic wavelength and then the intensity scattered from the sample is measured at different scattering angles. (2) The other technique is called time of f light, where shorter wavelength neutrons reach the sample earlier than longer wavelength ones and the number of scattered neutrons are recorded as a function of time elapsed since a triggering event.

gab(r ) − 1 =

Before starting to simplify eq 4, we define the following averages of the atomic form factors, weighted by the concentration of the chemical elements in the sample (ca)

∑ cafa (Q , E)

f2 =

1 dσ ͠ ) + (f 2 − f f * ) = F (Q N dΩ

(6)

a

∑ cafa (Q , E)f a* (Q , E) a

∑ fa

f b* cacbAab(Q ) + ( f 2 − f f * )

a,b

(7)

G (r ) =

∑ i∈a,j∈b

⟨e

∑ fa

f b* cacb(gab(r ) − 1)

a,b

(11)

(12)

allowing the determination of bond lengths and perhaps also coordination numbers provided that the corresponding maxima are well separated (which is, in general, not often the case). It is a common practice, particularly in X-ray diffraction, to ͠ ) by f ̅ 2 or by f 2 , a procedure which normalize F(Q compensates for the decay of the X-ray diffraction pattern as momentum transfer increases. In the first kind of normalization, the sum of the coefficients for all ab partials is unity, independently of the momentum transfer (note that this normalization is applied frequently to neutron data, too). This way, the normalized total scattering structure factor (referred to as F(Q) in the following) is defined as

(8)

where indices a and b are over each element, δab is the Dirac delta symbol, and Aab(Q) are the so-called Faber−Ziman partial structure factors. Equation 8 consists of two terms: the first one contains the structural information that is the coherent part, whereas the second term describes incoherent scattering that is independent of the structure. Focusing on the coherent part, which contains relevant information to the structure, the Faber−Ziman partial structure factors take the following form Aab(Q ) =

(10)

and the total radial distribution f unction (G(r), RDF in short), which can be obtained by an analogous Fourier transform to that shown in eq 10. G(r) is composed of PRDFs as

where the bar over the element for neutrons denotes averages over isotopes and spins. Substituting into eq 4, omitting arguments of atomic form factors of elements and collecting atoms (scattering centers) belonging to the same element, we obtain 1 dσ = N dΩ

∫ Q (Aab(Q ) − 1)sin(Qr)dQ

The Faber−Ziman formalism requires the determination of each partial; thus, the full description of the structure of an Ncomponent system at the two-particle level would require N (N + 1) independent measurements (equal to the number of 2 PRDFs in the system). This condition cannot be fulfilled in general (even though isotopic substitution in neutron diffraction, as well anomalous X-ray scattering do help a great deal). Even so, at short distances, the PRDFs might be separated because bond lengths (for instance, in molecular liquids) might appear at different distances. To make a good use of this information from one diffraction measurement, it is ͠ )) common to introduce the total scattering structure factor (F(Q in Q space as

2.4. Scattering from Liquids: Correlation Functions

f̅ =

1 2π 2rρ

1 dσ 2 = f ̅ F (Q ) + f 2 N dΩ

(13)

For the definition of scattering and real space functions in various formalisms, see ref 98. Following the idea of separation, intra- and intermolecular correlations may also be distinguished. In this case, the scattering function related to the intramolecular part can be described as a Bessel function, multiplied by a Gaussian term (see, e.g., ref 105). The former is the Fourier transform of the

−iQ⃗ ( ri ⃗ − rj⃗)

⟩ (9)

Although these functions do provide information about the structure, they do so in the reciprocal space whereas the correlations are present in the real space. Before going any F


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bond length, while the latter is the spread around the equilibrium bonding distance; the parameters of these two functions may be determined by fitting the high-Q part of the total scattering function. The intermolecular part can be obtained by subtracting the intramolecular contributions from the total scattering function. Diffraction methods are the most direct tools that are capable of extracting information on the structure of (molecular) liquids (including the ones of our interest): this means that there is no any other experiment that would suit our purposes better. Still, the situation is not perfect since data suffer from problems, even for the most accurate measurements. • The experimentally accessible momentum transfer (Q) range is finite, so that real (r) space resolution is limited. • These data provide information for two-particle correlations only. • Data from multicomponent systems suffer from information deficiency: in general, the number of independent experiments is less than would be necessary for determining the full set of the PRDF uniquely. As a final remark, it can be concluded that using even the most accurate diffraction measurements for molecular liquids it is not possible to provide higher order (beyond two body) correlations using diffraction (and indeed, experimental) data exclusively. Information from other experimental sources (e.g., spectroscopy) and help from computer simulation are necessary for obtaining detailed ideas about the structure of liquids, and even then the uniqueness of our solutions is lost immediately when we wish to venture beyond pair correlations, e.g., when presenting the distribution of bond angles (that are connected to three-particle correlations).

may be accessed. Obviously, since the comparison between diffraction experiments and computer simulations may only be made at the two-particle level, the correctness of any more detailed information, derived from computer simulations, cannot be proven; still, a good reproduction of measured data (structure factors) suggests that the structure provided by simulation is possible. In what follows, we briefly describe the technique of molecular dynamics106,107 simulation, as the overwhelming majority of simulation data on tetrahedral liquids has been provided by MD. Some basics of Monte Carlo methods107−109 will also be mentioned, mainly because they are the origin of one of the major structural modeling techniques, reverse Monte Carlo (RMC) modeling,110 which has been important for structural studies of molecular liquids. 3.1.1. Molecular Dynamics Computer Simulations. Molecular dynamics is a method for obtaining structural, thermodynamic, and transport properties by solving the classical equations of motion numerically at the molecular level, simultaneously for each atom/molecule in the simulated system. Newton’s equations of motion for a system of N interacting atoms may be written as → ⎯ mi ri⃗ ̈ = fi (14)

3. COMPUTATIONAL METHODS

Initial position and velocity coordinates are provided by us to the simulation at an initial time. As both positions and velocities are frequently given random initial values (within appropriate limits, though), the first stretch of an MD simulation is spent by equilibrating the system, usually at a prespecified temperature. Then, given the positions and velocities at any given moment of time, all past and future positions and velocities can be uniquely determined. This is done by solving (numerically, from moment to moment) the above system of ordinary differential equations for N particles. In three dimensions, we have 3N second-order ordinary differential equations and 6N initial conditions. The equations are solved simultaneously in small time steps (typically of 1−2 fs for a molecular liquid). A general algorithm of MD simulations may then be sketched as follows. (1) Input initial conditions: (a) interparticle interaction potentials (U) as a function of interatomic distances; (b) positions (ri⃗ ) of all particles in the system; (c) velocities (vi⃗ ) of all particles in the system. (2) Calculate forces according to eq 15. At this stage, the potential and kinetic energies (as well as, for instance, the pressure tensor) can be determined. (3) Update configuration: The movement (i.e., the new positions) of the particles is predicted (and, depending on the actual integrator algorithm, corrected) by numerically solving Newton’s equations of motion according to eq 14. (4a) Output step (if required): Coordinates (and velocities) are saved in an output file at regular intervals. The coordinates as a function of time represent a trajectory of

By definition, the force is the negative gradient of the interparticle potential function (the most important input in any computer simulation) → ⎯ ∂U fi = − ∂ ri⃗

3.1. Computer Simulations

In the broad area of “liquid structure, dynamics and thermodynamics”, the aim of computer simulations is to mimic the behavior of the real liquids by moving atoms/ molecules around in simulation boxes of at least a few hundred particles. Most frequently, classical interaction potentials between atoms/molecules are taken into account. The movements may be governed by Newton’s laws, which is the case of the deterministic molecular dynamics (MD) simulations, or may be random displacements, as in the stochastic Monte Carlo (MC) simulations. In either of these ways, the simulated system is wandering around in the phase space available for it, and after visiting a large enough number of points (in other words, drawing a long enough trajectory), properties of interest (such as, in the present case, radial distribution functions and/or structure factors) may be calculated as ensemble averages over (adequate parts of) the trajectory. Comparing averages calculated from computer simulations to the corresponding experimental results can help us to assess whether our knowledge about interactions between atoms/ molecules of the system in question is adequate. In case there is agreement between experiment and simulation, computer simulation techniques can complement experimental data, in our case by providing the most detailed information about the structure that can be imagined at all: sets of particle coordinates. As it was clearly stated in the previous section, diffraction data provide two-particle information only, whereas from a computer-simulated trajectory, any structural property G

(15)


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transformed to obtain the corresponding Faber−Ziman partial (atom−atom) structure factors (Aab(Q))

the system. After the system reaches equilibrium, macroscopic properties can be extracted from the output file by averaging over an equilibrium trajectory. (4b) Repeat steps 2, 3, and 4a as many times as required. The interparticle potential function is generally composed of intramolecular and intermolecular parts. Intramolecular interactions can be described by bond stretching, bond bending, and bond torsion around a dihedral angle. Concerning molecular liquids in this review, interatomic interactions nearly always contained a Lennard−Jones potential term defined as ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σ σ ULJ(rij) = 4ϵ⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

Aab(Q ) = 1 +

n(r ) ΔVρ

(16)

wab(Q ) =

∞

⎤ r[g (r ) − 1]sin(Qr )dr ⎥ ⎦

r(gab(r ) − 1)sin(Qr )dr

(19)

cacbfa (Q )fb (Q ) (∑ cafa (Q ))2

(2 − δab) (20)

n

F (Q ) =

∑ wab(Q )Aab(Q ) a≤b

(21)

where n is the number of atom types defined by the system. Note that in the X-ray case, the composition of F(Q) may only be made in the reciprocal space, due to the strong Q dependence of the atomic form factors. On the other hand, since coherent scattering lengths for neutrons do not depend on Q, the composition of the total may be performed in either the real or the reciprocal space; furthermore, the weighting factors are identical in Q and r space. 3.1.2. Monte Carlo Simulations. Monte Carlo (MC) methods have been widely used in research, as well as in industry and economy, for estimating multidimensional integrals. In statistical mechanics, an essential multidimensional integral is the partition f unction that fully characterizes an equilibrium system in a given thermodynamic state; moreover, the variation of the partition function with respect to relevant thermodynamic variables describes everything about the behavior of the system in question (for a treatise of statistical mechanics, see, e.g., ref 112). As a consequence, the very first application of a Monte Carlo simulation, by Metropolis et al.113 in the first half of the 1950s, for liquids concerned the thermodynamic properties of hard-sphere liquids. Note, however, that if one wishes to calculate the partition function by summing all possible microstates (realization of particle positions and momenta) of a system then a prohibitively huge amount of computations would be necessary even for a very small number of particles. It is therefore of utmost importance that instead of visiting every single microstate, the ones that are the most significant (i.e., may be realized via the largest number of actual distribution of the particle positions) should be enumerated; in other words, we would like to sample the possible microstates according to their importance (cf. importance sampling107−109). In this very brief introductory section, we will restrict ourselves to the description of how Monte Carlo methods may be used for predicting the structure of a liquid, based on the interaction potentials acting between the particles. In MC, the same kind of interparticle potential functions and the same concept of the simulated system ((at least) hundreds of

(17)

∫0

∞

where δij is the Kronecker symbol. The normalized total structure factor is the weighted sum of the partials

where n(r) is the number of atoms at a distance between r and r + Δr from a central atom, ΔV is the volume of a spherical shell between r and r + Δr, and ρ is the number density of the system. Liquids can be considered isotropic beyond nearestneighbor distances, so that for switching between the real and reciprocal space, a one-dimensional Fourier transform is sufficient. Partial radial distribution functions can be Fourier transformed and weighted according to the actual experiment, ͠ ). For thus composing the total scattering structure factor, F(Q neutron diffraction and one-component systems, the appropriate Fourier transform is given by ⎡ ͠ ) = b ̅ 2⎢1 + 4πρ F (Q ⎣ Q

Q

∫0

where ρN denotes the total number density of atoms. To calculate the normalized total scattering structure factor for a given X-ray diffraction experiment, the partial (atom−atom) structure factors are weighted by the coefficients wab and then combined into F(Q). These coefficients depend on the concentration of atoms of type a (ca = Na/N) and on Qdependent atomic form factors100 (fa(Q), which are approximated by the sum of five Gaussians and a constant term) for Xrays as follows, valid far away from X-ray absorption edges

where rij is the distance between the centers of atoms i and j, ϵ is the well depth of the interaction potential, and σ is the collision diameter. The r−12 repulsive term describes Pauli repulsion at short interatomic distances that is due to overlaps of electron orbitals; the r−6 attractive term accounts for attraction over larger distances (cf. van der Waals forces or dispersion forces). In quite a few cases, Coulomb interactions between partial charges (assigned to atoms) complement the Lennard−Jones terms. As calculation of structural properties from simulation trajectories (i.e., from particle coordinates) is an essential element in many studies reported here, it seemed worthwhile describing, starting with a simple, one-component example, how this calculation can be carried out. (For definitions of experimental quantities, see section 2.) For one-component systems, the RDF can simply be calculated from the atomic positions as

g (r ) =

4πρN

(18)

where ρ denotes the number density of the sample, b̅ is the coherent neutron scattering length of the atom type in question, Q denotes the momentum transfer (scattering variable), and the integral runs over interatomic distances r. In practice, a discrete integration using the so-called rectangular method111 is performed with a summation whose upper limit is restricted by the half length of the simulation box. For X-ray diffraction and multicomponent liquids, the situation is a little more complicated, even though the principles, naturally, are the same (see section 2). First, partial radial distribution functions (PRDF), gab(r), are calculated from the atomic coordinates. The PRDFs are then Fourier H


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liquids consisting of tetrahedral molecules over the past nearly 20 years.114,115 The ultimate goal of reverse Monte Carlo (RMC)110 modeling is to achieve full consistency, within errors, between the measured and the simulated diffraction data, in which the latter is calculated from a large three-dimensional atomic configuration. RMC does not need interatomic potentials, although they may be applied as additional input information (for details on reverse Monte Carlo with potentials, see ref 116). The state of agreement between a simulated (Fsim(Qp)) and a measured (Fexp(Qp)) total scattering structure factor can be reached by using random atomic moves and accepting or rejecting it on the basis of the improvement (i.e., minimizing the value) of the following cost function

particles in a box) are applied as in molecular dynamics. The concept of time is not present, so only static properties may be targeted. Instead of (the time-dependent) Newton’s equations of motion the equilibrium state, characterized by the energy minimum under the specified thermodynamic conditions, is searched for by exploring the configuration space by visiting (as many) state points (as possible) in a stochastic manner, with probabilities that are proportional to their importance. This is most frequently achieved by the algorithm proposed by Metropolis et al.,113 in which the importance of a given microstate is chosen according to the Boltzmann distribution (of internal energy).112 During the random walk, governed by a Markov chain in which the probability of reaching a given state depends only on the preceding state visited, the following conditions must be met: (1) detailed balance, i.e., that in the Metropolis scheme (with Boltzmann distribution and Markov process) the probability of a transition from state A to state B (pA→B) must be related to the probability of the reverse transition so that the ratio of the probabilities of realizing microstates A and B should be the ratio of the Boltzmann factors of the two microstates pA → B =

PB = e−(EB − EA )/kT PA

⎡ F exp(Q ) − F sim(Q ) ⎤2 p p ⎥ χ = ∑⎢ ⎢⎣ ⎥⎦ σ ( Q ) p p 2

(23)

where p goes over all measured points and σ (Qp) is a parameter formally equivalent to the σ parameter of the standard χ2 distribution that takes the role of a control parameter that is able to influence the level (or tightness) of agreement between experiment and RMC modeling. In order to avoid unphysical particle arrangements, a number of constraints should be effective during RMC calculations (for a detailed discussion, see refs 111 and 117; this is necessary since, as mentioned in the experimental section, diffraction data can only provide information about two-body correlations, whereas the precise structure (even the topology!) of a tetrahedral molecule is clearly beyond two-body effects, that is, if the system of interest contains molecules then at least the topology has to be provided as input (the exact distance may be provided by the measured diffraction data), see refs 111 and 118. Distances of closest approaches are also always input parameters: with the help of them, nonsensically close approaches between atoms/molecules may be avoided quickly. Note also that correct density is a simple but essential constraint. After setting up a proper initial particle configuration and calculating the initial total structure factor and the value of the cost function, the general algorithm of the RMC method may be formulated as follows. (1) Make a random move of an atom. (2) If closest approaches between atoms or the molecular shape are violated as a result of the trial move, go to step 6b. (3) Calculate PRDFs and then Fsim(Qp)s, based on the knowledge of atomic form factors and concentrations, through the expressions introduced in section 3.1.1. (4) Calculate the new cost function (eq 23). (5) Compare χ2new with χ2old as follows. • If χ2new ≤ χ2old, accept the trial move and go to step 6a. • If χ2new > χ2old, then accept (and go to step 6a) the move with a probability of exp−(χ2new − χ2old)/2. If this test fails then reject the trial move and go to step 6b. (6a) Update configuration according to the changes and return to step 1. (6b) Revert the configuration to the status before step 1 and return to step 1.

(22)

(2) ergodicity, i.e., starting from any microstate with nonzero Boltzmann weight, any other microstate with nonzero Boltzmann weight should be reachable through a finite number of Monte Carlo moves. The sketch of a Monte Carlo algorithm (à la Metropolis) that is able to realize the above maybe (1) start from an initial state A, with a known internal energy; (2) attempt transition to state B (by randomly moving a particle to a trial position); (3) calculate the internal energy for state B (i.e., for the trial position of the particle moved); (4) calculate the ratio of Boltzmann factors as e−(EB−EA)/kT • if EB ≤ EA go to step 5a, • if EB > EA then accept (and go to step 5a) the move with a probability of e−(EB−EA)/kT; if not accepted go to step 5b; (5a) update configuration according to the changes (i.e., accept and keep the trial position) and return to step 1; (5b) keep all positions as in state A and return to step 1. In the canonical (N,V,T) ensemble107,112 the internal energy first decreases and then, after finding its equilibrium value, oscillates around the equilibrium internal energy. Particle configuration may be saved at prespecified intervals, and averages may be calculated from them when the system is in equilibrium. The PRDFs of the system are simply averages over the (ensemble of) configurations collected. Structural information in the reciprocal space can then be computed the same way as described above for the MD case. 3.2. Structural Modeling Based on Diffraction Data: Reverse Monte Carlo

In the previous sections, computational methods have been introduced whose results (including RDF, PRDFs, or total scattering function) depend on the applied set of interparticle potentials. In this subsection, a simulation method is introduced that is biased by the agreement with the measured diffraction data and that has been quite extensively applied for I


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3.3. Tools for Characterizing the Intermolecular Orientational Structure on the Basis of Large Sets of Particle Coordinates (“Particle Configurations”)

Step 5 helps to avoid a situation when the simulation would stick in one of the local minima, similarly to what is done in the Metropolis Monte Carlo algorithm (see the previous subsection). Although the RMC algorithm was introduced here only for one total scattering structure factor, from very early on the possibility of considering a practically unlimited number of experimental (neutron, X-ray, and EXAFS) data simultaneously has existed. Also, fitting PRDFs and experimental (total, or composite) RDFs has been facilitated. At the end of equilibration part of the RMC calculation, i.e., when good agreement (within errors) with experimental quantities has been achieved, particle configurations may be collected for calculating averages of structure-related characteristics (PRDFs, neighbor and angular distributions, etc.). It may be useful to finally list the software that is currently available for reverse Monte Carlo modeling of molecular liquids: RMC_POT116 is the latest variant of RMC++111,118 that makes it possible to use interatomic potential functions, too. RMCProfile 119 has grown out of the systematic, continuous development of the RMC code of the early 1990s; this software is most frequently used in conjunction with structural investigations of disordered crystals. Although not strictly an RMC method, the technique of empirical potential structure refinement (EPSR)120,121 should also be mentioned as an inverse method, capable of producing particle configurations that are consistent with diffraction data. 3.2.1. Preparation of Reference Structures: Fused Hard Sphere Monte Carlo Simulations. This type of calculations is strongly bound to the application of RMC for molecular systems. Fused hard-sphere Monte Carlo calculations of molecular systems, with the same parameters (density; bond-length constraints, thus the fusion of hard spheres; cut offs; etc.) as the reverse Monte Carlo runs, may also be carried out for the liquids in question. The easiest way for this is running RMC without fitting experimental data. These calculations provide reference structures which possess all features that originate to excluded volume (pure steric) effects. Differences between hard-sphere and RMC structures are characteristic to the nature of intermolecular interactions. This simple way of interpreting diffraction results and corresponding RMC models has proven to be remarkably successful (see, e.g., refs 114 and 122−128). To our best knowledge, this simple approach is the only one at the moment that is able to distinguish between features that are inherent to random orientations of molecules and those that are inherent to the actual real system. For this reason, wherever available, such results will always be discussed in the remaining part of this review. Note that random orientation here refers to as random as possible, under the constraint of molecular shape and volume, as opposed to the random and uniform distribution of orientations in a (hypothetical) system of pointlike particles (i.e., volumeless molecules). Random orientation of molecules with well-defined volume sometimes looks surprisingly ordered: this is the consequence of the fact that bodies with anisotropic (i.e., nonspherical) shapes determine the ways that identical bodies may be packed around a central one. In other words, liquids of molecules of any shape possess an inherent orientational ordering due to the molecular shape and volume; this is particularly true for molecules possessing high symmetry, such as those that are the subject of this review.

For an adequate understanding of the structure, adequate tools are necessary for analyzing the large particle configurations provided by structural modeling. A fairly detailed review of computer-based tools for characterizing correlations between the orientations of molecules has appeared recently,129 so that here only concepts that are the most relevant for our subjects, disordered systems of tetrahedral molecules, need to be repeated briefly. 3.3.1. Distance-Dependent Dipole−Dipole Correlation Functions. A conceptually simple way of providing a description of mutual orientations of dipoles (or linear molecules or vectors that are defined within more complicated molecules) is to calculate the angle confined between the two vectors as a function of the distance between molecules (for examples, see, e.g., refs 128, 130, and 131). The advantage of this type of characteristics is that every single pair of molecules is counted; for a not very ordered typical liquid, however, the function may be rather featureless. Further disadvantages originate from the fact that the angle between two dipoles (or two molecular axes) is calculated by putting the two ends of the dipoles together: this way, parallel and chainlike (also, Tshaped and crosslike) orientations appear to be identical. This indistinguishability can be rather unpleasant, particularly when considering neighboring molecules. 3.3.2. Special Correlation Functions for Linear Molecules or Dipoles. Distance-dependent orientational correlation functions of linear molecules and molecular dipoles may also be characterized in the following (ad hoc) manner.122,129,132 In addition to the dipole−dipole angle, angles confined by the molecular axes and the line connecting molecular centers can also be calculated. For any given pair of molecules, two such angles exist. With the help of three angles, any popular mutual orientation of two molecules, like parallel, T-shaped, or chainlike, etc., can be characterized.129 Allowing a rather wide spread for the cosines of these three angles (e.g., ±0.25), the number of pairs that realize one of the predefined configurations can be calculated as a function of the distance between molecular centers. The counts are then divided by the total number of pairs (independent of the orientation) found in the same distance bin, that is, the normalizing factor is the center−center radial distribution function. Finally, the asymptotic value (at r = ∞) is rescaled so that for each particular orientation the asymptotic value is unity. These correlation functions can be interpreted in a similar way to what is usual for radial distribution functions, but the connection to absolute quantities is lost. For this reason, it is important to give an indication of the number of pairs realizing a given mutual orientation at a given distance. It has to be remembered that since only well-recognizable arrangements are taken into account, not all molecular pairs are classified here; this is a major difference from the more general distance-dependent dipole−dipole correlation function introduced above. 3.3.3. Perfect Tetrahedral Molecules without Unique Symmetry Axes: Rey Constructions. A great deal of the materials considered in this review contain molecules that are highly symmetric so that no unique direction vectors can be assigned, i.e., the approaches mentioned above cannot work. The best known example is carbon tetrachloride, CCl4, a perfectly tetrahedral molecule, but similar problems would be faced when dealing with molecules of other highly symmetric J


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shape (e.g., octahedra). The first unambiguous characterization of molecular orientational correlations for XCl4 liquids was provided by Rey;133−136 independently, a very similar approach was invented by Morita.137 Later, the method has been extended to liquids consisting of molecules of near-tetrahedral shape, also relevant from the point of view of the present work.127,128 Also, a so-called revised Rey (RR) method was introduced on the example of liquid methane.138 According to the approach, for each pair of tetrahedral molecules in a particle configuration, two parallel planes are constructed that contain the centers of these molecules, perpendicular to the line joining the centers. Molecular pairs are classified by the number of ligands (in carbon tetrachloride, chlorine atoms) between these planes, belonging to one and the other of the two molecules. Six simple orientational groups (Rey groups) arise (see Figure 1). These groups represent the

that are only a very small orientational modification of the other two (corner, C, and face, F) categories. They argue that, particularly at larger center−center distances, a substantial portion of edges would need only very small rotations in order to be transformed into either corners or faces, so small that the change could be unnoticeable in terms of the total potential energy. In such a case, the sharp distinction imposed by the original Rey construction may not be entirely justified. This is why Sampoli et al. introduced a further distinction between strongly and weakly defined edges by defining not only two (as in the original construction) but three regions between the two molecular centers.138 Via the fine tuning of the volumes of the three regions it could be achieved that the asymptotic values of randomly oriented pairs occur between about 0.1 and 0.23 (instead of the much larger spread of 0.03 and 0.42 that characterizes the original Rey construction). Unfortunately, the RR method has not been applied since its introduction, so that no real experience of its use can be referred to the two unfavorable properties that may be mentioned are (1) the arbitrariness introduced by the fine tuning and (2) the more complicated realization. 3.3.4. More Specific Descriptors of Orientations of Tetrahedral Molecules. Another method of creating orientation-related graphs for characterizing short-range ordering in liquids (and disordered crystals) of tetrahedral molecules is due to Pardo et al.6 Their description, which they call bivariate and explain in more detail in ref 139, consists of two different kinds of graphs; both are 2D contour plots as functions of two angles (or cosines of angles). One is about positional ordering of neighboring molecules around an appropriately oriented central one; these pictures may be considered as the two-dimensional variations of the so-called spatial distribution functions (see Svishchev et al.140). The other kind depicts a truly orientational property, the correlation between (a) the angle confined by two characteristic6 vectors defined within the two molecules in question and (b) the angle between the same characteristic vector defined within the central molecule and the vector joining the two molecular centers.6 This orientational correlation graph has no direct distance dependence: for that a series of pictures has to be inspected. Such pictures seem to have acquired a certain popularity when characterizing orientational relationships within the first coordination shell of tetrahedral molecules.6,139,141,142

Figure 1. Classification of mutual orientations of two tetrahedral molecules by the method of Rey.133

corner-to-corner (1:1), corner-to-edge (1:2), edge-to-edge (2:2), corner-to-face (1:3) (this is the so-called Apollo orientation,3 see later in great detail), edge-to-face (2:3), and face-to-face (3:3) orientations. The normalized populations of these groups, as a function of distance, can provide a very detailed picture of the orientational correlations found in systems of tetrahedral molecules. As a general rule of thumb, the sharper the features (maxima/minima) of these distancedependent functions the better defined is the structure. Also, larger deviations from the reference system indicate higher information content (and thus greater importance of the presence) of the experimental data. This, in turn, indicates the presence of intermolecular forces that are beyond simple hardsphere interactions. One important result of the original work of Rey133 should be quoted here: the author calculated the probability of each of the six groups when two perfect tetrahedra adopt random mutual orientations. Using the tetrahedral dice, i.e., a situation in which the participating tetrahedra can rotate freely and independently and no space-filling (steric) effects are considered, the following probabilities were established: P(1:1) = P(3:3) = 0.031 (ca. 3%); P(1:2) = P(2:3) = 0.228 (ca. 23%); P(1:3) = 0.061 (ca. 6%); P(2:2) = 0.421 (ca. 42%), that is, edge-to-edge arrangements are by far the most probable ones. Note already here that the corner-to-face (Apollo3) arrangements that for decades have been thought to be the most important ones may only be expected to occur with a probability of about 6%. It is because of these limiting values (more precisely, their distribution) that the revised Rey method was introduced by Sampoli et al.138 a few years ago. According to their observation, the 2:2 (or, according to their terminology, E−E, that stands for edge−edge) group contains far too many edges

4. LIQUIDS OF PERFECT TETRAHEDRAL MOLECULES Physical properties of XY4-type materials are listed in Table 1. An overview of structural investigations performed on XY4 liquids other than carbon tetrachloride is provided by Tables 6 and 7. Since liquid CCl4 has attracted a particularly large number of researchers, structural studies on carbon tetrachloride have been gathered separately in Tables 9 and 10. 4.1. Prototype: Liquid Carbon Tetrachloride, CCl4

Without any exaggeration, liquid carbon tetrachloride is the iconic material of the family (as well as of the entire group of materials concerned in this review): its structure has been studied for more than 80 years now.1 For this reason, the evolution of experiment and computer simulation/theory as well as of concepts regarding the intermolecular structure may be followed best on the example of liquid CCl4. Before going into details, a major and unresolved difficulty must be exposed: due to the lack of suitable experimental data, K


Chemical Reviews

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Table 6. Experimental Studies on XY4 (Except CCl4) Type as Well as on P4 of Molecular Liquids bond lengths (Å) system SiCl4

GeCl4

TiCl4

VCl4

SnCl4

CH4 CF4 CBr4

GeBr4 SnI4

C(CH3)4 P4

first author, year

ref

diffraction method

Qmax (Å−1)

center−ligandp

ligand−ligand

Rutledge, 1970 Baier, 1981 Jöllenbeck, 1987 van Tricht, 1977 Jóvári, 2001 Rutledge, 1975 Baier, 1981 Jöllenbeck, 1987 van Tricht, 1989 Jóvári, 2001 Iwadate, 2013 van Tricht, 1977 Jóvári, 2001 Gibson, 1979 Rao, 1982 van Tricht, 1989 Misawa, 1990 Jóvári, 2001 Rutledge, 1975 Jöllenbeck, 1987 Pothoczki, 2009 van Tricht, 1977 Jóvári, 2001 Habenschuss, 1981 Strauss, 1996 Harris, 1966 Waldner, 1997 Dolling, 1979 Bakó, 1997 Temleitner, 2010 Temleitner, 2014 Egelstaff, 1971 Ludwig, 1987 Wood, 1952 Fuchizaki, 2007 Fuchizaki, 2009 Narten, 1979 Rey, 2000 Thomas, 1938 Clarke, 1981 Granada, 1982 Katayama, 2000 Katayama, 2002 Katayama, 2004

143 144 145 146 147 148 144 145 149 147 150 146 147 151 152 149 153 147 148 145 125 146 147 154 155 156 130 157 158 159 160 3 161 162 163 164 165 166 167 168 29 169 170 171

X-ray X-ray X-ray neutron neutron X-ray X-ray X-ray neutron neutron X-ray neutron neutron neutron neutron neutron neutron neutron X-ray X-ray X-ray neutron neutron X-ray neutron X-ray neutron neutron neutron neutron X-ray neutron X-rayb X-ray X-ray X-ray X-ray X-ray X-ray neutron neutron X-ray X-ray X-ray

8 20 17 13.3 9 15 20 17 10 9 12.5 13.3 9 15; 20

2.06 2.019 2.019 2.012 2.02 2.16 2.112 2.12 2.118 2.11 2.17 2.159 2.17 3.484(26); 3.509(15)a

3.26

10 20 9 15 17 17 13.3 9 16 18 13.1 19.2 10.2 16 8 14 10 10 10.8 24 8.5 17 16 6.2 20 16 10 10

2.149 2.14 2.3 2.284 2.28 2.288 2.28 1.104(34) 1.1 1.36 1.3 1.91c 1.93 1.93 1.93 2.36 2.28 2.66 2.67 2.65 1.546 2.25 2.21 2.21 2.22l

remarks 208 K; 296 K

3.29 3.28 3.55

233 K; 295 K 3.45 3.58 3.518 3.54

3.485 3.49 3.78

295 K 295 K

3.72 3.72 3.72 1.8 2.2 2.2

92 K 510 bar; 610 bar; 770 bar 96 K; 120 K; 151 K 370 K 590 bar; 770 bar; 990 bar

3.15 3.15 3.79 4.35 4.35 4.33

433 K, 1 bar 610−1017K; 0.4−3.4 GPa 256−423 K; 0.397−32 bar 321 K;e 499 K;e amorphousd,f 323 Ke 283−323 Ke 1050K; 0.77−1.38 GPa liquid 0.77−GPa; amorphousf 0.8−1.01 GPa; density meas.

a

As determined for the various Q ranges of the measurements. bAnomalous X-ray diffraction: measured near the Br and Ge K absorption edges. cFor the plastic crystalline phase at 345 K. dBlack phosphorus. eYellow or white phosphorus. fRed phosphorus. lLow-pressure form. pPhosphorus− phosphorus bond length for P4.

diffraction with isotopic substitution might have been more widely applied, exploiting suitable isotopes of chlorine, 35Cl and 37 Cl; these two total scattering structure factors could have been combined with X-ray diffraction data. Such an investigation, unfortunately, has not been conducted for carbon tetrachloride (the experiment closest to this procedure was realized by the anomalous X-ray scattering study of liquid GeBr4 using three different X-ray energies161). As a consequence, external ideas (theory, modeling, etc.) had to be invoked in each case when interpreting the experimental results. Since the CCl4 molecule is sufficiently rigid and

i.e., due to the fact that three independent diffraction measurements have not been performed within one study, not even the two-body correlation functions can be determined unequivocally on a purely experimental basis. The closest approximation to this goal was made by Narten in 1976,234 who used one X-ray and one neutron diffraction data set, and Bhattarai et al. in 1998,226 who prepared one isotopically enriched sample and performed neutron diffraction on it as well as on the natural material. Both studies derived the C−Cl and Cl−Cl PRDFs by neglecting contributions from the C−C PRDF completely. We note here that, in principle, neutron L


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Table 7. Simulation Studies on XY4 (except CCl4) Kind and on P4 of Molecular Liquidsa system

first author, year

ref

remarks

SiCl4

van Loef, 1974 Zeidler, 1982 Dolgov, 1983 Montague, 1983 Sjoerdsma, 1985 van Tricht, 1986 Jöllenbeck, 1987 Neilson, 1997 Jóvári, 2001 Neilson, 2002 Pothoczki, 2009 Rey, 2009 Zeidler, 1982 Montague, 1983 Dolgov, 1983 Sjoerdsma, 1985 van Tricht, 1986 Jöllenbeck, 1987 Neilson, 1997 Jóvári, 2001 Neilson, 2002 Nath, 2007 Pothoczki, 2009 Montague, 1983 Sjoerdsma, 1985 van Tricht, 1986 van Loef, 1974 Neilson, 1997 Jóvári, 2001 Neilson, 2002 Pothoczki, 2009 Murad, 1980 Montague, 1983 Sjoerdsma, 1985 van Tricht, 1986 Misawa, 1990 Neilson, 1997 Jóvári, 2001 Neilson, 2002 Nath, 2007 Pothoczki, 2009 Rey, 2009 van Loef, 1974 Dolgov, 1983 Montague, 1983 Sjoerdsma, 1985 van Tricht, 1986 Jöllenbeck, 1987 Neilson, 1997 Jóvári, 2001 Neilson, 2002 Pothoczki, 2009 Rey, 2009

172 173 174 175 176 178 180 181 147 182 124 136 173 175 174 176 178 180 181 147 182 183 124 175 176 178 172 181 147 182 125 184 175 176 178 153 181 147 182 183 125 136 172 174 175 176 178 180 181 147 182 124 136

hard core consideration review on molecular liquidsc RISM RISM model calculation (semiexperimental Cl−Cl PRDF) RISM determination of PRDF for diffraction experimentc review, mostly diffraction MD, RMC review, mostly diffraction RMC MD review on molecular liquidsc RISM RISM model calculation (semiexperimental Cl−Cl PRDF) RISM determination of PRDF for diffraction experimentc review, mostly diffraction MD, RMC review, mostly diffraction test and comparison between published modelsd RMC RISM model calculation (semiexperimental Cl−Cl PRDF) RISM hard core consideration review, mostly diffraction MD, RMC review, mostly diffraction RMC MD, RISM RISM model calculation (semiexperimental Cl−Cl PRDF) RISM F(Q) calculation for different intra- and intermolecular spacings review, mostly diffraction MD, RMC review, mostly diffraction test and comparison between published modelsd RMC MD hard core consideration RISM RISM model calculation (semiexperimental Cl−Cl PRDF) RISM determination of PRDF for diffraction experimentc review, mostly diffraction MD, RMC review, mostly diffraction RMC MD

GeCl4

TiCl4

VCl4

SnCl4

a

considered diffraction data of first author,ref year Baier,144 1981 Rutledge,143 1970; van Tricht,146 1977 van Tricht,177 1977 van Tricht,179 1984 Jöllenbeck,145 1987 Jóvári,147 2001 Jóvári,147 2001; Jöllenbeck,145 1987 Baier,144 1981 Rutledge,143 1970 van Tricht,177 1977 van Tricht,179 1984 Jöllenbeck,145 1987 Jóvári,147 2001 Jóvári,147 2001; van Tricht,149 1989 Jóvári,147 2001; Jöllenbeck,145 1987 van Tricht,146 1977 van Tricht,177 1977 van Tricht,179 1984

Jóvári,147 2001 Jóvári,147 2001; Jöllenbeck,145 1987 Gibson,151 1979 Gibson,151 1979 van Tricht,177 1977 van Tricht,179 1984

Jóvári,147 2001 Jóvári,147 2001; van Tricht,149 1989 Jóvári,147 2001; Jöllenbeck,145 1987

Rutledge,148 1975; van Tricht,146 1977 van Tricht,177 1977 van Tricht,179 1984 Jöllenbeck,145 1987 Jóvári,147 2001 Jóvári,147 2001; Jöllenbeck,145 1987

Table continues as Table 8. bDevelopment of interaction model. cIn German. dMisawa’s two-molecule approach.

structure of this liquid. These considerations include, on one hand, theoretical results of Rey133 (see above). 4.1.1. Diffraction Experiments. References to X-ray and neutron diffraction experiments on liquid carbon tetrachloride are gathered in Table 9.

possesses very high symmetry and also since no strong directional intermolecular forces are present between the molecules at liquid temperatures, geometry-based considerations may prove to be important in understanding the M


Chemical Reviews

Review

Table 8. Simulation Studies on XY4 (except CCl4) Kind and on P4 of Molecular Liquidsa system CH4

CF4

CBr4

GeBr4

SnI4

C(CH3)4

P4

a

first author, year

ref

remarks

comparison with diffraction data of first author,ref year

Murad, 1979 Habenschuss, 1981 Strauss, 1996 Tsuzuki, 1998 Rowley, 1999 Guarini, 2007 Li, 2009 Chao, 2009 Rey, 2009 Sampoli, 2011 MacCormac, 1951 Waldner, 1997 Burtsev, 2003 Nosé, 1983 Potter, 1997 Bassen, 1998 Rey, 2009 Montague, 1983 Evans, 1988 Bakó, 1997 Rey, 2009 Temleitner, 2010 Temleitner, 2014 Evans, 1988 Ludwig, 1987 Swamy, 1980 Fuchizaki, 2000 Fuchizaki, 2001 Pusztai, 2008 Fuchizaki, 2009 Rey, 2009 Rao, 1981 Sarkar, 2001 Wong, 1982 Mountain, 1985 Rey, 2000 Rey, 2008 Rey, 2009 Evans, 1988 Scheidler, 1993 Hohl, 1994 Morishita, 2001 Morishita, 2002 Senda, 2002 Jóvári, 2002 Katayama, 2003

185 154 155 186 187 188 189 190 136 138 191 130 192 193 194 195 136 175 196 158 136 159 160 196 197 198 199 200 123 164 136 201 202 203 204 166 135 136 196 205 206 207 208 209 210 211

MD RISM RISM, RMC b; quantum chemical calculation on dimers b; quantum chemical calculation on dimers MD, inelastic neutron scattering b b; quantum chemical calculation on dimers MD MD; inelastic neutron scattering potential development RMC IR spectroscopy MD MD RISM integral equation theory Monte Carlo MD RISM MD, RISM RMC MD RMC RMC MD, RISM hard-sphere RISM RISM MD MD RMC MD MD integral equation theories using hard spheres d MC MD ab initio calculation, MD MD MD MD, RISM RMC ab initio MD ab initio MD ab initio MD ab initio MD RMC comparison with other structure factors

Habenschuss,154 1981 Strauss,155 1996

Waldner,130 1997

Waldner,130 1997 Dolling,157 1979 Bakó,158 1997 Temleitner,159 2010 Temleitner,159 2010; Temleitner,160 2014 Egelstaff,3 1971 Ludwig,161 1987 Egelstaff,3 1971

Fuchizaki,163 2007 Fuchizaki,163 2007; Fuchizaki,164 2009 Narten,165 1979 Narten,165 1979 Narten,165 1979 Rey,166 2000

Granada,29 1982 Granada,29 1982 Clarke,168 1981; Granada,29 1982 Katayama,169 2000 Katayama,169 2000 Katayama,169 2000

Table 7 continued. bDevelopment of interaction model. cIn German. dMisawa’s two-molecule approach.

As it has already been mentioned, the first liquid state diffraction study using X-rays is due to Menke in 19321 (the gaseous phase was studied even earlier, in 1929, by Debye251). As nicely summarized by Narten et al. in 1967,214 “Eisenstein2 was the first to apply to liquid CCl4 the method of Fourier analysis. Bray and Gingrich213 repeated this work at 25 and −20 °C, and Gruebel and Clayton215 obtained the X-ray diffraction pattern at 25, 51.8, and 115 °C”, that is, the experimental information necessary for a qualitative understanding the structure of the liquid was, in principle, available about 50 years ago. The momentum transfer range could be extended by using modern synchrotron radiation techniques (see, e.g., ref

124). It is instructive to collect some of the (corrected) intensity curves and structure factors that have been obtained by the technique of X-ray diffraction over the past 80 years in one figure (Figure 2). Although two of the earliest measurements (from 19321 and 19432) produced data that are rather different from those gathered later, the agreement between results from very different instruments is remarkable. The history of neutron diffraction on liquid carbon tetrachloride started in the late 1960s;220 indeed, since then the materialjust as in the X-ray casehas become one of the standards at the various neutron centers, also for the purpose of N


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Table 9. Diffraction Studies Performed on Liquid CCl4 bond lengths (Å) first author, year

a

ref

Brockway, 1934 Menke, 1932 Bray, 1943 Eisenstein, 1943 Narten, 1967 Gruebel, 1967 von Reichelt, 1974 Narten, 1976

212 1 213 2 214 215 216 214

Orton, 1977 Murata, 1978 Nishikawa, 1984 Morita, 2009 Rao, 1968 Egelstaff, 1971 van Tricht, 1977 Clarke, 1979 Bermejo, 1988 Misawa,1989 Bhattarai, 1991 Akatsuka, 1997 Pusztai, 1997 Bhattarai, 1998 Rey, 2000 Jóvári, 2000, 2001 Veglio, 2005 neutron data of Morita, 2009

217 218 219 137 220 3 146 221 222 223 224 225 114 226 166 147,227 9 137

diffraction method electron X-ray X-ray X-ray X-ray X-ray X-ray X-ray neutron X-ray X-ray X-ray X-ray neutron neutron neutron neutron neutron neutron neutron neutron neutron neutron X-ray neutron neutron neutron

wavelength (Å)

Qmax (Å−1)

C−Cl

Cl−Cl

remarks

1.760(5) 1.54; 0.71 0.71; 0.56 0.71 0.7107 0.7107 1.54; 0.71 0.7107 1.1; 0.752 0.7107 b b 0.201a 1.075; 0.803 1.06 0.9 c 0.4997c c 0.7 c 1.119 0.7054 0.7107 0.66; 1.06 1.2805 c

12 12.5 12 16 12.5 7;15 16 9.8; 15.7 10 23 17 30 7.4; 10 10 13.3 40 10 10 16 12 8 13 16.1 9.2; 16 7.5 37

Synchrotron X-ray study. bEnergy-dispersive X-ray study. cTime-of-flight neutron study.

d35

gas phase

1.74 1.85 1.773(3) 1.81 1.767(3) 1.766(3)

2.92 2.95 2.896(5) 2.92 2.886(3) 2.884

25 °C; −20 °C 27 °C 25 °C 25−115 °C 20 °C

1.76

2.88

23 °C

1.75 1.86(5) 1.77 1.770(2) 1.766(2) 1.766;1.769 1.776 1.75;1.77 1.76−1.79 1.7

2.90 2.97(5) 2.89 2.918(1) 2.898 2.883;2.868 2.898 2.86; 2.86 2.88−2.9 2.9

22 °C

−20−160 °C 1 bar to 3.5 kbar 20−275 °C 1 bar to 3.5 kbard

1.77 1.77 1.763

2.89 2.879

Cl isotopic substitution applied.

liquid CCl4 by means of two distance parameters: the intramolecular C−Cl and Cl−Cl ones. Most values quoted in this review (see Table 9) have been determined via this approach. Another possibility, used primarily by computer modellers, in (for instance) reverse Monte Carlo simulation is to assume that the molecules are flexible, thus letting the (intramolecular) C−Cl and Cl−Cl distances find their optimum values, in accordance with (primarily, but not exclusively, the high-Q part of) the measured data. This idea was first made use of in the second half of the 1990s;114 it became clear already at the first instance that the accuracy of intramolecular distance values determined this way cannot be better than the spacing used for the radial distribution function (usually not finer than 0.1 Å). Nevertheless, for reproduction (within errors) of the measured total scattering structure factor this accuracy has proven to be adequate.114,124,147 Table 9 summarizes the bonded (C−Cl) and nonbonded (Cl−Cl) intramolecular distances determined by diffraction methods over the many decades; for comparison, values obtained from gas electron diffraction212 are also quoted. As it is evident, differences in most cases are not significant: the C− Cl distance is consistently between 1.75 and 1.8 Å, whereas the nonbonding Cl atoms appear to be about 2.9 Å from each other within a given CCl4 molecule. 4.1.2. Computer Simulations and Theoretical Investigations. Interestingly, the first computer simulation involving liquid carbon tetrachloride was performed not on the pure substance but on a solution containing one single n-butanol molecule as a solute.252 The main reason why this study remains a curiosity is that the authors chose a one-site model

comparing capabilities of reactor and spallation neutron sources.222 Figure 3 gathers some of the total scattering structure factors determined by neutron diffraction over the past 45 years. Again, the agreement between these functions is very good, outlining the fact that there really has not been a dispute over the measurable structural information during the past (at least) two decades. There was one important addition to the story of “neutron diffraction on liquid CCl4” in 1998:226 Bhattarai et al., with great efforts put into the synthesis of the isotopically enriched sample, eventually they were able to make use of the technique of isotopic substitution on a sample containing the 35Cl isotope. The contrast between this material and the “normal” sample, with natural chlorine, is not great (about 5% for the Cl−Cl PRDF) but clearly more than just noise. Unfortunately, they had no more isotopic samples, and they made no attempts to combine their data with corresponding X-ray diffraction results either; therefore, the separation of the three partial radial distribution functions could not be achieved on a purely experimental basis. 4.1.1.1. Molecular Structure. It may be surprising that this important point appears in this section; note, however, that in the liquid phase, the only direct information on the molecular structure may come from diffraction experiments. As Eisenstein wrote 70 years ago about the measured intensity function,2 “Certain considerations lead to the belief that this intensity function at large angles is determined chiefly by the atomic structure at small values of R or in this case by the C−Cl and Cl−Cl concentrations.” This statement has been the basis of fitting the large-Q part of the total scattering structure factors of O


Chemical Reviews

Review

Table 10. Simulation/Theoretical Studies on the Structure of Liquid CCl4a first author, year

ref

remarks

Egelstaff,3 1971

Lowden, 1974 van Loef, 1974

229 172

Granada, 1979 Nishikawa, 1979 Steinhauser, 1980 Steinhauser, 1981 Nishikawa, 1981 Mcdonald, 1982 Zeidler, 1982

230 231,232

model fitting

Clarke,221 1979 Murata,218 1978

233

molecular dynamics

Narten,234 1976

235

molecular dynamics

236

plastic crystal X-ray

237

molecular dynamics

173

review, in German on molecular liquids RISM

Montague, 1983

175

Dolgov, 1983 Nishikawa, 1985 Sjoerdesma, 1985

174 238,239 176

van Tricht, 1986 Shimni, 1986

178

Kolmel, 1989 Stassen, 1992

241 242

Chang, 1995

243

240

Tironi, 1996

244

Jedlovszky, 1997 Neilson, 1997

245

Fox, 1998

246

Soetens, 1999

247

Rey, 2000 Neilson, 2002

166 182

Torii, 2003

248

Mahlanen, 2005 Pardo, 2005

249

Pardo, 2007

6

Rey, 2007

133

Pothoczki, 2009 Morita, 2009

124

Li, 2010

250

181

8

137

RISM hard core consideration


RISM fitting with assumption RISM-related geometrical considerations RISM lattice gas; theory; thermodynamics molecular dynamics algorithm development potential development potential development RMC; orientational correlations review, mostly diffraction potential development ab initio, MD ab initio, MD review, mostly diffraction quantum chemistry, electrostatic effects quantum chemistry; dimers RMC; orientational correlations RMC; orientational correlations MD; orientational correlations RMC; orientational correlations RMC; orientational correlations MD; potential development

Narten,234 1976; van Tricht,146 1977 Narten,234 1976 Narten,234 1976; van Tricht,146 1977; von Reichelt,216 1974 Nishikawa,219 1984 van Tricht,146 1977 van Tricht,146 1977

Narten,234 1976

Narten,234 1976 Narten,

234

Figure 2. X-ray diffraction results, covering the past 80 years, on liquid CCl4, in the form of both corrected intensities (top) and normalized total scattering structure factors (bottom). Color coding of references: black;1 red;2 light green;213 blue;214 dark green (with Cu Kα) and brown (with Mo Kα);216 magenta;234 orange;218 cyan.124 (Top) Black dotted line shows the f 2 term that appears in eq 13.

1976

Narten,234 1976

Narten,234 1976; Pusztai,114 1997 Narten,234 1976

Veglio,9 2005 Veglio,9 2005

Figure 3. F(Q) of liquid CCl4 as determined by neutron diffraction experiments: a selection from the past 50 years. (Inset) High momentum transfer range part. Color coding of the references: black;220 red;3 light green;234 blue;146 cyan;221 orange;6 magenta (neutron data of Morita137); dark green.227

Jóvári,227 2000; Jóvári,147 2001 neutron data of Morita,137 2009 Narten,234 1976

a

RISM: restricted interaction site model228 integral equation based theory.

(i.e., a single sphere) for representing the tetrahedral CCl4 molecules: no PRDFs involving chlorine could therefore be P


Chemical Reviews

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the structure, in comparison with the estimated (C−Cl and Cl−Cl) PRDFs of Narten.234 In 1992, Stassen et al.242 succeeded in increasing the system size considerably: in their MD simulations, 864 rigid molecules were considered in the microcanonical (N,V,E) ensemble. Apart from exploiting advanced computer facilities, they modified the way the potential energy is calculated: beyond a certain cutoff distance (typically more than 10 Å), only an isotropic “molecule−molecule” interaction was taken into account. Concerning structural properties, only partial radial distribution functions were reported; these, according to the authors, “...are very similar to previous MD results”. Chang et al, in 1995, set out on developing a polarizable intermolecular potential for liquid CCl4 that would be applicable to not only the bulk but also at interfaces too.243 The site−site interaction potential function contained (pairwise additive) Lennard−Jones and Coulomb contributions, as well as a nonadditive part that results from the polarizability of the atoms. This latter part had to be determined in each time step by an iterative scheme, and therefore, calculation of the energies/forces was rather intensive computationally; for this reason, a relatively small system, containing 256 molecules, was applied. The simulation was performed in the isobaric− isothermal (N,p,T) ensemble, and instead of using rigid molecules, the SHAKE algorithm107 was applied to keep the molecular geometry within the required boundaries. Comparison with intermolecular “experimental” structure factors234 was provided, with a similar pattern already seen in earlier MD studies;233,253 this observation raises the question whether complicated potential schemes are necessary for reproducing structural features. The distribution of the angle between an intramolecular C−Cl vector and the line connecting two molecular centers (i.e., C atoms) was also calculated as a function of the distance between molecular centers, although the partition (“binning”) of the C−C distances was somewhat arbitrary at this stage. (This simple new tool may be considered as the first step toward adequate characterization of orientational correlations in liquid CCl4, see below.) Just 1 year later, Tironi et al.244 argued that an interatomic interaction described by (refined) Lennard−Jones parameters only, i.e., without any electrostatic terms, is sufficient for mimicking many properties of liquid carbon tetrachloride. Although the main areas for their (quite convincing) arguments were thermodynamic and transport properties, they do provide a comparison between their C−Cl and Cl−Cl PRDFs and those of Narten.234 The overall level of agreement between MD and experiment (remember, Narten had to work with the assumption that the C−C PRDF was negligible) is very similar to previous comparisons of this type.241,242 However, Tironi et al. took one further step and criticized quite unequivocally the PRDFs derived by Narten:234 “Since the agreement between experiment and MD is satisfactory for the Cl−Cl pair, and the chlorine−chlorine pair contributes more than 70% to the structure factor, there is only little room to bring the molecular dynamics results closer to the experimentally derived functions for the C−Cl case.” During the late 1990s, further serious potential development efforts have been made by Fox et al.246 and by Soetens et al.,247 both including electrostatic contributions. Molecular dynamics studies of the latter contribution, by Soetens et al. in 1999,247 resulted in a fairly detailed description of the structure of (simulated) liquid CCl4 (even though details of the electrostatic properties of the molecule were later debated by further

calculated (and naturally, orientational correlations do not exist for such “molecules”). The first computer simulation on “real” liquid CCl4 was the molecular dynamics study of Steinhauser and Neumann in 1980.233 Their system consisted of 64 rigid molecules that interacted via a four-center Lennard−Jones (4CLJ) potential, as suggested earlier by Narten.234 As demonstrated by their Figure 2, reproduction of the (somewhat featureless) “experimental” intermolecular total radial distribution functions (of Narten234) was quite successful. This means that theiralthough, according to computing facilities available that time, small configurations were adequate for a detailed analysis of the structure. Indeed, the authors used the so-called g-coefficient analysis that results from the expansion of the angle-dependent pair correlation function of molecules. Following some mathematical elaboration, information on the distribution of molecular centers as well as on the relative orientation of molecules has been obtained. Unfortunately, the orientational information was given only in the form of functions resulting from the initial assumption that the total structure factor can be split into a center-of-mass and an orientational part, so that no definite and easily understandable conclusion could be drawn on this important property. It is worth stressing, however, that the MD-simulated structure of Steinhauser et al.233 was already sufficient for a detailed clarification of the mutual orientations in liquid carbon tetrachloride already more than 30 years ago had the appropriate tools133 been available for analyzing the configurations at that time. Two years later, McDonald et al.237 in their MD study concentrated on the plastic crystalline Ia phase of CCl4, although they mention some results for the liquid too. They used a slightly bigger system (108 rigid molecules) and a more elaborated potential model, including the carbon atom as well; in one attempt, they also introduced electrostatic (octopole) terms. The C−C interaction energy Lennard−Jones parameter (ϵCC) was taken from an earlier study on dense fluid methane,185 whereas for the distance LJ parameter, σCC, two very different values, 3.2 and 4.6 Å, were tried. These choices originate from a comparison made with the theoretical (RISM) results of Lowden and Chandler,229 as well as with the simulation study on methane mentioned above,185 and reflect the uncertainty present at the time concerning intermolecular interactions. McDonald et al.237 were the first who showed comparison to an “experimental” structure factorunfortunately, only after subtracting the intramolecular contributions, whose process is a potential source of systematic errors (see also ref 114). Agreement with experimental data in the reciprocal space might be termed as “semiquantitative”; it is perhaps not unfair to state that agreement with real space data, the total intermolecular radial distribution functions is actually somewhat worse than it had been for the earlier MD calculations of Steinhauser et al.233 Kölmel et al.,241 in 1989, were the next to consider liquid CCl4 as the main target of their molecular dynamics simulation study. Due to the advances of simulation methodology, they had the opportunity to consider not only the standard (N, V, E) but also the (N,p,T) ensemble; with this the pressure could be maintained at the atmospheric pressure value. The authors have put great efforts into the development of interaction potentials: the (many) classical pair potential parameters of the rather complex functional form were fitted to results of detailed quantum chemical calculations. Unfortunately, only the partial radial distribution functions were provided as representatives of Q


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quantum chemical calculations248). Apart from drawing PRDFs (as a function of temperature), comparison with the intermolecular structure factors of Narten234 is provided: agreement with measured data appears to be the closest out of studies reported to that date. More importantly, a comparison with neutron data containing both intra- and intermolecular contributions114 was also made. There is a close match between simulation and experiment up to about 3 Å−1, whereas beyond that (interestingly, in the region of, supposedly, primarily intramolecular contributions), only positions of extrema agree but intensities differ. Rey et al., in the year 2000,166 also entered the field of potential development for methyl-chloromethane compounds (including pure carbon tetrachloride, in which the number of methyl groups connected to the central atom is zero): by ab initio quantum chemical calculations for the dimers, they found a close agreement with Soetens et al.247 in terms of the parameters of electrostatic interactions (partial charges). It may be interesting to note that both Rey166 and Soetens247 report a small positive partial charge for the chlorine atoms that is compensated by a sizable (ca. 0.7 e) negative partial charge of the central carbon atom. This is the feature that, again, was later criticized by Torii,248 who found negative partial charges for the chlorines, in accordance with commonsense expectations (it is a pity that Torii has not derived an actual interaction potential for carbon tetrachloride). Despite this feature of the potential that may well be found baffling by some, the reported agreement with the distinct structure functions, as measured in the framework of the work in question,166 using X-ray diffraction is rather reasonable. (Note that in a way, this work may be considered to be the first integrated MD-assisted interpretation of diffraction data.) Just 1 year later, in 2001, Jóvári et al. performed molecular dynamics simulations on a number of XCl4 (X = C, Si, Ge, V, Ti, Sn) liquids.147 No potential development was attempted; instead, the main novelty was that this work applied considerably larger systems than the ones reported previously: 1500−3000 molecules were put in cubic simulation boxes. Excellent, nearly quantitative(!), agreement with total scattering structure factors from neutron diffraction (including both intraand intermolecular contributions!) was found. As these MD calculations were carried out without any fancy extras, one might wonder whether the sheer system size is the key to a better accord with experimental diffraction data. This was the first instance when mimicking the structure of liquid carbon tetrachloride seemed easier and more straightforward than any time previously: had the early workers used larger simulation systems, full agreement with experiment might have been achieved two decades earlier. As a kind of review of available interatomic potential functions, Rey in 2007133 reported a number of molecular dynamics calculations for liquid CCl4 in which also the system size was varied (between 216 and 400 molecules). He was able to conclude that as far as the structure is concerned “The basic lesson is that the results are largely independent of the model used.” This work therefore may be considered as an apt closure of classical computer simulation studies on liquid carbon tetrachloride. (Note that in the same paper a new (arguably, even revolutionary) way of analyzing orientational correlations has also been introduced; see various sections of this review.) There is a well-separated group of computer modeling studies that employs the reverse Monte Carlo methodology110 (see Table 10). During these simulations, particle coordinates

are modified gradually so that the agreement between measured and calculated structural quantities is made perfect (to the level of consistency within errors) by the end of the calculations (see section on reverse Monte Carlo modeling above); it is therefore not surprising that in most of the cases8,114,124,137,147 the experimental total scattering structure factor could be reproduced, thus providing a basis for detailed structural analyses (see below). In these studies, the number of flexible molecules was usually a couple of thousands, with the exception of ref 245, where only 512 rigid molecules were applied, and the target functions were intermolecular structure factors from Narten:234 these choices make this particular RMC study somewhat less reliable than the others mentioned. 4.1.3. Evolution of Ideas Concerning Orientational Correlations: The Apollo Model and Beyond. Whenever we speak about the “structure” of a material, we all like to think about this (sometimes, particularly in the case of liquids, rather abstract) property as a three-dimensional model that we can inspect visually. For crystalline materials, the unit cell can serve as such a support; on the other hand, for liquids we only have a (more or less) “representative” neighborhood of a particle (usually the first coordination sphere). For liquids consisting of molecules of well-defined shape, what we are most interested in is the way (neighboring) molecules arrange themselves with respect to each other, i.e., the correlations between molecular orientations. In this section, the evolution of ideas concerning mutual orientations of molecules and correlations between these orientations is followed through the 80 year history of experimental studies of liquid CCl4; it is thought to be rather instructive to track where brilliant ideas were born and also where an attractive (to the limit of being nearly seductive) idea started to mislead the entire line of investigation. The earliest mention, from 1943, of an “orientation” is due to Bray,213 while talking about the real space correlation function they derived “The peak near 6.4 Å represents the average distance between the centers of adjacent molecules, whereas the subsidiary peaks between about 3.5 and 5 Å represent frequently recurring distances between nearest approaching atoms in different molecules. The presence of peaks implies slight preferred orientations, probably due to valence saturation within the molecule, and a consequent slight repulsion between nearest chlorine atoms in different molecules.” Narten et al.214 (in 1967) were the first to try and interpret the peaks of the radial distribution function they derived. First, they established that the data were fully consistent with the presence of perfect tetrahedral molecules. They also pointed out the importance of constructing a “model for the liquid structure, which may then be tested against the diffraction data”, which sounds a little like the philosophy of the RMC and EPSR methods. These authors provided a remarkably clear general view of the intermolecular structure of liquid CCl4: “The properties of liquid carbon tetrachloride seem to be determined largely by the interaction of argonlike chlorine atoms. A molecular arrangement which approaches a close packing of chlorine atoms as closely as the geometry of the CCl4 molecule permits appears to be the configuration realized in the liquid. A model based on this assumption is in agreement with the diffraction data. In order to obtain this agreement, it is necessary to accept C−C distances of 5.77, 6.13, and 6.77 Å, which are smaller than the van der Waals diameter of the CCl4 molecule, 7 Å. Thus, there must be a considerable barrier to free rotation in the liquid.” The question that remained R


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one of its chlorine atoms located in a hollow of the nearest neighbor, giving rise to the Cl−Cl contact distance of 3.8 Å...” This is exactly what Egelstaff et al. proposed 5 years before3 (although reference is not made to that work in this respect) with the difference that this geometry has not been a “suggestion” or just and “idea” any longer but something that could be “derived” from diffraction data. Retrospectively, this may have been the point from which a number of misleading interpretations have been made for at least 20 years on, without any considerations concerning the most probable mutual orientation of two tetrahedra (cf. the work of Rey133). Just a few examples from the late 1970s and 1980s are given: Nishikawa231,232 in conjunction with their new X-ray diffraction measurement writes “A chlorine atom of one molecule lies in a hollow formed by three off-axis chlorine atoms of the other molecule. 3-fold axes of these molecules align. Moreover, it is assumed that the average orientation is set in the eclipsed form for chlorine atoms. In this arrangement, molecules form a bodycentered cubic lattice...” Following further theoretical efforts, the same authors conclude in 1985239 “It may be said that carbon tetrachloride molecules have a tendency to keep the most stabilized orientational correlation, namely, the head−tail head−tail packing in the liquid even if the molecules are vigorously moving.” To their credit, in another publication from the same year,238 they clearly warn “Of course, the bcc model may not be the only one model representing the experimental intensity.” (The bcc model is a more extended, crystal-like version of the Apollo model.231) Perhaps the most sophisticated of the “two-molecule” orientational models was the one introduced by Misawa in 1989,223 where the idea of aligned molecular axes was dropped and, instead, a more complicated arrangement was named as the most representative: “This orientation is similar to an interlocking configuration already proposed for liquid CCl4; i.e., a chlorine atom a of neighboring molecule is nestled into a hollow on the central molecule, and a chlorine atom b of the central molecule is also located near a hollow of the neighboring molecule, although this configuration deviates somewhat from the ideal interlocking.” The author has provided values for 13 structural parameters that describe the preferred orientation precisely, an incredibly tedious and careful work. However, when considering more general features, the conclusion (from the same work223) reads “...the assumption we made (that)... the overall structure of liquid CCl4 is determined primarily by a packing of uncorrelated molecules, holds satisfactorily”. These two descriptors cannot really be attributed to the same structure; clearly, more adequate ways of characterizing orientational correlations were needed. Finally, it should be noted that two-molecule representations are most common when quantum-chemical calculations are performed (and this is actually one way of developing pairwise interaction potentials too, see, e.g., ref 247). It is instructive to mention at this point that no such study has found the Apollo pairs to be the most favorable energetically, despite the plausibility of such arrangements. For instance, the work of Mahlanen249 pointed out that each face-to-face-type mutual orientation has a lower potential energy minimum value than any of the corner-to-face orientations. This finding is in full agreement with the earlier study of Soetens247 using a smaller basis set and a smaller set of orientations. Although such calculations do certainly not strictly concern bulk phase behavior, they present a strong indication that the Apollo

unanswered at this stage is what kinds of mutual arrangements of molecules are realized in the real liquid? 4.1.3.1. Invention of the Apollo Model. Only a couple of years later, in 1971, Egelstaff et al.3 explicitly mentioned “orientational correlations” already in the title of their paper. They were clearly determined to reveal the most probable mutual orientations of two neighboring CCl4 molecules: following a lengthy mathematical elaboration, they first state that “We conclude therefore that there is a clear evidence that correlation of molecular orientation must be taken into account and has an important effect on Sm(Q).” (Sm(Q) is, in the terminology of the authors, the “molecular structure factor”, which is essentially a neutron-weighted total scattering structure factor for a molecular system.) The authors of ref 3 then go on and make an attempt to identify the most characteristic arrangement of two molecules: “In order to illustrate the effect of correlation of molecular orientation we shall use a model which we consider fairly plausible for CCl4 in which the C−Cl bond of the one molecule is in line with that of the other molecule and the chlorine atom lies in the hollow formed by the three off-axis chlorines of the other molecule...” (see Figure 2 of ref 3). This is the very birth of a concept that was to influence the field for decades. It should be noted that these authors did not mean that this arrangement would be the “perfect, one and only” description of the orientational structure. They simply suggested this model as a possibility, about which they further noted: “Naturally this is not really a rigid orientation in the liquid and it cannot hold for all molecules since one cannot even make a crystal in this way. However, it is not seriously inconsistent with the known liquid density.” Again, no exclusivity, not even dominance of the Apollo arrangement, was claimed at this stage. The “exact” Apollo idea, i.e., when the two molecular axes are collinear,3 was criticized within 3 years by Lowden and Chandler,229 even though the basis of their criticism, which was formed by their theoretical estimate of the C−C PRDF, may perhaps be called “shaky”. Moreover, Lowden et al. also advocated an arrangement in which neighboring molecules interlock, so that one Cl atom of the one molecule is nestled in the hollow formed by three chlorines of the other molecule. In the remaining parts of this review, we will also call such arrangements (“generalized”) Apollo structures: the essential feature, the “corner-to-face”-type docking, is the same as in the original suggestion;3 only the collinearity of the molecular axes is missing. 4.1.3.2. More Elaborated Apollo Models. Reichelt, in 1974, performed X-ray diffraction measurement on room-temperature carbon tetrachloride.216 While interpreting their results, even though they started from the “Apollo assumption” of Egelstaff,3 they emphasized the importance of antiparallel (i.e., face-to-face) arrangements too−this, apparently, has not influenced further developments for quite some time. Chronologically, the next very detailed discussion of molecular orientations in liquid CCl4 is due to Narten, from 1976.234 He remeasured X-ray and neutron diffraction data and derived approximate C−Cl and Cl−Cl partial radial distribution functions (with the assumption that the C−C PRDF does not contribute). Although this was a bold and successful move, the conclusions concerning orientational correlations were far too detailed (at least, as we see it now, nearly four decades later): “...each of four neighboring molecules has one of its chlorine atoms nestled into one of the four hollows of the central molecule. At the same time, the central molecule has S


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Soetens et al.,247 in their molecular dynamics simulation study, were the first to point out the importance of “edge-toedge”-type arrangements; it is rather intriguing how this configuration of pairs of CCl4 molecules, that is the most populous in a “random” model of tetrahedral liquids (see follow-up publications of Rey133 and Pothoczki124), could avoid being spotted until the end of the second millennium. The requirement of distance dependency was followed by Rey et al. in 2000,166 although (this time) in a rather arbitrary manner (yet). This work also considered seriously the edge-toedge-type correlations and excluded those corner-to-cornertype arrangements in which the two corners were actually the closest parts of two neighboring molecules. On the basis of a radial distribution function-based comparison with randomly oriented molecules, they found that edge-to-edge- (in their terminology, interlocked) and corner-to-face-type orientations are present at short distances. They also pointed out (in agreement with ref 114) that “...an excluded volume picture of structure is excellent for nonpolar liquids...” (in their series, CCl4 was one of such molecules). The next wave of reverse Monte Carlo studies appeared in the first half of the 2000s: Jóvári et al.147 considered a series of XCl4 liquids, while Pardo et al.8,9 put the emphasis on comparison with the (metastable) plastic crystalline phase of CCl4. For the liquid, the former work confirmed the findings of Pusztai et al.114 while providing a quantitative account for the populations of the three categories of orientations that were distinguished (corner-to-face, corner-to-edge, corner-to-corner): Apollo neighbors were found to be about 4% of all the nearest neighbor molecules. The first of the series of the works of Pardo et al.9 only established the presence of orientational correlations, whereas the second paper8 stated that “...neither Apollo-type or interlocked (i.e., edge-to-edge) orientations are truly dominant over others...” and that “...on the other hand, face to face type orientations are more abundant...”; these statements concern nearest neighbors only. In a later analysis of the same experimental data, Pardo et al. in 20076 introduced bivariate distribution functions for characterization of local order and emphasized (again, after Chang243 and Rey166) the importance of distance-dependent considerations. The newly introduced tools also found the face-to-face arrangements dominant among the closest neighbors. 4.1.4. Structure of Liquid Carbon TetrachlorideAs We Understand It today. A completely new way of characterizing distance-dependent orientational correlations in a particle configuration (from MD, RMC, ...) was introduced in 2007 by Rey133 (see section 3.3; note also that a very similar method was introduced independently later by Morita137). For the first time, each and every molecular pair could be counted and categorized into 6 groups whose definition is unambiguous. The first application was on MD trajectories;133 very soon, Rey groups were calculated for large reverse Monte Carlo particle configurations.124 The picture that emerges from these relatively recent studies is that for liquid CCl4, most molecular pairs take the edge-toedge (or 2:2) mutual orientation if the entire distance range is taken into account. If focusing on the shortest intermolecular (i.e., C−C) distances, first face-to-face (3:3) at around 4 Å, then edge-to-face (2:3) at around 5 Å, followed by edge-toedge (2:2) at 5.7 Å and corner-to-edge (1:2) at 6.7 Å arrangements become dominating within the first coordination sphere. The importance of Apollo (1:3) (as well as of corner-

idea is not the most appropriate choice even when isolated pairs of molecules are considered. 4.1.3.3. Ideas Based on Bulk Models: Computer Simulation and Structural Modeling. One crucial feature of the mutual orientations mentioned so far is that they all have been derived on the basis of two (in any case, very few) molecules; this may be acceptable as a starting point, but the fact that it is a bulk liquid that is to be characterized (with the proper density and packing fraction) should also be taken into account. Such “bulk” models are most readily provided by computer simulations (molecular dynamics, Monte Carlo) and structural modeling (reverse Monte Carlo, EPSR). Steinhauser et al.233 started from the early ideas of Sackmann,254 who already in the late 1950s found that “By means of simple geometrical considerations he showed that free rotation of molecules cannot exist in the condensed phase... In the paper of Sackmann (Figures 1 and 2) two interlocking structures are proposed...” One of these two structures is the “rocket” (a.k.a. Apollo) model, whereas the other one is the “face-to-face” mutual orientation. Steinhauser233 also pointed out that a suggestion already from the 1930s (!), by Biltz,255 may have served as the origin of Apollo-like ideas: “Biltz realized already that the close packing of molecules in the condensed phase leads to an interlocking structure: Each molecule has its halogen atoms nestled into the hollows of its neighbor and vice versa.” Steinhauser then went on and criticized the Apollo idea of Egelstaff et al.3 but not the “nestling-into-the-hollow” part, only the “rocket shape” of the dimers. Interestingly, computer simulation studies have not touched upon the issue of orientational correlations for about 15 years. Chang et al. in 1995243 applied molecular dynamics simulation to (among others) liquid CCl4. They pointed out that discrepancies between conjectures based on even large(-ish) 3D structural models may originate in the fact that the preferred mutual orientation of two molecules may change rapidly with the distance between molecular centers: “Due to the broad features of the angular distribution functions, it is implausible to consider only one type of configuration dominating the local orientation.” From this point on, it has been clear that an appropriate tool for characterizing mutual orientations must have the attribute of being distance dependent. The first reverse Monte Carlo modeling investigations appeared in 1997.114,245 Only the work of Pusztai et al.114 used a sufficiently large number of (flexible) molecules while fitting the total scattering (as opposed to intermolecular) structure factor. Although the main conclusion of both RMC studies was that the Apollo model could not be an appropriate tool for characterizing the liquid structure of CCl 4 , Jedlovszky245 suggested that some of the generalized Apollo structures were most important. In contrast, Pusztai et al.114 were able to exclude these kinds of arrangements via applying hard-sphere-like reference structures that represented the influence of purely steric effects. They proposed that a dominant arrangement is the corner-to-corner type (whose name later caused some misunderstanding, see e.g., refs 133 and 166); that time, this name was just a way of distinguishing clearly the non-Apollo-type structures. As later it has become apparent,124 this category included any arrangement where two corners were in the vicinity of each other, regardless of how the rest of the tetrahedral molecule was positioned. T


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4.2. Liquids of Molecules with a Perfect Tetrahedral Shape: The XY4 Series

to-corner (1:1)) pairs is negligible in comparison with the groups listed above. Long (nanometer124) range orientational correlations, involving particularly the alternating (2:3) and (1:2) groups, have been identified independently via molecular dynamics simulation133 and reverse Monte Carlo modeling.124 Note that both MD and RMC results are consistent with TSSFs, resulting from diffraction experiments. The longest distance over such correlations was about 4 nm (40 Å). When compared to hardsphere-like (i.e., randomly oriented reference structure in which only steric effects are present), these long-range correlations are missing completely, even though the orientational structure within the first coordination sphere looks qualitatively similar. It is instructive to realize that in this particular case, the influence of diffraction data could be spotted most clearly. These results are demonstrated by Figure 4.

Although the first experimental (X-ray diffraction) study on a liquid belonging to this group of materials, SnI4, was published more than 50 years ago,162 followed by sporadic experiments around 1970 on liquid CF4,156 SiCl4,143 and GeBr4,3 the first systematic investigations appeared only during the second half of the 1970s.146,148 “Systematism” might have been an important concept here: each liquid (see Table 6) consists of molecules of perfect tetrahedral shape. Therefore, in the absence of strong intermolecular directional forces (which condition is fulfilled for each of the materials considered), the primary factor that influences intermolecular (e.g., orientational) correlations may well simply be the size ratio of the central and ligand atoms. In this section, experimental (see Table 6) and theoretical/computer simulation (see Table 7) studies on these liquids are discussed, along with the evolution of ideas concerning correlations between mutual orientations of tetrahedral molecules in a similar style presented for liquid CCl4 above. 4.2.1. Fluid Methane, CH4. Had its liquid phase been more accessible, this material could easily have played the role of the prototype tetrahedral liquid: unfortunately, at atmospheric pressure, methane is liquid only for a roughly 20 K wide range, well below room temperature, between about 90 and 110 K (see Table 1). This property has made experimental studies of the structure difficult: the first (and only) X-ray diffraction determination of the total scattering structure factor of liquid methane (92 K; ambient pressure) was performed in 1981 by Habenschuss et al.154 These authors chose to consider methane molecules as superatoms, i.e., each molecule was taken as one single scattering center; this way, only molecular center− molecular center correlations could be elucidated (in other words, no direct information on the orientations was provided). Fifteen years later, in the other diffraction study that can be found in the literature, the structure of supercritical fluid (per deuterated) methane was investigated by high-pressure neutron diffraction at 370 K, compressing the material to liquid-like densities;155 note that data from these thermodynamic states cannot be compared with results on the proper liquid state, that is, there would be room for further diffraction experiments on the liquid/fluid phase(s) of this essential alkane (and, at the same time, tetrahedral liquid). Computer simulation studies are more abundant (see Table 7). Starting from the late 1970s (Murad et al.185), via continuous potential development efforts (see, e.g., refs 186, 187, 189, and 190), by 2011138 a rather neat picture has evolved: Sampoli et al.138 were able to reproduce the inelastic neutron scattering results of Guarini et al.188 quantitatively, that is, sets of particle coordinates could be prepared that were fully consistent with some of the available experimental data, so that orientational correlations could rightfully be inspected in detail. Concerning the orientational structure, the first statement is from 1981 by Habenschuss et al.:154 “...the hydrogen bulges result in significant orientational correlations between methane molecules, similar to those found in liquid carbon tetrachloride, albeit weaker.” (Note that this is an implicit advocation of the Apollo model, cf. the work of Narten on liquid CCl4.234) This finding that the authors meant for the nearest neighbors was based on detailed comparison of theoretical RISM integral equation calculations (for an example of RISM, see ref 229) and of earlier molecular dynamics computer simulations by Murad et al.185 to the X-ray data. Beyond first neighbors, “...the

Figure 4. Orientational correlations in liquid CCl4 according to the method of Rey. (Left) RMC modeling; (right) hard-sphere reference system, both by Pothoczki et al.124 Color coding of the Rey groups: black (1:1); red (1:2); dark green (2:2); turquoise (1:3); dark blue (2:3); magenta (3:3).

Figure 5 displays snapshots of RMC particle configurations for liquid CCl4 (particle coordinates are from Pothoczki124). It

Figure 5. Snapshots of the RMC configuration of liquid CCl4. (Left) Overview. (right) Realization of the edge-to-face (2:3) mutual orientation between two molecules. Gray spheres, carbon; green (and red), chlorine.

is interesting to notice that when the size ratios of atoms and the packing fraction are set to be realistic in the figure only a one-component liquid is visible, since carbon atoms are completely buried in the nests formed by chlorine atoms; the same observation was made by Pusztai.114 When the packing fraction is decreased specific orientations become well recognizable (see the chlorine atoms marked in red). U


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reverse Monte Carlo modeling; the main conclusion concerning molecular orientations was that “...there are no predominating angles at any center distance, except for very close distances...” It may be worth mentioning that liquid CF4 is one of the few cases for which structural conclusions were drawn on the basis of vibrational (in this case, from IR) spectroscopy data: Burtsev et al.192 claim to have seen that “...the coordination number n is proportional to the density of the liquid whereas the nearestneighbor distance Rnn is practically invariable...” While the effort is certainly valuable, the strength of this conclusion is characteristic to the usefulness of experiments other than diffraction for structural investigations. The first molecular dynamics simulation on liquid (and solid) CF4, as a test case, was carried out by Nose and Klein in 1983.193 No structural details were reported; this is not too surprising since this work was one of the first seminal papers that introduced the concept of constant pressure (N,p,T) molecular dynamics. Potter et al.194 developed a more sophisticated set of potential functions for liquid fluoromethanes, including CF4; the main focus of application was to simulate (via direct MD) the liquid−vapor coexistence in these systems (no detailed structure description was provided). Still, on the computer simulation side, the Monte Carlo (as well as RISM integral equation theoretical) calculations of Bassen et al.195 can be mentioned, who compared their results to neutron diffraction data measured by the same group.130 The only discernible outcome, as far as the issue of molecular orientations are concerned, was that the Monte Carlo simulations confirm previous results obtained by RMC. Liquid CF4 (above its boiling point, at 158 K, under pressure) was part of a recent extensive MD investigation on many XY4 liquids;136 the author applied the rigid version of the potential of Potter et al.194 and calculated characteristics of the orientational correlations using his scheme.133 Unfortunately, no direct comparison with experimental (diffraction) data was provided. It appeared that the occurrence of the various Rey groups was quite similar to the pattern observed for liquid CCl4: at the shortest C−C distances, face-to-face arrangements dominate that, at somewhat larger separations, become edge-toface and edge-to-edge mutual orientations. It is quite clear that there is room for further investigations concerning the structure of liquid/fluid carbon tetrafluoride, both on the experimental and on the computer simulation sides: proper analyses of the orientational correlations are available only from a computer simulation,136 for one thermodynamic state (which happens to be above the ambient pressure boiling point of the material). Carbon tetrabromide, in contrast to CF4, is a crystalline solid at room temperature and ambient pressure that needs to be melted (at around 365 K) to obtain the liquid phase. The first diffraction experiment on the liquid was performed by Dolling et al. in 1979,157 during a rather extensive experimental (neutron diffraction) study of the various crystalline form of the material. Two more neutron diffraction experiments have followed that were aimed at investigating the liquid by Bakó et al. in 1997158 and Temleitner et al., who reported their earlier experiment in 2010.159 The three data sets are in good agreement. Recent synchrotron X-ray diffraction data are also available.160 Whereas the plastic crystalline phase received proper attention,256,257 only one molecular dynamics simulation can be found in the literature that deals with liquid CBr4: the work

structure of liquid methane differs little from that of a nonassociated fluid such as liquid argon”. The latter finding was later confirmed by Strauss et al.,155 who complemented their neutron diffraction measurements (on the supercritical fluid, see above) by both integral equation (RISM228) theory and reverse Monte Carlo (RMC110) computer modeling. Computer simulations have been long engaged with developing suitable interaction potentials,186,187,189,190 without even mentioning bulk structure. Some of these works, on the other hand, report on quantum chemical calculations on dimers (see, e.g., refs 186, 187, and 190); all of these studies confirm that the lowest energy dimers are among the face-to-face types, which is the same finding as was mentioned for CCl4 (see above). Rey, in 2009, published a comprehensive MD study on many XY4 liquids, including methane. Using his scheme developed earlier,133 the author was able to point out that suggestions concerning mutual orientations of neighboring molecules made on the basis of inelastic neutron scattering experiments188 were impossible to maintain. Instead, an orientational structure that resembles that found in liquid CCl4 was promoted. Another very detailed characterization of correlations between molecular orientations is provided by the recent, very extensive, molecular dynamics study of Sampoli et al.138 As it has already been noted, they modified the original Rey133 classification scheme of mutual orientations, so that results for the 5 interatomic potential functions they consider were presented in the framework of the modified scheme. They find, first, that only the potential parameters introduced by Tsuzuki et al.186 (which they call as the TUT potential) are able to account for the previously measured188 inelastic neutron scattering spectra. The most frequent arrangement found for this potential in the first coordination sphere is that of the F−F (or, in the original Rey method, 3:3, face-to-face) type, followed by E−F (2:3, edge-toface) pairs; this is in disagreement with the suggestion of Habenschuss.154 On the contrary to earlier findings,154,155 Sampoli et al. found clear oscillations, i.e., orientational correlations, out to about 12 Å, as far as in the third coordination sphere. In our opinion, at present the works of Rey136 and Sampoli et al.138 provide the most appropriate and plausible description of the microscopic structure of liquid/fluid methane. 4.2.2. Liquid Carbon Tetrahalides: The CX4 Series (X = F, Cl, Br, I). Carbon tetrachloride has already been exhaustively discussed. Carbon tetraiodide, CI4, does not have an accessible liquid phase, since the molecule is rather sensitive to high(ish) temperatures: it decomposes before it melts (due to the stressed I−C−I bond angle; the closest to a disordered phase is the total scattering study of diffuse scattering in the crystal23, that is, in this group, we are left with two materials, liquid CF4 and CBr4none of them is liquid under ambient temperature and pressure. Liquid CF4 may be obtained by cooling the gaseous form down to between about 90 and 145 K at atmospheric pressure: this is what the authors of the first diffraction experiment on this liquid did in the 1960s.156 Although this was a very ambitious program and performance half a century ago, the authors were not able to go beyond the description of the radial distribution function. Thirty years later, the only neutron diffraction study was performed in the supercritical fluid phase at liquid-like densities (at 370 K and pressures between 590 and 990 bar) by Waldner et al.130 This latter study is very similar to that on fluid methane,155 also in that it was accompanied by V


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of Evans196 considers not only carbon tetrabromide but also liquids of other spherical-top molecules such as GeBr4 and SF6, along with P4. Unfortunately, the static structure was only marginally mentioned; the focus was on dynamic properties. Liquid CBr4 also appears in the seminal MD simulation study of Rey:136 he applied 4000 molecules that interact via the potentials developed originally for the ordered crystalline phase.258 Although comparison with structural data was missing from this work, orientational correlations were described using the method developed previously by the author himself.133 On the other hand, extensive reverse Monte Carlo modeling studies accompanied all the latest diffraction experiments.158−160 Bakó et al.158 first approximated and subtracted the intramolecular contribution to the total scattering structure factor, and the RMC modeling was based on the intermolecular part only using rigid molecules. The artificial (and sometimes, problematic) splitting of the measured data into intra- and intermolecular was shown to be unnecessary by others in the same year (1997),114 so that the two RMC studies that followed in this millennium159,160 have applied flexible molecules and modeled directly the measured total structure factor. Despite these differences, the intermolecular parts of the partial radial distribution functions of the three RMC investigations are quite similar. Concerning orientational correlations, Bakó et al. produced an average orientation for the subshell containing the closest four molecules (cf. Figure 12 of ref 158). This arrangement they call interlocking and is similar to an edge-to-face (or 2:3) pair of the original Rey construction (see ref 133). Both works of Temleitner use the Rey method for the characterization of orientational correlations: the main difference between the two investigations is that in the earlier one, from 2010,159 conclusions were drawn on the basis neutron diffraction data only, whereas the more recent one, from 2014,160 reports structural models that were consistent with both neutron and (synchrotron) X-ray diffraction results. As it was shown in the latter work, the additional data set has not brought about new features of the orientational structure. As it was concluded, “Orientational correlations in the resulting structural models agree with general characteristics found for liquids of tetrahalides”, that is, in the first coordination sphere of central CBr4 molecules, the nearest neighbors are found in the 3:3 (face-to-face) arrangement; a little further away, 2:3 orientations dominate. At higher distances, edge-to-edge (2:2) arrangements become the most frequent. Correlations between molecular orientations can be observed up to abut 15 Å. These findings correspond very well to those reported by Rey,136 based purely on molecular dynamics computer simulations. In summary, it may arguably stated that as far as the liquid structure of carbon tetrabromide is concerned, the above description is about the most detailed that may be provided, that is, liquid CBr4 is one of the few examples for which no further investigations seem to be urgent. 4.2.3. Liquid Tetrachlorides: The XCl4 Series (X = C, Si, Ge, V, Ti, Sn). These materials have been relatively popular subjects of diffraction experiments over the past 50 years (see Table 6). One of the reasons may be that all of them are liquids at room temperature and ambient pressure (see Table 1), so that no special apparatus is needed for reaching the appropriate temperature/pressure. Although the first studies (in the mid1970s) were performed on single materials (SiCl4, refs 143 and 259), later comparative investigations on more than one member of the family have become customary (see, e.g., X-ray

diffraction on GeCl4 and SnCl4, ref 148; SiCl4 and GeCl4, ref 144; neutron diffraction on CCl4, SiCl4, TiCl4, and SnCl4, ref 146; on each tetrachloride in the series, refs 147 and 230). As an extension to these investigations concerning neat liquids, mixtures of these tetrachlorides have also been measured.144,145,260 Interestingly, a rather wide range of neutron data are available, whereas unfortunately, no comprehensive synchrotron X-ray diffraction investigation is available at present (even though the technique is perfectly fit for such studies, as exemplified by liquid TiCl4150). The published data are in reasonable agreement for a given material (although some problems have been reported, see ref 147 concerning liquid SnCl4), and a database of experimental total scattering structure factors provides a solid foundation for subsequent simulation/modeling studies. Some examples of measured diffraction data on these materials are shown in Figure 6.

Figure 6. Normalized total scattering structure factors124,160,163 from X-ray diffraction (top left, shifted by the y axis), halogen−halogen partial radial distribution functions (top right), and orientational correlation functions from Rey analysis (bottom panels), as obtained for RMC modeling results123,124,160 of liquid CCl4, CBr4, SnCl4, and SnI4. Color coding to the materials: CCl4 (black), CBr4 (red), SnCl4 (blue), SnI4 (dark green). Of the 6 Rey groups, the 1:3 (bottom left), 3:3 (bottom middle), and 2:2 (bottom right) types have been selected.

Interestingly, for this group of liquids, quite a few theoretical studies have been carried out (see Table 7) using the RISM integral equation formalism.261 Comprehensive calculations were published by, e.g., Montague175 and Dolgov174 in the first half of the 1980s and later by van Tricht;178 in the best cases, the intermolecular part of the measured structure factor could be approached at a semiquantitative level (see, e.g., the case of SiCl4 in ref 175). The main difficulty here is that since particle coordinates are not present there may only be speculations presented concerning molecular orientations. As far as computer simulations are concerned, there are relatively few investigations published (see Table 7); a major reason for this may be that potential parameters for rarely used atoms, like Sn, V, and Ti, are not easily available. Interestingly, vanadium tetrachloride drew attention in this respect early on in 1980;184 the main reason was that the (coherent, i.e., relevant from the point of view of the structure) scattering cross section of vanadium for neutrons is negligibly small, so that neutron diffraction measures (nearly) exclusively Cl−Cl correlations. The interatomic potentials were of the Lennard−Jones types; they found good agreement, at the gClCl level, with neutron W


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terms of being able to find the (many) parameters that are needed to convert the geometrical description of two neighboring molecules into the intermolecular part of the structure factor. The (only one) arrangement they come up with looks similar to a 1:3 or 2:3 (or perhaps a 2:2 one, hard to tell from their figure) arrangement according to the terminology of Rey.133 Unfortunately, as it was already mentioned when discussing liquid CCl4, such models cannot really account for the preferred orientation, as they change as a function of distance between molecular centers in the bulk phase. An interesting and, from the point of view of this present review, rather relevant question was posed by the title of a work by Sjoerdsma in 1985:176 “Do tetrachlorides have a common liquid structure?”. The answer in that work was based on a very detailed inspection of Cl−Cl PRDFs; since the authors did not find the desired level of agreement, their answer was negative. In a pursuit of an underlying similarity of the structure of the same tetrachlorides, Rey136 as well as Pothoczki124,125 (and in a somewhat implicit manner Jóvári in their earlier work147) found an affirmative answer on the basis of the Rey group analyses of the tetrachlorides in question. The general picture that emerges on the basis of an extensive MD136 and an extensive RMC124 study is that with the exception of liquid SnCl4, at the shortest distances (molecules that touch each other), face-to-face (3:3) arrangements are most frequent that lose their importance very rapidly as the intermolecular distances grow. At larger separations, in the vicinity of the first maximum of the center−center PRDF, edge-to-face (2:3), whereas a little further away, just beyond the first maximum, edge-to-edge (2:2) arrangements tend to form. For SnCl4, the only difference is that it is the edge-to-edge orientations that are most important at the shortest distances, causing a prepeak of the curve depicting the distance-dependent occurrence ratio of the 2:2 group. The range of orientational correlations was found to be most extended for liquid CCl4,124 whereas liquid VCl4 and TiCl4 are the closest to a hard-sphere-like behavior.125 As it pointed out in the relevant RMC studies,124,125 orientational correlations found in the corresponding hard-sphere reference systems are qualitatively similar to those found in the real (MD and RMC) particle configurations, including the anomaly connected with liquid SnCl4, that is, steric effects (molecular shape, packing fraction) do play an outstanding role in determining intermolecular correlations. Some examples of distance-dependent orientational correlations functions can be seen in Figure 6. 4.2.4. Other Combinations: GeBr4, SnI4, and Neopentane, C(CH3)4. These are liquids consisting of molecules of perfect tetrahedra that do not belong to any of the groups discussed above but for which a significant amount of structural information has been gathered over the past decades (see Tables 6 and 7). 4.2.4.1. Germanium Tetrabromide. GeBr4 melts just above room temperature, so that preparing a liquid sample is not difficult. The first diffraction measurement was carried out by Egelstaff et al.3 (by neutron diffraction, at 333 K), and the total scattering structure factor was reported in the same paper in which the Apollo model was introduced (not only for liquid CCl4!). Interestingly, in the late 1980s, this liquid served as one of the first molecular examples161 of the use of the technique of anomalous X-ray scattering:101 measured intensities were reported at various X-ray energies, and two different methods were applied for obtaining partial structure factors and radial

diffraction data of Gibson.151 Rocha et al.262 developed a force field for liquid SnCl4 that they showed to work well for gasphase clusters and for the liquid. Also, for studying phase equilibria, a potential model was introduced for SiCl4;263 these interactions were applied in grand canonical Monte Carlo simulations that, unfortunately, reported no results on the structure.263 The most comprehensive MD computer simulation study appears to be that of Jóvári et al.,147 who applied two kinds of potential functions, the more complicated being a 5-site Lennard−Jones plus partial charges type. As it was mentioned already during the discussion of liquid CCl4, the main novelty of this work was the use of unusually large simulation boxes, containing 1372 (5-site potential model) and 2916 (simple 4-site, repulsive-only potential) molecules. The original paper shows the worst match, obtained for liquid GeCl4, with measured neutron diffraction data (in the reciprocal space); retrospectively, it may be argued that already this one is actually in quantitative agreement with experiment. It may have been therefore worthwhile analyzing these molecular dynamics results on their own and/or perhaps calculate (and compare with corresponding experimental data) the X-ray-weighted total scattering structure factors; unfortunately, the authors have not provided such details. Still, it is now clear that as far as the microscopic structure is concerned, classical molecular dynamics simulations are capable of producing model structures that are consistent (within errors) with diffraction results. This statement is corroborated by the recent MD work of Rey,136 who also simulated large systems, containing 4000 molecules, of liquid SiCl4, VCl4, and SnCl4 (among other XY4 liquids). Although this author has not provided direct comparison with diffraction data, based on the findings of Jóvári et al.,147 we can be assured that the match must be pretty good here too. Rey136 performed detailed analyses of the orientational structure, based on his own scheme.133 Reverse Monte Carlo structural models are available for each liquid of this group.124,125,147 For liquid SiCl4, GeCl4, and SnCl4, RMC could be performed on the basis of both neutron and X-ray diffraction data; agreement with both kinds of results was shown to be quantitative.124 Considering the evolution of ideas about orientational correlations, early speculations suggested that they may be enhanced in comparison with previously studied tetrahedral liquids (such as CCl4).143 As the center−Cl bonding distance grows, intermolecular Cl−Cl distances can be expected to interfere with the intramolecular ones, and thus, the molecular structure is expected to influence orientations of neighboring molecules; this effect was first evidenced by Rutledge 40 years ago148 and shown later clearly by Jóvári et al. for each tetrachloride in this group.147 The molecular dynamics study of Murad et al. on liquid VCl4184 was not specific about the nature of orientational correlations but showed that the free rotator approximation was a very poor one, so that such correlations must exist. The essentially reverse Monte Carlo work of Jóvári et al.147 was mainly concerned with dismissing the importance of the Apollo model for tetrachlorides other than CCl4. They found corner-to-corner-type arrangements important by using, again, the vague definition introduced earlier by Pusztai,114 which basically meant anything but Apollo; this vagueness caused some misunderstanding later.133,183 Nath et al.183 applied the two-molecule approach of Misawa,223 introduced originally for liquid CCl4, for some of the tetrachlorides considered here. They reported success in X


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that shown for the reciprocal space.164 Also in 2009, another MD simulation was performed at ambient conditions,136 with the specific aim of characterizing orientational correlations between the tetrahedral molecules of liquid tin tetraiodide; the potential functions used in this work were identical to those of Fuchizaki,164,199 so that the agreement with the measured total scattering structure factor (which is not provided by Rey in his paper136) should be the same as that shown by Fuchizaki.164 Yet another computer model was prepared in the same time period by Pusztai et al.,123 where the reverse Monte Carlo method was made use of. Agreement with experimental data is perfect, and in addition, results for a corresponding hard-sphere reference system were also provided; as mentioned above, the structure factor of the reference system was in semiquantitative agreement with the X-ray data. Orientational correlations using the Rey method133 were calculated both by Pusztai et al.123 and by Rey;136 there is a general agreement between the two methods (MD and RMC), i.e., at short distances, edge-to-edge and edge-to-face arrangements are the most frequent, whereas face-to-face (3:3) orientations are not as important as had been observed in other tetrahedral liquids (cf. refs 124, 133, and 136). The main difference concerns the occurrence of corner-to-face (1:3; Apollo like) molecular pairs: in the RMC model,123 the authors found a maximum probability of about 20%, two times as much as MD predicts. In the high-pressure MD study, the ratio of Apollo-like arrangements was claimed to be even higher164 (although no exact value was provided and only two kinds of arrangements, 1:3 and 3:3, were considered). (Some characteristics of the orientational correlations in liquid SnI4 are given by Figure 6.) On the basis of the above, it can be argued that the atmospheric pressure structure of liquid tin iodide is well understood; however, as far as the very interesting higher pressure liquid states are concerned, there is room (and also need) for further computer modeling. 4.2.4.3. Neopentane, C(CH3)4, or CMe4. Strictly speaking, this alcane is not an XY4 liquid: it is four methyl (CH3−) groups that are connected to a central carbon atom (the molecular structure is discussed in detail by Siam et al.264). The reason we consider this liquid here is that, as it was rather plausibly depicted by Rey et al.,166 the bulge of the methyl group is about the same size as that of a halogen (Cl or perhaps Br) atom. The liquid phase of this material is available at very narrow temperature range: it exists only between 257 and 282.5 K at ambient pressure. This may be the reason why only one extensive diffraction study, the X-ray diffraction measurements of Narten165 from the late 1970s, is available in the literature. Justified by the weak X-ray scattering abilities of hydrogen, the methyl groups were taken as units, i.e., H atoms were not considered individually. This choice has determined analyses since then: each work mentioned below has taken the same approach. The data were interpreted by the author himself, based on integral equation theories using essentially hard spheres; a close agreement was demonstrated,165 and the conclusion concerning orientations was drawn that they “...are of a similar nature as found in liquid carbon tetrachloride, where a central molecule is interlocked with four of its 12 nearest neighbors...” Similar theoretical apparatus was used by Rao et al.,201 who advocated the structures (including the Apollo model) proposed by Egelstaff et al.3 Later, the same group202 applied Misawa’s twomolecule approach153,223 for describing orientations: they

distribution functions. Even though the authors themselves were critical about the accuracy of their PRDFs, this work has provided ample experimental structural data in the reciprocal space that may be used for further analyses. Indeed, the same group went on and interpreted their diffraction results197 by comparing the experimental findings to (1) earlier RISM integral equation calculations by Swamy et al.198 and (2) predictions of various structures ranging from uncorrelated models to numerous crystal-like arrangements. The main finding of the work of Ludwig et al.197 may be summarized as “...the liquid structure is, to a great extent, determined by the packing of the large halogen atoms...”, but no specific orientations were mentioned. The dedicated theoretical (RISM) work mentioned above198 claims, on the basis of simple distance considerations, that “...the Apollo model of Egelstaff et al.3 is inadequate for the present case and that the structure of liquid GeBr4, is better approximated by the one suggested for liquid CCl4, by Narten234”. Unfortunately, only one computer simulation investigation is available for liquid GeBr4, that of Evans et al.,196 who applied five-site Lennard−Jones-type potentials for a system of 108 molecules and obtained rather reasonable PRDFs (that, by the way, were not very close to the RISM predictions). Unfortunately, further details of the structure remained undisclosed; on the other hand, microscopic dynamics was discussed in quite some detail. In summary, liquid GeBr4 still provides some room for structural studies that may either be the extension of the MD simulation of Evans et al.196 (larger systems, comparison directly with experimental data in the reciprocal space) or be a standard reverse Monte Carlo calculation that applies both neutron and X-ray diffraction data as input. 4.2.4.2. Tin Tetraiodide. Although the melting point of crystalline SnI4 is as high as 416 K, the first X-ray diffraction experiment was performed already more than 60 years ago by Wood et al.,162 who at that time could only presume that the liquid would contain isolated tetrahedral molecules; their data were fully consistent with this presumption. Interest in this liquid was raised again more than 50 years later, and new (synchrotron) X-ray diffraction measurements have been carried out by Fuchizaki et al.;163 the main reason was that the same group claimed to have discovered a liquid−liquid phase transition in liquid SnI4 at a pressure of around 1.5 GPa.164 (Note that this latter experiment required the most upto-date high-pressure equipment available at a synchrotron source.) No neutron diffraction experiment is known on the disordered phases of SnI4. As far as computer simulation studies are concerned, many publications from the group of Fuchizaki163,199,200 mention and/or apply molecular dynamics calculations for calculating thermodynamical properties; explicit information on the structure however is provided only in the one that describes the two liquid phases proposed for SnI4.164 The interatomic potential was a four-center (on the iodine atoms) Lennard− Jones type, described earlier by the same people.199,200 For the atmospheric liquid, the total scattering structure factor was calculated and compared to the X-ray data;163 the match is at the semiquantitative level and, interestingly, not of noticeably higher quality than achievable by using proper hard-sphere constraints (cf. ref 123). Comparison with the higher pressure forms (at 0.4 GPa) was provided in the form of the total (cumulative) radial distribution function; the quality of agreement between simulation and experiment is similar to Y


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stated that “Clearly, the Apollo model is untenable”, and indeed, the picture they provide is closer to an edge-to-edge (or perhaps an edge-to-face; 2:2 or 2:3) arrangement. Computer simulations have been also applied for liquid neopentane since the early 1980s: Wong et al.203 proposed potential models for two kinds of sites, carbon and methyl, and showed that the intermolecular structure factor derived from experiment could be reproduced satisfactorily. Mountain204 made use of (Lennard−Jones type) carbon and methyl potential parameters suggested earlier by Jorgensen265 and reported partial C−C, C−Me, and Me−Me radial distribution functions (along with a detailed discussion of the dynamics, also of the plastic crystalline phase). Rey et al.166 applied ab initio quantum chemical calculations for deriving proper interaction potentials for the family of chlorinated neopentanes; subsequent MD simulations showed that the interactions can reproduce X-ray diffraction results quite well. The potential refined for neopentane166 was later applied by Rey135,136 for extensive molecular dynamics simulations, from which details of the orientational correlations could be discerned. As pointed out in the work assembled for a number of XY4 liquids,136 the orientational structure in liquid neopentane is nearly identical to that observed for liquid CF4, i.e., among the molecular pairs with the smallest intercenter separation, face-to-face, edge-to-face, and edge-toedge arrangements are frequent (in order of occurrence).

occur at a pressure of around 1 GPa, above 1000 K169 (the actual presence of two liquid phases was later proven convincingly the same group171). Katayama et al. later provided the full data set they had measured on solid and liquid red P;170,211 due to experimental difficulties at extreme pressures and temperatures, they were forced to use an instrument where the maximum value of the scattering variable was about 10 Å−1. Note that in their series of measurements, white phosphorus (and its molten version) was, regretfully, left out completely. Liquid P4 was considered in an early classical MD simulation of Evans et al.196 (along with other tetrahedral liquids), who applied a single Lennard−Jones potential parameter pair and were able to reproduce the radial distribution function derived from the measurement of Granada et al.29 with reasonable accuracy. The more recent computer simulations all have attempted to tackle the change of bonding through the transition between the various forms of phosphorus, and therefore, quantum effects had to be handled explicitly. Hohl et al.206 wished to understand how white liquid P turns into red liquid P as the white liquid is heated above 473 K; this change is the result of a polymerization reaction that, if allowed to proceed, produces solid red P (in the form of precipitates). They had a very small simulation cell containing 26 P4 tetrahedra and applied a plane wave description of the electrons within the density functional theoretical framework.268,269 Hohl et al. did perform a rather detailed analysis of mutual orientations and found that “...neighboring molecules prefer to orient face to face...”; this is in full agreement with findings based on the Rey method133 for many tetrahedral liquids.124,136 Computer simulations that followed the discovery of the liquid−liquid phase transition address the high-T, high-p structures of liquid P on both sides of the transition207−209 using also quantum simulation algorithms. These works, however, have not considered the orientational structure, even though some of the calculations were able to achieve remarkable agreement209 with the reciprocal space data of Katayama et al.169 Reverse Monte Carlo modeling has gained only marginal applications: the most recent such study by Jóvári et al.210 considered the high-pressure data of Katayama et al.169 It was demonstrated that whereas below 1 GPa diffraction data were consistent with the presence of P4 tetrahedra, this is not the case for the liquid above 1 GPa. Older data, taken under ambient conditions,29 were also modeled by reverse Monte Carlo in the early days of the method: Scheidler et al.205 showed that the center−center pair distribution function was similar to that of a one-component simple liquid. Further RMC-based investigations may therefore be expected (and desired): a large amount of diffraction data await interpretation, including details of the (temperature and pressure dependence of) orientational correlations.

4.3. X4 Types: The Structure of Liquid Phosphorus (P4)

From a structural point of view, phosphorus is a fascinating element: under ambient conditions, it has three main allotropes, the (crystalline, and extremely poisonous and flammable) white, the (amorphous and harmless) red, and the (crystalline) black version.266,267 Each allotrope has its own melting point: white P melts at 317 K, whereas the other two forms possess melting points around 900 K.266 In each phase, phosphorus atoms are bonded to three neighbors via covalent bonding; what makes the white form and its melt peculiar from the point of view of this review is that both were shown to contain P4 perfect tetrahedral molecules.168,267 Vapors from each form also contain P4 units.167 Due to the interesting phase behavior the structure of molten white P was studied already in 1938 by X-ray diffraction (along with the solid red and black forms);167 this study was the first that established that while in the liquid the presence of tetrahedral molecules is likely, in the red (and black) form(s) a “puckered network” may be formed. The next to consider the structure by (this time, neutron) diffraction experiments were Clarke et al.168 and Granada et al.:29 they conducted a series of measurements on both reactor and spallation (“Linac”) neutron sources and also ventured into the supercooled liquid and plastic phases of white P. These authors formulated the potentially outstanding importance of liquid phosphorus while studying tetrahedral liquids: “...a homonuclear tetrahedral unit such as phosphorus P4 is of considerable interest since it possesses a similar geometrical structure but avoids the complications encountered in the analysis of the multicomponent liquids...” The neutron data just mentioned happen to be the only ones regarding the normal liquid phase at ambient temperatures and pressures: the next, exciting, experiments were performed by synchrotron X-ray diffraction at high T and p.169−171,211 The apropos of this series of demanding measurements was that a first-order liquid−liquid phase transition was discovered to

4.4. Connection with the Structure of Crystalline Phases: The Case of Carbon Tetrabromide, CBr4

In previous sections we have shown the evolution of ideas concerning the structure of liquids consisting of molecules of the perfect tetrahedral shape. It is possible to extend similar studies to the gaseous and crystalline phases as well. In the gaseous phase, the structure of solitary molecules can be determined with high precision, due to the relatively long time between collision of freely translating and rotating molecules. In contrast, in the crystalline phase(s) the equilibrium positions of molecules become fixed in space, although a number of Z


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(see Figure 7). This is an interesting and infrequent combination and this is why quite a few investigations have

studies have shown that under certain thermodynamical conditions (essentially at temperatures far enough from the absolute zero), molecules are still distinguishable (see Table 4). In this section, the relation between the structures of the liquid and crystalline phases of a suitable example, CBr4, is demonstrated. Contrary to the simple description of the crystalline structure, which operates with displacive movements of independent atoms around their equilibrium positions, for molecules the moves become correlated because covalent bonds bound atoms of a given molecule together. Looking at the crystalline phases of the previously studied materials (see Table 4), we can find at least two classes of structural alignment where the observed symmetry of the crystal is incompatible with placing each atom of a molecule at their desired positions. As a result, disorder appears in these cases. In one class of disordered alignments, which is called substitutionally disordered or partially disordered by several authors, all of the atoms of a molecule occupy valid crystallographic sites, without vacancies, but in a random manner. Several phases of chlorineand bromine-containing methane derivatives belong to this class in Table 4. The next kind of disorder belongs to the category of orientational disorder, but the number of permitted orientations is restricted to only two. This appears in the hightemperature phase (P63/m) of CHBr3 and CHI3, where the axis (the CH group) of the molecule is allowed to flip up and down parallel to the direction of the crystallographic c axis.43,46 Finally, the plastic crystalline or orientationally disordered phase (also belonging to the orientational disorder category) appears, where the orientation of the molecules would be distinct (but more then two available) or random. Most frequently this appears in conjunction with high-symmetry space groups. Thus, only the center of molecules shows translation symmetry, and the rotation of the molecules may be hindered by the neighbors. Among the subjects of this review, numerous examples may be listed that show this kind of disordering: CH4,270 CBrxCl4−x,6,8,9,271,272 NH3,60,273 and neopentane.33,135 CBr4 is one of the most frequently studied cases: its plastic crystalline phase is available slightly over room temperature, it may be studied by neutron and X-ray diffraction alike, and theoretical studies are abound (see below). Although CBr4 has several crystalline phases,274 only the monoclinic and cubic (plastic) ones have been studied in detail by diffraction methods. (For the high-pressure rhombohedral phase, only one diffraction study has been reported20 that provided the lattice parameters.) The two stable (monoclinic and cubic) phases at ambient pressure were already known more than 100 years ago.275 Below 320 K CBr4 forms monoclinic (phase II, β or ordered phase) and above 320 K up to the melting point (at 365 K) cubic (phase I, α, plastic crystalline or orientationally disordered phase) crystalline phases.275 After a long quest276−278 the correct crystal structures have been determined by More et al.21,279 in 1977. Powers and Rudman made some improvement by supposing rigid tetrahedral molecules in the monoclinic phase.280 The monoclinic form has a symmetry of C2/c; the unit cell contains 32 molecules, whose atomic equilibrium positions are distinct.21 The connection with the cubic phase could also be spotted, as the so-called asymmetric unit, containing 4 molecules, can be taken as a pseudocubic cell. Focusing on the disordered phase, diffraction studies have found an interesting situation: the diffraction pattern shows few Bragg peaks as well as a significant amount of diffuse scattering

Figure 7. Measured differential cross sections159 from neutron diffraction (left) and simulated Br−Br partial radial distribution functions (left, inset) of liquid (blue solid line) and plastic (red solid line) and ordered (dark green solid line) crystalline phases of CBr4. Orientational correlation functions, as calculated by the method of Rey133 (right) in the liquid160 (solid lines) and plastic crystalline159 (dashed lines) states. Color coding to Rey groups: black (1:1); red (1:2); dark green (2:2); turquoise (1:3); dark blue (2:3); magenta (3:3).

been devoted to the plastic phase of carbon tetrabromide.157,159,256,257,281−286 As mentioned above, More et al.21 were the first to determine its symmetry as face-centered cubic (Fm3̅m), with the carbon atoms occupying the lattice points. Unfortunately, the questions related to the subject of this review, such as how molecules are oriented relative to the crystalline lattice and how are they oriented relative to each other, have not been considered very deeply. Early diffraction studies related to our subject, explaining the results by taking into account the rotation probability of molecules,157,279,281 showed that the most probable orientations are 45° around the crystal axes (direction [110]). However, thermal displacements as large as 30° were found.281 Later, coupled rotation and translation effects were also investigated,287 revealing anharmonic librations of the molecule. The first studies that focused on the diffuse scattering were executed by Powell and Dolling,157,281 who performed total scattering neutron powder dif f raction measurements on the plastic and the liquid phases. They modeled the scattering pattern by rigid, free rotating, noninteracting molecules (the liquid single-molecule scattering analogue model of the plastic crystal) and found good agreement beyond 4 Å−1 and a similarity to the liquid phase. A single-crystal measurement282 revealed cigar-shaped intensity contours, which could not be explained by independently rotating molecules. Coulon and Descamps283 published the first statistical mechanical model consisting of 6 possible molecular orientations to describe the observed diffuse scattering. Their model took into account orientational disorder and steric hindrance between neighboring molecules, which successfully reproduced both the cigar-shaped contours observed earlier282 and (at least, qualitatively) the diffuse part of the powder pattern.157 As this study was focused on the explanation of the scattering phenomenon, no attempt has been made to describe AA


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Table 11. Experimental Studies on Liquids Consisting of Molecules with C3v Symmetry system

first author, year

ref

diffraction method

Qmax (Å−1)

CHCl3

Orton, 1977 Bertagnolli, 1978 Bertagnolli, 1978 Bertagnolli, 1978 Bertagnolli, 1980 Bertagnolli, 1984 Pothoczki, 2010

217 290 291 292 293 294 126

Shepard, 2015

295

Jóvári, 2002 Pothoczki, 2010

296 126

CHF3

Hall, 1991 Mort, 1997 Neuefeind, 2000

297 298 299

CH3I

Jóvári, 2002 Pothoczki, 2007 Neuefeind, 2000 Mort, 1998 Ishii, 1998 Mort, 1998 Pothoczki, 2010 Novikov, 2002 Novikov, 2003 Gibson, 1979 Pothoczki, 2014 van Tricht, 1988 Misawa, 1990 Pothoczki, 2014 Pothoczki, 2014 Triolo, 1978

296 300 299 301 302 301 126 303 304 151 115 305 306 115 115 307

10 12 17 14 20.5 13.9;a 19.5a 18 8 20 30 8.5 18 10.5 40 40 17 17 16 16 17 30 30 30 13

Misawa, 1992 Kruh, 1964 Narten, 1968 Chieux, 1984 Damay, 1990 Bausenwein, 1994 Ricci, 1995 Wasse, 2000 Wasse, 2000 Thompson, 2003 Guthrie, 2012 Kratochwill, 1973 Bertagnolli, 1976 Bertagnolli, 1976 Bertagnolli, 1978 Radnai, 1988

308 309 310 311 312 313 314 315 316 317 273 318 319 320 321 322

X-ray X-ray neutron neutron neutron neutron X-ray neutron X-ray neutron neutron X-ray neutron neutron neutron X-ray neutron neutron X-ray X-ray neutron neutron neutron neutron neutron neutron neutron X-ray neutron neutron X-ray X-ray X-ray neutron neutron X-ray X-ray neutron neutron neutron neutron neutron neutron neutron neutron X-ray neutron neutron X-ray X-ray

CHBr3

CH3F CClF3 CBrF3 CBrCl3 POCl3 VOCl3 PCl3 PBr3 PI3 SbCl3

NH3

CH3CN

a

bond lengths (Å) CCl: 1.767; ClCl: 2.9 CCl:1.766(4); CH:1.163(204) CCl: 1.764(3); CH: 1.096(9) CCl: 1.764(3)b; CH: 1.100(4)b CCl: 1.748(4) CCl: 1.76(6); CH: 1.10(6)

remarks

CDCl3 isotopic substitution: 35Cl, 37Cl polarization analysis isotopic substitution: H/D

CCl: 1.758; CH: 1.085

CBr: 1.93(10); CH: 1.065(105) CH: 1.11(2); CF: 1.32(1) CH: 1.073(2)c; CF: 1.3324(9)c CH: 1.088; CF: 1.327

CI: 2.13(6); CH: 1.08(6) CF: 1.416 CF: 1.328; CCl: 1.773 CF: 1.34; CCl: 1.76 CF: 1.328; CBr: 1.904 CCl: 1.76; CBr: 1.949

18 15;a 20b 16 12 20 16 15 16 12.8 20 9 16 24 23 14.5 30 15 24 20 12 14.5 16.8 16.8 10 15

PO: 1.44; PCl: 2.0 ClCl: 3.568(16),a 3.548(35)b PCl: 2.04; ClCl: 3.12 PBr: 2.248; BrBr: 3.469 PBr: 2.24; BrBr: 3.44 PBr: 2.22; BrBr: 3.43 PI: 2.55; II: 3.85 SbCl: 2.347; ClCl: 3.49

153 K D: 153 K, 250 K; H: 153 K

wide and small angle, supercritical

+inelastic neutron scattering +inelastic neutron scattering

SbCl: 2.35; ClCl: 3.48

ND: 1.010(4) ND: 1.0255(15); DD: 1.622(4) ND: 1.026(2); DD: 1.649(4) ND: 0.99(2); DD: 1.55(2) NH: 1.03(1); HH: 1.64(2) ND: 0.99; DD: 1.7 CMeC: 1.456; CN: 1.153 CMeC: 1.46; CN: 1.17; CH: 2.09 CMeC: 1.46;b CN: 1.15;b CH: 2.11 CMeC: 1.48; CN: 1.15; CH: 2.12 CMeC: 1.47; CN: 1.15; CH:2.08

199 K; 228 K; 277 K 277 K; with water mixture deuterized sample ND3 449 K; 0.318−0.7 g/cm3 213 K, 0.121 MPa; 273 K, 0.483 MPa 235 K; isotopic substitution: 15N, D 230 K; isotopic substitution: 15N, D 230 K 0 GPa, 1 GPa D D, 15N

With 0.7 Å neutrons. bWith 0.5 Å neutrons. cAt 250 K.

atoms).256,257 Besides the reproduction of experimental results and dynamical properties, the PRDFs for the first shell were provided. They concluded that short-range orientational correlations would be the reason for the similar diffuse scattering pattern of the liquid and plastic crystalline phases. By examining the structure of the liquid, Bakó et al.158 also suggested the similarity of orientational correlations in the plastic crystalline and liquid phases. In the meantime, a reliable

the relative orientations of molecules, except that the steric hindrance situation is handicapped energetically. In the early 1980s several experimental studies282,284,285 were performed to reveal dynamic properties: characteristic times for self-rotation and correlations with neighboring molecules have been obtained. Following this boom of experimental efforts, molecular dynamics simulation studies were reported (with 4096 molecules using pair potentials between bromine AB


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Table 12. Simulation Studies of Liquids with Molecules of Symmetry C3va system

first author, year

ref

remarks

CHCl3

Hsu, 1979 Bertagnolli, 1981 Zeidler, 1982 Evans, 1982 Evans, 1983 Bertagnolli, 1984 Dietz, 1984 Dietz, 1985 Böhm, 1985 Kovacs, 1990 Tironi, 1994 Bertagnolli, 1995 Barlette, 1997 Fries, 1997 Chang, 1997 Richardi, 1998 Fox, 1998 Idrissi, 2003 Torii, 2005 Martin, 2006 Lamoureux, 2009 Pothoczki, 2011 Yin, 2013 Caballero, 2013 Agarwal, 1983 Jóvári, 2002 Ramesh, 2006 Pothoczki, 2010 Pothoczki, 2011 Mort, 1997 Hloucha, 1998 Neuefeind, 2000 Neuefeind, 2000 Chung, 2011 Evans, 1983 Freitas, 1995 Jóvári, 2002 Pothoczki, 2007 Rothschild, 2007 Pothoczki, 2011 Neuefeind, 2000 Mort, 1998 Mort, 1998 Pothoczki, 2012 Caballero, 2012 Pothoczki, 2014 van Tricht, 1988 Misawa, 1990 Gabrys, 2007 Pothoczki, 2014 Pothoczki, 2014 Johnson, 1978

323 324 173 325 326 294 327 328 329 330 331 332 333 334 335 336 246 337 338 339 340 128 341 342 343 296 344 126 128 298 345 299 346 347 348 349 296 300 350 128 299 301 301 351 271 115 305 306 352 115 115 353

RISM calculation of the expansion coefficient of the generalized RDF review on molecular liquids MD review RDF calculation MD MD MD MD MD RMC MC interaction model MD MC, MOZ, SSOZ MD MD MD, MC, ab initio ASEP/MD atomic simulation RMC ab initio-based potential, classical MD MD, nuclear quadrupolar resonance experiment far-IR, MD RMC MD, ab initio (dimer calculation), vibrational relaxation RMC RMC MD MC MC EPSR(EPMC), RMC MD MD MC RMC RMC MD simulation on pressurized liquid RMC MC MD MD MD, RMC MD MD, RMC RISM calculation of orientational correlations RMC MD, RMC MD, RMC RISM

CHBr3

CHF3

CH3I

CH3F CBrF3 CClF3 CBrCl3 PCl3 PBr3

PI3 SbCl3 a

comparison with diffraction data of first author,ref year Bertagnolli,291 1978 Bertagnolli,290−293 1978 and 1980 Bertagnolli,290−293,324 1978, 1980, and 1981 Bertagnolli,290−292 1978 Bertagnolli,291−293 1978 and 1980 Bertagnolli,291−293,324 1978, 1980, and 1981 Bertagnolli,290−293,324 1978, 1980, and 1981 Bertagnolli,291−293 1978 and 1980

Bertagnolli,290,291,293,294 1978, 1980, and 1984

Bertagnolli,292 1978

Bertagnolli,332 1995

Pothoczki,126 2010 Pothoczki,126 2010

Jóvári,296 2002 Pothoczki,126 2010 Pothoczki,126 2010 Mort,298 1997 Neuefeind,299 2000 Neuefeind,299 2000 Mort,298 1997

Jóvári,296 2002 Jóvári,296 2002; Pothoczki,300 2007 Jóvári,296 2002; Pothoczki,300 2007 Neuefeind,299 2000 Mort,301 1998 Mort,301 1998 Pothoczki,351 2012 Pothoczki,351 2012 Pothoczki,115 2014 van Tricht,305 1988 Misawa,306 1990 Misawa,306 1990 Pothoczki,115 2014; Misawa,306 1990 Pothoczki,115 2014 Triolo,307 1978

RISM: restricted interaction site model228 integral equation based theory. Table continues as Table 13.

contours reported earlier282).286 To explain the results, a Monte Carlo analogue of the earlier work of Coulon and Descamps283 has been performed: the centers of mass of the molecules were allowed to move freely, and molecules could be oriented via 6 different ways; sterically incompatible orientations between neighbors have been excluded. This model proved that

interatomic potential has been developed for the ordered phase,258 showing the validity of the rigid molecule model there. At the end of the 2000s, a new synchrotron X-ray diffraction measurement was performed on single-crystal samples, including the plastic crystalline phase, which revealed a series of transverse polarized regions (same as the cigar-shaped AC


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Table 13. Simulation Studies of Liquids with Molecules of Symmetry C3va system NH3

CH3CN

a

first author, year

ref

remarks

McDonald, 1976 Narten, 1977 McDonald, 1978 Klein, 1979 Jörgensen, 1980 Klein, 1981 Hinchliffe, 1981 Kincaid, 1982 Impey, 1984 Mansour, 1987 Ferrario, 1990 Gao, 1993 Bausenwein, 1944 Sarkar, 1997 Kristóf, 1999 Diraison, 1999 Hannongbua, 2000 Liu, 2001 Honda, 2002 Boese, 2003 Tongraar, 2006 Skarmoutsos, 2009 Tassaing, 2010 Vyalov, 2010 Idrissi, 2011 Vyalov, 2011 Bertagnolli, 1978 Kratochwill, 1978 Hsu, 1978 Steinhauser, 1981 Evans, 1983 La Manna, 1983 Böhm, 1983 Böhm, 1984 Fraser, 1987 Jörgensen, 1988 Kovacs, 1990 Radnai, 1994 La Manna, 1992 Radnai, 1996 Terzis, 1996 Richardi, 1997 Fries, 1997 Grabuelda, 2000 Guardia, 2001 Gee, 2006

253 354 355 356 357 358 359 360 361 362 363 364 313 365 366 367 368 369 370 371 372 373 374 375 376 377 321 378 379 380 381 382 383 384 385 386 330 387 388 389 390 391 334 392 393 394

MD calculation of molecular correlation function quantum chemical calculation MC, potential development MC, potential development MD MD, quantum mechanical calculations MC MD MD MC, interatomic potential model MC, interatomic potential model site−site Ornstein−Zernike, RISM, RMC modeling as heptamer cluster MC ab initio calculation, classical and path integral MD MC (277 K, 1 atm) ab initio MD (260 K) MC ab initio MD (Car−Parrinello) quantum mechanics/molecular mechanics (QM/MM) MD IR, MD MD, MC MD (Voronoi polyhedra analysis) MD (mostly dynamics) NMR RISM statistical theory MD, spectroscopy methods, review ab initio (quantum chemistry) MD potentials for methyl derivatives RISM MC MD RMC MC RMC MC (spatial distribution functions) MC, theory interaction model interaction model MD MD MD

comparison with diffraction data of first author,ref year Narten,310 1968 Narten,354 1977

Narten,354 1977 Narten,354 1977 Narten,354 1977

Bausenwein,313 1994 Narten,310,354 1968 and 1977 Ricci,314 1995 Narten,354 1977 Ricci,314 1995 Narten,354 1977 Ricci,314 1995 Ricci,314 1995 Ricci,314 1995 Narten,354 1977; Ricci,314 1995

Bertagnolli,319,320 1976 Kratochwill,318 1973 Bertagnolli,319−321 1976 and 1978

Bertagnolli,319−321 1976 and 1978

Radnai,322 1988 Radnai,322,387 1988 and 1994

Table 12 continued.

orientational correlations are responsible for the peculiar singlecrystal patterns. The last reported work on this subject was performed by Temleitner and Pusztai159 using total scattering neutron powder diffraction data sets on the liquid and on both of the crystalline phases (monoclinic ordered and cubic plastic). Interpretation of the measured diffraction patterns was made by the reverse Monte Carlo method110 (RMC++111 for the liquid and RMCPOW288 for the crystalline phases), applying flexible molecules. This way all kinds of atomic and molecular moves were included, some of which had been neglected by earlier modeling techniques of the static structure. Excellent agree-

ment with experimental data has been obtained for each phase. Comparing the new results to those of earlier studies on the disordered phase, the previously observed streak system286 was qualitatively reproduced, although the distribution of bromine atoms was close to random in the coordinate system of the lattice. For the ordered phase distinct equilibrium positions but significant thermal displacements were found, explaining the disordered character noticed earlier for this phase.289 Turning to the real space behavior, the most striking point was that “...positional correlations are nearly identical in the plastic crystalline and the liquid phases...” in terms of the bromine− bromine PRDF (Figure 7). This way the steric effects have AD


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Review

5.1. Five-Atom Molecules with C3v Symmetry: Chloroform, Methyl Iodide, and Their Derivatives

been identified as the main reason for orientational correlations. Analyses of orientational correlations were performed via applying the method of Rey,133 and a similar result has been found for the liquid and plastic crystalline phases (see Figure 7). This is in accordance with molecular dynamics simulations of Rey.136 Finally, the order−disorder transition was examined between the two crystalline phases and found the transitions of 2:1, 3:1, and 3:2 kinds of correlations (from the ordered phase) to 2:2 kinds (to the disordered phase) at short distances. The similarity of ligand−ligand PRDFs of liquid and plastic crystalline phase is not a unique characteristic of CBr4: similar findings have also been reported for CH4,270 CCl4,6 and CBr2Cl2272 as well. Although ligand−ligand PRDFs were not reported, molecular dynamics simulation for CBrCl3271 and for neopentane135 also provided almost identical orientational correlations for the two phases, based on the method of Rey.133

Experimental and computer simulation investigations for these systems are summarized in Tables 11 and 12, respectively. Chloroform, CHCl3, is the prototype liquid of this group, for which the volume of available literature easily exceeds (by far) that concerning all other relevant compounds added together. It is therefore practical to consider chloroform separately in a similar manner to the handling of carbon tetrachloride previously. 5.1.1. Liquid Chloroform. Chloroform, whose molecules may be formed by replacing one chlorine atom of a CCl4 molecule by a hydrogen atom, is one of the most common solvents in the practice of organic chemistry, as well as in the chemical industry (for a schematic drawing of the molecule, see Figure 8). It used to be widely applied as an anesthetic (perhaps

5. LIQUIDS OF NEARLY TETRAHEDRAL MOLECULES The molecules of such materials may be derived from the corresponding perfect tetrahedral compounds by replacing one (or more) ligand atom(s) by a different type of atom. The geometry becomes “distorted” (i.e., of lower symmetry than the Td symmetry of the generic molecule) due to (sometimes even just slight) size differences: one (or more) bonding distance(s) change(s), and as a result, bond angles drift away from the perfect tetrahedral values (of 109.5°). For defining the geometry of such molecules, it is no more sufficient to provide just the center−ligand bonding distance: most frequently one needs at least two bonding distances plus two bond angles for a unique description of the molecular shape. For the molecules to be discussed below (as well as for those already mentioned above), Table 4 provides these pieces of information (for known crystalline states of the material in question). With the deterioration of molecular symmetry, defining unique axes of (nearly) tetrahedral molecules becomes possible, and therefore, less sophisticated ways of characterizing correlations between molecular orientations may be applicable. Most molecules in this family possess dipole moments, and the primary molecular axis is most frequently identical to the orientation of the dipole, so that distance-dependent dipole− dipole correlation functions (see, e.g., ref 129 section 3.3) are relevant tools for characterizing the structure. As mentioned in the introductory sections, the Rey construction133 needed to be extended for near-tetrahedral molecules (see refs 127−129): due to the fact that the four “corners” of the tetrahedral molecules are now occupied by nonidentical atoms, the 6 original groups may be divided into subgroups that also account for the different types of ligand atoms. For instance, if one of the four corner atoms is different from the others (generic formula XYZ3 or YZ3, see below) then within the 3:3 Rey group the following three subgroups appear: (Y,Z,Z-Y,Z,Z), (Y,Z,Z-Z,Z,Z), and (Z,Z,Z-Z,Z,Z). For such types of molecules, instead of the 6 original Rey groups, 21 subgroups appear,128,129 whereas for XY2Z2-type molecules, the number of subgroups is 28.127,129 In what follows, the various distortions are categorized into two main groups, resulting in molecules with C3v and C2v symmetries. As we will see, some of the systems mentioned (ammonia, NH3, and acetonitrile, CH3CN) represent transitions between the prime targets of this review and other, somewhat related, groups of materials (H-bonded liquids and liquids of linear molecules, respectively).

Figure 8. Normalized total scattering structure factors from neutron (deuterated forms, left) and X-ray (middle) diffraction on liquid CHCl3 (top) and CH3I (bottom). Red (neutron) and blue (X-ray) solid lines represent the experimental data,126,300 whereas black solid lines denote corresponding curves for the hard-sphere reference model. Results126,128 of the Rey analyses (right) and schematic drawings of the molecule (right, inset) are also shown. Color coding to the Rey groups (different kinds of ligands are not distinguished): black (1:1); red (1:2); dark green (2:2); turquoise (1:3); dark blue (2:3); magenta (3:3).

this is why the general public is well aware of the existence of this material: in many classic detective stories, chloroform has been used for narcotizing victims). Although ample experimental and computer simulation data are available, there still is disagreement (albeit not as sharp as for the case of carbon tetrachloride) concerning their interpretation. The basic question is whether the appealing quasi-Apollo arrangement (for an elaborate display, see ref 295), where the H atom of a molecule is locked in (or at least, turned toward) the hollow formed by the three Cl atoms of a close neighbor, may or may not be a decisive factor in describing the atomic structure. Below we review relevant publications while keeping an eye on of this issue. 5.1.1.1. Diffraction Experiments. Orton et al.217 were the first to apply X-ray diffraction for the study of liquid CHCl3; interestingly, the motivation they stated was simply that there had not been such data available for this particular liquid, in contrast with others (in particular, with CCl4). This early work did not get further than subtracting the intramolecular contributions and showing the intermolecular part. Within 1 AE


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the liquid structure. In response to this claim, Bertagnolli395 calculated his composite RDFs (the ones that were available then293,324) from the simulated PRDFs and refuted the claim, stating that “...the model for chloroform as proposed by Evans does not satisfactorily reproduce our experimental neutron scattering data...” (corroborated also by Evans in a minireview326). Following these premature simulation attempts, Dietz et al.327 used MD simulation with a newly parametrized 5-site potential and provided comparison with the intermolecular parts of the measured structure factors of Bertagnolli et al. Good agreement was reported, apart from the sample that was isotopically enriched in 37Cl;292 Dietz therefore argued that there may have been systematic errors in evaluating the PRDFs from the scattering experiments (as published in ref 294). (Note that this was (one of) the very first instances where the validity of an experiment was questioned on the basis of computer simulations; also, the importance of comparing model structures to reciprocal space information was demonstrated again.) A year later the same authors328 published detailed analyses of the molecular orientations, based on MD data; unfortunately, the only strong statement was that “...simulations suggest that chloroform is a much less structured liquid than was claimed previously from neutron scattering results...” Still in the mid-1980s, Böhm et al.329,384,396 proposed new sets of interaction potentials (“...in part from ab initio data...”) for a group of methyl derivatives, including chloroform. Their molecular dynamics calculations were shown to be reasonably consistent with neutron and X-ray diffraction results on the intermolecular structure (in the reciprocal space), except, again, with neutron data obtained for the specimen enriched in 37Cl. In the 1990s, Kovacs et al.330 opened the flow of computer simulations with MD using potentials of Dietz327 with modified partial charges. Tironi et al. 331 conducted a detailed comparative study with three sets of potential functions;327,330,397 the ones of Dietz et al.327 were found to provide the best agreement with a number of properties (including, e.g., self-diffusion coefficient and shear viscosity). This very detailed (in parts, even technical) investigation even made an important statement concerning the orientations of molecules: “For closely approaching molecules the most favorable configuration will correspond to an antiparallel orientation of the dipoles”, that is, the quasi-Apollo arrangement was found unfavorable again. Still during the mid-1990s, Bertagnolli et al.332 revisited their old subject and performed a reverse Monte Carlo study of liquid chloroform, based on their composite RDFs (excluding intramolecular contributions). They found, first, that agreement with data from samples that had been isotopically enriched by 35 Cl and 37Cl was poor; although such frank statements are very welcome, it should be noted that since the modeling was not conducted on the original experimental data (the TSSFs), there is a possibility that the problems with these functions entered at some point of the data evaluation stage. Detailed analyses of orientations were also presented: the conjecture was that “...for very small C−C distances the vectors of the dipole momentums have an orientation between an antiparallel or orthogonal configuration...” Among the possible antiparallel arrangements, the ones belonging to the 3:3 Rey group were emphasized: the (Cl,Cl,Cl−Cl,Cl,Cl) and (Cl,Cl,H−Cl,Cl,H) subgroups (cf. ref 128).

year, the extensive work of Bertagnolli et al. started with another X-ray diffraction290 and two neutron diffraction experiments; the latter used CDCl3 with natural291 as well as isotopically enriched292 chlorine. A neutron diffraction measurement on the hydrogenated compound followed within 2 years,293 and immediately after this set of data has been gathered, Bertagnolli et al. were the first to attempt and derive some of the partial structure factors324 (namely, the C−C and Cl−Cl ones). In 1984, the same group completed their series of neutron diffraction experiments by determining the TSSF of the zero-hydrogen sample, in which H (which has a negative scattering length for neutrons) and D were mixed so that their coherent contributions cancel each other.294 In the same work, all 6 partial structures were calculated (via the traditional matrix inversion method) and presented; the authors, very honestly, wished to demonstrate the uncertainties of the so-derived partials and even noted that “...the precision of the H−H and C−H correlation functions is not very good...” It is worth noting that due to the relentless efforts of this group, liquid chloroform is one of the very few 3-component materials for which 6 independent total scattering structure factors have been measured, thus enabling the simple computation of all six partial structure factors/radial distribution functions. Furthermore, in the same work, possible orientations of neighboring molecules were also considered using a primitive approach that took the shortest intermolecular site−site distances into account. Again, possible problems and ambiguities were discussed at length in the paper,294 and eventually, the following conjectures appeared: “...a configuration with hydrogen pointing into the hollow formed by three chlorine atoms must be excluded. One must prefer a configuration in which the dipole axes of the molecules are inclined by 45° and shifted so that the hydrogen atom is directed toward the hollow between two chlorine atoms...” The series of diffraction experiments mentioned above have not been repeated for the next 25 years until Pothoczki et al.126 measured the TSSF of liquid CDCl3 by neutron and (synchrotron) X-ray diffraction. These experiments were parts of an extensive computer modeling study of liquid haloforms,126,128 and indirect interpretation of the data was attempted. Very recently, in 2015, yet another set of diffraction data appeared295 consisting of a (laboratory-based) X-ray TSSF and three neutron TSSFs (from a spallation source) that applied H/D isotopic substitution (D contents = 0%, 50%, and 100%); all these have been modeled using the empirical potential structure refinement (EPSR) method,120,121 so again, no direct interpretation was presented. 5.1.1.2. Computer Simulations (and Integral Equation Theoretical Calculations). The first nonexperimental study was that of Hsu et al.,323 almost immediately following the first neutron diffraction experiments, who applied the RISM formalism228,261 of integral equation theories and calculated the neutron-weighted TSSF. The comparison with neutron data of Bertagnolli291 appeared to be rather favorable (nearly quantitative agreement). Since no electrostatic interactions were taken into account during the calculations, it could be concluded that “...to a good approximation the local structure of liquid chloroform is determined by packing or steric effects...” Evans,325 in 1982, applied a 5-site potential function including partial charges and determined the PRDFs and some dynamical properties via molecular dynamics simulations; based on satisfactory agreement with the latter, it was proposed that these calculations may be exploited for a detailed description of AF


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reverse Monte Carlo calculations, augmented by hard-sphere reference structures; the particle configurations were later analyzed by using the original and modified Rey method.128,129,133 The reproduction of experimental data was perfect when using RMC modeling, whereas the hard-sphere reference structure was not able to capture major features of the reciprocal space information (see Figure 8). The PRDFs calculated from the RMC particle configurations were found to be in reasonable agreement with MD results327,329,338 and with the early RMC results of Bertagnolli.332 Some results from the Rey analyses are provided in Figure 8; they show that face-toface arrangements are the most important at the contact distance between neighboring molecules and that the quasiApollo arrangements (Rey group: 1:3) cannot be dominant. Dipole−dipole correlation maps (Figure 10 of ref 128) reveal that antiparallel mutual orientations are clearly dominant. Shephard et al.295 in 2015 published their interpretation of new X-ray and neutron diffraction data, taken at 2 temperatures. The EPSR method120,121 was applied for modeling the TSSFs. They introduced an ad hoc definition of polar stacks in which the quasi-Apollo arrangement is realized. The claim is that at room temperature 29% of the molecules participate in such stacks, leading to the appearance of super dipoles in the system. This is an exciting proposition, albeit not without some suspicion around: (1) dielectric measurements have not been able to detect such objects; (2) it disagrees with previous conjectures, some of which had also been made so that full consistency with diffraction data was achieved. 5.1.2. Analogues: Bromoform (CHBr3), Methyl Iodide (CH3I), Phosphorus Oxychloride (POCl3), and Vanadium Oxychloride (VOCl3). 5.1.2.1. Liquid Bromoform. CHBr3 is a close relative of chloroform that is convenient to investigate, being a liquid at room temperature (of the other two haloforms, CHF3 is a gas, whereas CHI3 is solid). Its gasphase molecular structure was determined very early on, in 1937, by electron diffraction;400 microwave spectroscopy was able to provide the C−H distance 15 years later.401 Concerning the liquid, bromoform appears to be understudied by diffraction methods (which, by the way, is not true for spectroscopy, see, e.g., ref 402 and references therein): only two neutron126,296 and one (synchrotron) X-ray126 measurements have been reported. The early neutron experiment296 was just an initial attempt to determine (at least some of) the PRDFs, with moderate success, while the more recent diffraction data formed the basis of a reasonably extensive reverse Monte Carlo modeling study (see below); note that each experiment was conducted on a deuterated specimen, CDBr3. Two molecular dynamics simulations (more than 20 years apart, in 1983343 and in 2006344) have been found that concerned liquid bromoform and both targeted dynamical/spectroscopic properties primarily. As may be expected, the basic difference between the two simulations lies in the interatomic potentials they applied: the early work took most parameters from their chloroform potential326 and adjusted the partial charge for the bromine atom empirically,343 whereas the work of Ramesh et al.,344 in 2006, applied ab initio quantum mechanical parametrization. Unfortunately, only the earlier publication showed PRDFs and then noted that in the absence of experimental diffraction data to compare with they wished not to perform any further analyses of the structure. The most detailed information concerning the structure comes from the reverse Monte Carlo calculations of Pothoczki et al.126,128 The RMC models reproduced the two TSSFs (from

The same paper reported results for one particular integral equation formalism, the so-called site−site Ornstein−Zernike (SSOZ) theory;398 the very clear conclusion was that this theory “...is unable to describe the short-range structure of liquid chloroform...” Two more integral equation approaches may be mentioned from the second half of the 1990s: those of Fries et al.334 and Richardi et al.336 Interestingly, the former one found that “...in the most probable two-particle configurations, the molecules have a narrow contact with nearly parallel dipoles...”, whereas Figure 5 of the latter paper336 seems to suggest quite the opposite. Computer simulations toward the end of the second millennium tended to develop interatomic potentials more and more on the basis of quantum chemical calculations. Chang et al.335 developed a polarizable potential model which was applied for simulating the liquid−vapor interface. This philosophy was utilized by Barlette et al.333,399 and Fox et al.246 While the latter work reported thermodynamic values only, Barlette et al., in their Monte Carlo simulations, calculated the dipole−dipole correlation function and found that the parallel arrangement was most likely below 4 Å ; wrongly, they stated that this finding was consistent with the experimental theoretical results of Bertagnolli et al.294,332 Unfortunately, this ambiguity makes the whole work somewhat less reliable. Already in the 2000s, the potential of Chang et al.335 was applied in a detailed MD investigation of (static and dynamic aspects of) orientations and reorientations. Here, in accordance with results of the classic studies,331,332 antiparallel arrangements were detected for the nearest neighbors. Torii in 2005338 wished to establish the importance of various electrostatic moments, notably the quadrupolar one, by surveying systematically 6 variations of an appropriate potential model. In conjunction with parametrizing the electrostatic field surrounding a chloroform molecule, he performed quantum chemical optimization calculations for the dimers: three nearly degenerate arrangements have come up, two of which showed antiparallel mutual orientations. Martin et al.339 utilized a mixed quantum/classical mechanical (QM/MM) scheme in their simulations that provided a satisfactory agreement with earlier diffraction experiments (some results in the reciprocal space are also provided). In 2009, a new polarizable potential model was introduced by Lamoureux et al.,340 who calculated, apart from a number of energy-related characteristics, the PRDFs that were found to be consistent with literature data. In 2013, Yin et al.341 reported on a painstakingly detailed quantum chemical potential optimization procedure; the resulting interaction potentials provided a good reproduction of the experimentbased PRDFs of Pothoczki et al.128 and the temperature dependence of the self-diffusion constant. Ab initio quantum chemical calculations for the dimer were also conducted, and just to add to the confusion, the quasi-Apollo arrangement was found to be the most favored energetically (which is not really decisive with respect to the bulk liquid). Finally, the potential developed by Martin et al.339 has been used in recent MD simulations of Caballero et al.342 on liquid CHCl3, in conjunction with nuclear quadrupole resonance (NQR) experiments, for understanding rotational dynamics and orientational structure. Although no dipole−dipole correlations were shown, based on the Rey group characteristics, the face-toface (3:3; at the shortest distances) and edge-to-face (2:3) arrangements were found to be important. Pothoczki et al.126,128 not only presented two freshly measured diffraction data sets but also conducted detailed AG


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comparison with experimental findings of Mort et al.298 could be made; satisfactory agreements were found, and details of mutual orientations of the molecules have not been pursued any further. It is therefore thought to be fair to note that although the volume of experimental information seems to be appropriate, some further computer modeling would be desirable in order to reveal orientational correlations. 5.1.2.3. Liquid Iodomethane (Methyl Iodide). The structure of CH3I/CD3I molecules in the gas phase was finally determined via vibrational (IR) spectroscopy at the beginning of the 1970s.403 From our point of view, this liquid is an interesting model system, since the molecules are exactly the inverse of those of chloroform/bromoform in terms of the ratio between bulky and small ligands (3:1 in bromoform and 1:3 in iodomethane). Unfortunately, the available experimental information on the structure is rather limited: similarly to bromoform, there is a report on an early neutron diffraction experiment296 and then a combined neutron and (synchrotron) X-ray investigation300 (neutron data were taken from the deuterated sample, CD3I). Note that the contrast between Xray and neutron diffraction is spectacular: while the former is overwhelmed by the I−I correlations, the latter is dominated by H(/D)-related pairs (see Figure 1 of ref 300). Measured data (as well a schematic drawing of the molecule) are shown in Figure 8; the packing of these head-heavy molecules is depicted in Figure 5 of ref 300. Computer simulations are also quite scarce for this liquid: of the two investigations found, the early MD study of Evans et al.348 worked with a 5-site potential that contained Lennard−Jones terms and point charges; unfortunately, only dynamical properties were reported. The Monte Carlo simulations of Freitas et al.349 used a 2-site (united atoms for the methyl group) potential model, also with LJ and partial charges, and focused on thermodynamic properties; however, the three PRDFs were also shown. The radial distribution functions, particularly the C−C and I−I ones, appear to be consistent with those reported on the basis of the 2 experiments and RMC modeling.300 On the basis of the PRDFs, the authors speculated that at contact distances the antiparallel, while at somewhat farther, linear arrangements are significant. Detailed analyses of orientational correlations were provided by Pothoczki et al.;128 distance-dependent correlation functions based on Rey’s construction133 are shown in Figure 8. Edge-toface (2:3) and, to a lesser extent, face-to-face (3:3) configurations dominate at the shortest distances: the important subgroups are (H,H−I,H,H), (H,H−H,H,H), and (I,H,H,-H,H,H), that is, CH3I molecules avoid contact between their bulky parts. This also apparent when dipole−dipole-type specific orientations are considered (see Figure 8 of ref 128): of the chainlike arrangements, clearly the tail-to-tail (i.e., methylto-methyl) types are the most preferred. T-shaped pairs are also important at these short distances in which, again, the methyl groups get close to each other (T1 type, cf. Figure 3 of ref 128). Figure 9 displays snapshots of RMC particle configurations for liquid (deuterated) iodoform CD3I (particle coordinates are from Pothoczki;300 the left panel of the present figure appeared in ref 300 too, as Figure 5). Even when the size ratios of atoms and the packing fraction are set to be realistic, each atom is well visible; this is in contrast with, e.g., liquid CCl4 (see Figure 5). With a packing fraction that is decreased slightly, specific orientations become well recognizable (see the hydrogen atoms marked in red).

X-ray and neutron diffraction) perfectly, whereas the corresponding hard-sphere reference system was able to achieve a semiquantitative agreement with the X-ray data only. Some of the PRDFs (notably, C−C and Br−Br) agree quite well with those of the early MD study of Agarwal et al.343 More importantly, detailed characteristics of orientational correlations have been displayed: it was found that while an overall similarity with the structure of liquid chloroform is apparent, there are important differences too. The ratio of corner-to-face (1:3) arrangements is at least two times larger for bromoform, whereas the importance of face-to-face (3:3) configurations has decreased. The increasing presence of the quasi-Apollo (1:3) pairs is eye catching, particularly in light of the superdipole idea presented recently for liquid chloroform;295 note, however, that since most of these pairs are of the (H−H,Br,Br) type (and not of the (H−Br,Br,Br) one), the molecular dipole moments are not collinear (as they should be, according to the superdipole speculation295). 5.1.2.2. Liquid Trifluoromethane (Fluoroform, CHF3). This member of the haloform family is a gas at room temperature, so that any experiments are bound to be more difficult; still, a surprisingly good amount of diffraction data are available for the liquid/fluid phase.297−299 The reason may be that these materials are from the family of cooling fluids that have attracted concern about their role in the environment. Hall et al.297 and Mort et al.298 report on pulsed neutron measurements, whereas Neuefeind et al.299 describe reactor-based neutron and synchrotron X-ray measurements. Although the number of independent TSSFs measured was always more than one, experimental information has never been sufficient for an unambiguous separation of all six partial structure factors/radial distribution functions. The experiments therefore, very thoughtfully, have been accompanied by computer simulations/modeling. Mort et al.298 performed molecular dynamics simulations using potential functions consisting of Lennard− Jones and Coulombic parts and showed that intermolecular total composite RDFs were in good agreement with their experimental counterparts. Via a tedious shortest distance analysis between neighbor molecules the authors conjectured that a straddle arrangement, equivalent of the 2:2 Rey group (subgroup (H,F-F,F)), satisfied most of the distance-based requirements. Interestingly, a major conclusion of this study was that “...trifluoromethane does not hydrogen bond in the liquid phase...”; i.e., at the time of this investigation, this issue was considered seriously. Neuefeind et al.299,346 applied Monte Carlo as well as RMC and EPSR (called EPMC, short for empirical potential Monte Carlo, that time) modeling for interpreting their X-ray and neutron data. The orientational structure of the crystalline and liquid phases were compared; it was found that various T-shaped arrangements are common in the first coordination shells of molecules in both phases. Pure simulation studies have also been conducted: the Monte Carlo calculations of Hloucha et al.345 at the late 1990s used a 5-site representation of the molecules and successfully reproduced a number of thermodynamic and dielectric properties. The latest simulation study is that of Chung et al.347 from 2011; they first performed a very detailed quantum chemical optimization calculation series for 15 dipole arrangements and then determined classical interatomic potential parameters. Of the dimers, a 2:3-type arrangement (subgroup (F,H−F,F,H)) was found to provide the minimum energy. Molecular dynamics calculations were then conducted. The resulting PRDFs were combined into intermolecular composite RDFs, so that a AH


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shows a perfectly antiparallel face-to-face arrangement as the most probable configuration. 5.1.2.5. Oxychlorides of Phosphorus and Vanadium, POCl3 and VOCl3. These molecules are exact analogues of chloroform; the main difference is that the (noncarbon) central atom is bound to the oxygen atom by a double bond. POCl3 is liquid at room temperature; there are two reports from the beginning of the 2000s (probably of the same experiment though) on neutron scattering investigations (both diffraction and inelastic scattering).303,304 The published TSSF looks perfectly reasonable; unfortunately, apart from quoting intra- and intermolecular distances, no further analysis of the structure was conducted. Liquid VOCl3, together with VCl4, was subjected to neutron diffraction measurements (at two wavelengths) a good 20 years earlier in 1979.151 These data were treated by the most sophisticated tools of the time; molecular parameters were determined, and the intermolecular scattering parts were separated. Nevertheless, the most specific statement that could be made was that both materials “...appear to show strong orientation correlation effects in the liquid phase but further work is required...” Currently, more than 35 years later, this further work, perhaps the easiest would be RMC, would still be appreciated on the two liquid oxychlorides just mentioned.

Figure 9. Snapshots from an RMC configuration of liquid CD3I. (Left) Overview. (Right) Realization of the edge-to-face (2:3; H,H− H,H,H) mutual orientation between two molecules. Large gray balls, carbon; violet balls, iodine; small gray (and red) balls, hydrogen.

5.1.2.4. Various Halogenated Methane Derivatives with C3v Symmetry. There are quite a few such combinations, particularly if compounds with two kinds of halogen atoms are taken into account. A comprehensive, systematic study is not available; most liquids in this section have been studied only once; still, these studies should be mentioned in this review. Methyl fluoride, CH3F, was considered along with fluoroform (see above) by Neuefeind et al.299 using X-ray diffraction and Monte Carlo simulation; due to the lack of neutron data, only very vaguely determined PRDFs could be shown, and the structure of this fluid was not discussed in any detail. Liquid bromotrifluoromethane, CBrF3, and chlorotrifluoromethane, CClF3, were the subject of the combined neutron diffraction/ computer simulation study of Mort et al.;301 the MD calculations were needed since only one experiment was available for these 3-component systems. A great deal of information was found to be provided on the molecular structure: intramolecular distances could easily be identified. The simulated intermolecular RDFs agreed reasonably well with the corresponding diffraction results; as for orientational correlations, only speculations were presented, instead of proper analyses (the appropriate tools were not yet available then). The supercritical fluid phase of chlorotrifluoromethane, CClF3, was investigated by small and wide angle neutron scattering by Ishii et al.302 as a function of the density. Even though long-range density fluctuations were put into the focus of this publication, the data presented would be appropriate for further structural modeling and revealing the (short and longrange) orientational structure. Finally, recent neutron diffraction experiments, molecular dynamics simulations, and reverse Monte Carlo modeling on liquid (and plastic crystalline) bromotrichloromethane, CBrCl3, are mentioned.271,351 Both the MD and the RMC calculations reported by Pothoczki et al.351 match the measured TSSF perfectly, and the RDFs resulting from the two MD simulations are also in good agreement, that is, the actual structures provided by these two publications are identical. Both works concern orientational correlations in detail but in a different manner, and therefore, the interpretation looks somewhat different. A key statement may be mentioned from the work of Caballero et al.:271 “...these findings do not contradict the analysis based on a bivariate angular distribution used...” by Pothoczki et al.351 For an easily understandable demonstration of the short-range orientational relations, one may look at Figure 8a of the latter paper, which

5.2. Four-Atom Molecules with C3v Symmetry: Phosphorus Halogenides and Ammonia

Molecules in this group may be imagined as if a lone electron pair of the central atom would play the role of the marked ligand of the previous section. Due to the repulsive effect of the lone pair, according to the well-known VSEPR principle,404 the three real ligands move out-of-plane, thus forming the basal plane of a rather deformed tetrahedron whose top corner is occupied by the central atom. Perhaps the best-known such molecule is ammonia, NH3, that, for various reasons, will be considered separately later in this section; similar molecules, whose central atoms are usually from the nitrogen group of the periodic table, are discussed immediately. A summary of experimental and computer simulation investigations for the 4-atom tetrahedral liquids can also be found in Tables 11 and 12, respectively. 5.2.1. Liquid PBr3 and Related Materials. 5.2.1.1. Liquid PBr3. Phosphorus tribromide is a (not too dangerous, in contrast with the trichloride) liquid under ambient conditions, and perhaps this is the reason why several diffraction measurements could be performed conveniently on this system that has become a prototype of tetrahedral XY3 materials. Starting from the late 1980s, two neutron305,306 and one synchrotron X-ray115 diffraction experiments have been carried out. Van Tricht et al.305 determined the neutron-weighted TSSF up to about 13 Å−1 using monochromatic neutrons from a reactor source. Apart from determining the structural parameters for the PBr3 molecule (which were found to be in agreement with electron diffraction results405), the intermolecular contribution was compared to that of liquid antimony trichloride, SbCl3.307 Although atomic size ratios of the constituents are quite different in the two molecules, due to the similarity of the (neutron) weights of the partial structure factors (see Table 2 of ref 305), the rather featureless intermolecular structure factors were found to be similar. The other known neutron diffraction investigation is that of Misawa,306 who measured the TSSF up to 20 Å−1 using timeof-flight detection of neutrons from a spallation source (for AI


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dipole correlation map it is clear that at the shortest center− center distances, just above 4 Å, the antiparallel arrangement dominates. Making now the connection with Rey groups (see the corresponding arrows in Figure 10 that point to the appropriate distance ranges), the antiparallel molecular pairs are of the 3:3 (subgroup (Br,Br,P−Br,Br,P)) and 2:3 (subgroup (Br,P−Br,Br,P)) types. The other sharp maximum of the dipole−dipole map is found at a distance of about 5 Å, where the corresponding orientation is the parallel one. These molecular pairs take the arrangements of the 1:3 (subgroup P−Br,Br,Br) and 2:3 (subgroup P,Br−Br,Br,Br) types. The arrangements make the parallel orientation found in this computer modeling study vaguely resemble that proposed by Misawa,306 which latter appears to be a highly idealized and simplified representation. 5.2.1.2. Liquid PCl3 and PI3. X-ray diffraction results on these two liquids were also reported by Pothoczki et al.115 (to our knowledge, these are the only available diffraction data on these liquids), as parts of the extensive structure study mentioned above. Again, molecular dynamics (with the same family of interatomic potentials) and hard-sphere Monte Carlo simulations have been conducted, followed by RMC calculations. Interestingly, MD was able to achieve quantitative agreement with data on the chloride, and moreover, the adequacy of even the hard-sphere model may be argued (see Figure 1 of ref 115). For the iodide, which had to be heated up to about 350 K for reaching the liquid phase, the situation is not as idyllic: MD provides the worst (but still, at least, semiquantitative) prediction among the phosphorus halides, whereas the hard-sphere reference model is inadequate. RMC refinement of the MD particle configurations was able to easily achieve full consistency with experiment. Dipole−dipole correlation functions revealed that these two liquids are more disordered, even in the first coordination shell, than PBr3: only one clear maximum could be detected at the contact distance (of about 4 and 4.5 Å in PCl3 and PI3, respectively) that corresponds to the antiparallel arrangement (see Figure 5 of ref 115) (and even these maxima are weaker than they were for liquid PBr3). Molecular pairs with more or less antiparallel mutual orientations belong to groups 2:3 (subgroup P,Cl/I−P,Cl/I,Cl/I), 2:2 (subgroup P,Cl/I−P,Cl/I), and 1:2 (subgroup P−P,Cl/I). As it was stated by the authors, there are only subtle differences between the two liquids, which may be explained simply by the size difference between the molecules. In summary, arguably the structure of liquid phosphorus halides could be clarified to the desirable detail; this is particularly valid for PBr3 for which both X-ray and neutron diffraction data were reproduced by classical MD simulations. 5.2.1.3. Liquid SbCl3. This material is solid at room temperature and had to be heated to about 350 K to reach the liquid state. Interest in this material was risen by noticing that “...the physical properties of liquid SbCl3 are not unlike that of water. The liquid is sometimes described as associated...”307 The unexpectedly large dielectric constant of 33.2 (at 348 K),408 as well as the large molecular dipole moment of 3.9 D, might also have made researchers curious about this liquid. As a consequence, in 1978, Triolo and Narten published a combined X-ray and neutron diffraction study307 in order to reveal the structural properties that bring about these unusual characteristics; some parts of the interpretation were published separately.353 About a decade later, Misawa also determined the TSSF of liquid antimony trichloride by neutron

technical details of this particular setup, see ref 406). The author conducted a very detailed analysis of the measured data and provided, with some assumptions, even partial radial distribution functions that looked similar to the ones obtained by more sophisticated methods (see below). Misawa also estimated the most probable orientations of neighboring molecules using the same approach, fitting a large number of parameters, he had previously applied for liquid carbon tetrachloride:223 the resulting geometry is a parallel one, similar to that found in the crystalline phase of PI3.64 The only X-ray diffraction experiment was carried out in conjunction with an extensive computer modeling effort115 in which molecular dynamics simulation and reverse Monte Carlo modeling were both applied, and hard-sphere reference systems were also prepared by Monte Carlo simulation. It was found that both the neutron306 and the X-ray diffraction data were reproduced at a nearly quantitative level by the MD simulation that applied the OPLS all-atom force field,407 see Figure 2 of ref 115. (Note that this is not true for the hard-sphere reference system, for which significant deviations were detected from both sets of experimental data, see again Figure 2 of ref 115.) The RMC calculation that followed the MD simulation acted as a refinement to the MD configuration and was able to achieve a perfect fit to both X-ray and neutron diffraction data. For characterizing orientational correlations, a unique combination of the dipole−dipole angular correlations and the, appropriately modified, Rey construction was used, see Figure 10: this is arguably the most sophisticated approach that has been applied to any tetrahedral liquid. From the dipole−

Figure 10. Orientational correlations in liquid PBr3.115 (Top left) Dipole−dipole orientational correlation function (darker areas denote larger probabilities). (All other panels) Results from Rey analyses. Solid lines refer to the representation without distinguishing ligand types, whereas lines with symbols denote the specific subgroups (Y denotes the top of the molecules, above the P atoms, when the molecules lie on their basal planes formed by their three Br atoms). (Top right) Green solid line, 1:3; empty circles, Y−Br,Br,Y; full circles, Y−Br,Br,Br. (Bottom right) Blue solid line, 2:3; empty circles, Br,Y− Br,Br,Y; full circles, Br,Y−Br,Br,Br; stars, Br,Br−Br,Br,Y; empty squares, Br,Br−Br,Br,Br. (Bottom left) Black solid line, 1:1; red solid line, 3:3; empty circles, Br,Br,Y−Br,Br,Y; full circles, Br,Br,Y− Br,Br,Br; stars, Br,Br,Br−Br,Br,Br. AJ


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diffraction,308 extending the momentum transfer range up to 20 Å−1. Triolo et al.307,353 claim to have found “...close Sb···Cl contacts in a very well-defined distribution centered around 3.40 Å...” and suggest that “...this structure can be described in terms of chains of SbCl3 molecules stacked like umbrellas, the dipole axes of molecules within a chain being strongly correlated...”. The two preferred orientations suggested by Misawa (see Figure 10 of ref 308) are not quite consistent with this bold speculation, although the method of analysis seems to have relied too heavily on fitting arbitrarily chosen parameters of the mutual arrangement of only two molecules (cf. also the cases of liquid CCl4153,223 and PBr3306). Unfortunately, no larger scale simulation/computer modeling of the bulk liquid is available at present, that is, the field is open to significant development, hopefully leading to a satisfactory understanding of the microscopic structure. 5.2.2. Liquid/Fluid Ammonia, NH3. Ammonia is one of the most important intermediate products of the chemical industry worldwide, providing the starting point for the synthesis of countless compounds. Since the material is easily compressible, its transportation very frequently takes place in the liquid/fluid phase; perhaps this is why there has been continuous interest in the structural properties of the fluid over the past 50 years. The reasons why this material occupies a special position within this group, of the 4-atom molecules with C3v symmetry, is that (a) frequently the H atoms are not distinguished (similarly to the case of methane, CH4, see above) and the entire molecule is treated as just one site (see, e.g., ref 354) and, more importantly, (b) NH3 molecules are able to form directional bonds, the so-called hydrogen bonds409 that determine the structure of liquid water, a feature which makes liquid/fluid ammonia distinct from all other systems mentioned in this review. Much of the available literature is on this latter property, the hydrogen bonding, partly because its presence and extent in the liquid phase has been extensively discussed (see, e.g., refs 410 and 411). For instance, as pointed out by ref 356, the density of ammonia, in contrast with that of water, decreases upon melting, and therefore, the existence of an extensive hydrogen-bonded network cannot easily be envisaged, even though the boiling point (240 K) is significantly higher than those of hydrides of other Group V elements; the ammonia dimer, on the other hand, is clearly connected via a nearly linear hydrogen bond.412 Perhaps it is this duality that is the main reason why a consistent, clear picture of the microscopic structure of liquid ammonia is still missing, despite the large number of experimental and computer simulation investigations (see below). 5.2.2.1. X-ray Diffraction Experiments. As early as in 1964, X-ray diffraction experiments were carried out by Kruh et al.,309 who determined the scattered intensities from liquid samples between temperatures just above the melting point (196 K), at 199 K, up to 277 K (note that the latter value is well above the boiling point, 240 K, that is, the experiment must have been performed at an unspecified pressure that was higher than the atmospheric value). They found a hydrogen-bonding molecular distance of about 3.6 Å as well as signatures of non-hydrogenbonded nitrogen neighbors at about 4.1 Å. The authors were also able to find some correspondence between the radial distribution functions of the liquid and the crystalline phases, although of the 11 neighbors detected they found 7 hydrogen bonded, which is clearly a nonsensical result for molecules that can only form 4 regular hydrogen bonds (1 donor, 3 acceptor).

A few years later, in 1968, another laboratory X-ray diffraction study appeared by Narten310 (whose main focus was water− ammonia systems this time). Retrospectively, most of the criticism formulated against the earlier study309 was a little unfair, but the author had major points captured: (1) the first neighbor distance had to be corrected to 3.44 Å ; (2) the crystal-like model cannot account for the experimental RDF; (3) the number of hydrogen-bonded neighbors cannot be 7. Narten (nearly 10 years!) later reanalyzed the same data set so that only center−center (i.e., N−N) correlations were taken into account. 354 No major change in terms of data interpretation was reported, and the conclusion concerning the first neighborhood of nitrogen atoms was drawn as “...some of the 12 neighboring molecules are in van der Waals contact, some are hydrogen bonded...” Apparently, no further X-ray diffraction measurements have been reported. 5.2.2.2. Neutron Diffraction Experiments. The importance of neutron diffraction was recognized early on; still, the first such experiment was performed only in 1984 (20 years after the first X-ray diffraction measurement) by Chieux and Bertagnolli311 using the fully deuterated compound (ND3). As it became clear already in this first report, neutron data are dominated by N−H(D) and particularly by H(D)−H(D) correlations (for ND3, these two contributions amount to about 90% of the signal); for this reason, it is the molecular structure that is visible most clearly. The same group has followed on with their efforts, and within about 10 years, total scattering structure factors of fluid heavy ammonia, ND3, have been determined, extending well into the supercritical region.313,413,414 In 1990, Chieux and co-workers started comparative neutron diffraction investigations of the solid and liquid phases.312 High-pressure experiments on pure fluid ND3 have recently been extended to the purely supercritical region by Guthrie et al.273 Isotopic substitution was first used by Ricci et al.,314 who determined the total structure factor of pure ND3, pure NH3, and a 50− 50% mixture of the two. From this information, it was possible to derive partial radial distribution functions: unfortunately, a serious contradiction with earlier X-ray data,310,354 in terms of the N−N PRDF, was revealed. Ricci et al. argued that the clear maxima found by X-ray diffraction at 3.7 and 4.6 Å were artifacts of the Fourier transformation and that real maxima could be found at 3.4 and 7 Å. Instead, they went on, hydrogen bonding may be detected on the N−H PRDF: a shoulder at around 2.4 Å was thought to be a clear manifestation of H bonds. A similar set of data was measured by Thompson et al. nearly a decade later,317 who confirmed the findings of Ricci et al.314 and cleaned some disturbing features (e.g., the artificial maximum of the N−H PRDF around 1.7 Å) of the earlier NDIS data (the two measurements were performed on the same instrument). During the first half of the 2000s, an exhaustive series of neutron diffraction experiments has been conducted by Wasse et al. on (alkali and alkaline earth) metal solutions in liquid ammonia.315,316,415−417 These authors also applied the technique of isotopic substitution, this time, on the nitrogen atom of ND3 molecules: they made use of the 15N isotope. Pure liquid ammonia has usually been measured, along with the metal solutions, in these experiments: findings concerning its structure seem to be in agreement with results of refs 314 and 317. 5.2.2.3. Computer Simulations. The first molecular computer simulation studies appeared in the second half of the 1970s.253,355,356 In the very first MD simulation, McDonald and Klein considered 108 ammonia molecules near the triple AK


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point at 196 K;253 they calculated (and showed only(!)) the PRDFs. The agreement with much later neutron diffraction data is remarkable: (1) there is only one single first maximum of the N−N PRDF (at around 3.4 Å), and (2) there clearly is a maximum at around 2.3 Å on the N−H PRDF, corresponding to hydrogen bonding. Considering the fact that at the time the authors had no idea about (20 years later) upcoming NDIS investigations, the success of this pioneering computer simulation study, in terms of predicting the intermolecular structure, is stunning. The immediate follow-up simulations265,356−360 have dealt with serious potential development, so that by the mid 1980s, the solid phases361 and details of the thermodynamics362 could be considered sensibly. Hydrogen bonding was scrutinized in 1993 by Gao et al.,364 both between dimers and in the bulk liquid. The following, rather plausible, conclusions were drawn for the normal liquid, close to its boiling point (at 240 K): (1) “...results indicate that each ammonia forms on average three hydrogen bonds...”; (2) “...the liquid contains winding chains of hydrogen bonded monomers...”; and (3) “roughly linear hydrogen bonds predominate in the liquid”. These findings are based on an at least semiquantitative agreement of the PRDFs with neutron diffraction results published 10 years af ter (!) this simulation study. In addition, results of detailed analyses of angular correlations within the first coordination shell were provided for two, competing, interatomic potential models.363,364 From around the millennium, although the classical approach was still present366,370 (sometimes involving clustering and three-body effects365,368), ab initio simulations started to appear. Diraison et al. in 1999367 presented a thorough comparison between classical MD, conventional ab initio MD, and path integral MD strategies for studying the structure of liquid ammonia; unfortunately, due to the methodologyoriented approach, the hydrogen-bonded bulk structure has not been analyzed in detail. Ab initio MD was 2 years later applied for studying protonic defects (created by adding and removing one proton from a system representing liquid ammonia);369 note that such investigations must go beyond the capabilities of classical interaction potentials. Agreement with PRDFs and partial structure factors from neutron diffraction314 has slightly improved, and based on this fact as a kind of reliability factor, solvation shells of proton defects have been looked at (this information is not accessible experimentally). Boese et al.371 dedicated their very detailed quantum chemistry-based work to the understanding of the hydrogen bond in ammonia dimers, clusters, and, finally, bulk liquid ammonia. Unsatisfied with earlier basis sets, the authors introduced a new density functional that was able to account for the nonlinear hydrogen bond in the dimer. A number of intriguing take-home messages were formulated: (1) “...the propensity to form a strongly bent hydrogen bond−which is characteristic for the equilibrium structure of the gas-phase ammonia dimer−is overwhelmed by steric packing effects that clearly dominate the solvation shell structure in the liquid state...”; (2) “...the propensity of ammonia molecules to form bifurcated and multifurcated hydrogen bonds in the liquid phase is found to be negligibly small...”. Finally, the following note reflects the slight controversy that is still appreciable in the field: “Thus, even functionals that lead to unreasonably linear hydrogen bonds in the limiting case of the in vacuo ammonia dimer, such as BLYP, yield a good description of liquid ammonia−albeit for the wrong reason!” Finally, mixed quantum/classical mechanical (QM/MM) schemes also have

appeared: Tongraar et al. in 2006372 introduced two such approaches for investigating liquid ammonia. They found agreement with Boese et al.371 in that the importance of steric effects was emphasized here too. Supercritical fluid ammonia was the focus of quite a few recent simulation studies.373−377 These studies all applied classical interatomic potentials; the work of Vyalov et al.375 provides a useful comparison of 6 such parameter sets at a temperature of 273 K, based on which it appears that the relatively simple forms suggested by Kristóf et al.366 work surprisingly well. 5.2.2.4. Concluding Remarks Concerning the Structure of Liquid Ammonia. Formally, there is a sufficient amount of experimental data available (particularly by neutron diffraction), and it is also fair to say that a fairly large number of computer simulations have attempted to find agreement with/predict the experimentally determined 2-body correlation functions. Again, formally, this may seem like a success story: already in the 1970s, very promising computer simulation results appeared253 that were able to explain and, moreover, predict measurable structural properties. Moreover, simulation technology has improved enormously in all respects, so that essentially all simulations mentioned above have been able to establish consistency with published experimental results on the structure. A word of warning may still be appropriate here: no X-ray diffraction data have appeared over the past nearly 40 years, which is problematic particularly for the investigation of near/supercritical fluids. Neutron diffraction results with isotopic substitution seem also to be missing at elevated pressures and temperatures (exactly where the practical/ industrial interest might expect their presence). There is still an unresolved discrepancy between X-ray and neutron diffraction concerning the N−N PRDF.314,354 Last, but not least, none of the computer simulation studies has calculated the quantity that may be measured directly, the total scattering structure factor; it is our strong belief that only such an approach would eventually be able to establish consistency between X-ray and neutron diffraction results. 5.3. Tetrahedricity vs Linearity, with C3v Symmetry: Acetonitrile, CH3CN

The acetonitrile (or methyl cyanide) molecule may be derived from the ammonia molecule by inserting two carbon atoms, in a chain geometry, between the N and the H atoms of NH3. The resulting shape, shown, e.g., in Figure 4 of ref 319, is that of an elongated (i.e., seriously deformed) tetrahedron. The N−C−C axis is linear (see, e.g., ref 418 for an experimental determination of the molecular structure), due to the effect of hyperconjugation between the π electrons of the C−N triple bond and the electron density of the three C−H bonds of the methyl group (for an appropriate organic chemistry textbook, see, e.g., ref 419). Due to the elongated (quasi-linear) geometry as well as to the large electron density of the triple bond on the nitrile end of the molecule, the dipole moment of the CH3CN molecule is rather large, abut 3.9 D in the vapor phase.420 The large dipole moment combined with the lone electron pair of the N atom at the terminal position may explain that acetonitrile is miscible with water over the entire composition region. The material is conveniently liquid under ambient conditions and is used as an effective aprotic dipolar solvent in the everyday practice of chemical syntheses. AL


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RDFs, it was possible to predict orientational correlation functions: parallel and antiparallel arrangements were found for the closest neighbors, whereas at the most probable molecular distances, a weak tendency appeared for perpendicular and skewed arrangements. The role of the (large) dipole moment was stated to be marginal in forming the overall structure of the liquid. 5.3.3. Computer Simulations. The duality mentioned in the title of this section manifests itself readily while attempting to determine the structure of the liquid by computer simulation methods: 3-site (united atom: N, C, Me (=CH 3 )) 382,386,388,390,391,393,394 as well as 6-site (all atom)381,383,392 potential functions have been developed over the three decades of research. Obviously, the simulations using 3-site potential models cannot provide information concerning the tetrahedral behavior of acetonitrile molecules: it is therefore suffice to mention here that no major discrepancies concerning structural features have been detected between any two of the publications listed above. Not surprisingly, the latest work, from 2006,394 applied the most sophisticated potential model, and therefore the claim that their model “...produces the most rounded representation of the properties of liquid acetonitrile” may be justified. Switching now to achievements of simulations with 6-site potential models, the fact that their molecules, as mentioned above, are, in fact, elongated tetrahedra has not been exploited. For instance, in the most recent MD simulation, representing significant potential development efforts, by Grabuelda et al.,392 only those PRDFs are displayed that are identical to the ones obtainable on the basis of 3-site models; it is also stated that they “were identical to those obtained and analyzed by Jorgensen et al. 386” When demonstrating orientations of neighboring molecules (Figure 2b of ref 392), hydrogen atoms are removed in order to improve visibility. The summarizing statement of their findings was that they saw “...many parallel and antiparallel alignments of neighboring dipoles and many short head-to-tail distances. To find some kind of order beyond the nearest-neighbor level was difficult and the simulation box appeared as a disordered box of molecules.” The good news is that this situation appears to be in full consistency with essentially all other simulation results (regardless of the number of interaction sites in a molecule); note, however, that absolutely no information is available on the tetrahedricity aspects. The only reverse Monte Carlo calculation on the liquid phase387,389 applied a 3-site model of the CH3CN molecule and the X-ray diffraction data of Radnai et al.322 as input. Agreement with experimental data may be termed as acceptable, in comparison with the goodness-of-fits shown in this review so far. Perfect agreement was reported with partial RDFs of the Monte Carlo simulation of Jorgensen386 that also used a 3-site representation of the molecule, that is, the PRDFs of Jorgensen386 are consistent with these X-ray data322 at the same level as those obtained by the RMC investigation in question.387 The authors provided a most detailed analyses of the orientational structure: they found general agreement with previous work. Nearest neighbors were found to occupy antiparallel positions, whereas (even shifted) parallel arrangements appeared much less important. Unfortunately, no RMC study on a 6-site model of acetonitrile is available yet, so that the tetrahedral aspect could not be considered so far; another missing point is the joint RMC modeling of X-ray and neutron data, that is, reverse Monte Carlo modeling still has future tasks to fulfill.

Experimental and computer simulation investigations for liquid acetonitrile are also listed in Tables 11 and 12, respectively. 5.3.1. Diffraction Studies. The first X-ray diffraction investigation was published in 1973,318 followed by two more measurements within the next 15 years.321,322 These works agree in terms of the intramolecular distances (see a detailed comparison in ref 322) and also in terms of the shape of the intermolecular part. Neutron diffraction investigations are even less numerous: the same group, about 40 years ago, carried out a reactor-based measurement on a sample with the natural abundance of nitrogen isotopes319 and on another specimen with isotopically enriched 15N.320 Interestingly, both of these works emphasized the determination of the intramolecular structure; this seems like an indication that the total scattering structure factor is actually dominated by intramolecular contributions (and therefore, on the basis of only one measurement, it is hard to say anything definite about the intermolecular contributions). The situation may be like this, but still, the very first (X-ray) diffraction data was interpreted by a rather complicated crystal-like structure318 (even a unit cell is mentioned, in which molecules are placed rather regularly, cf. Figure 15 of that work). One more experimental study is worth mentioning here, that of Kratochwill from 1978,378 who attempted the determination of intermolecular relaxation rates by 13C NMR of the nitrile carbon; this information, in turn, allowed the author to speculate on the relative orientation of neighboring CH3CN molecules. The author found good agreement with (their own) previous X-ray diffraction results.318 In summary, there is ample experimental information available for the liquid structure of acetonitrile, although neutron diffraction with H/D isotopic substitution and synchrotron X-ray diffraction could improve the situation further. 5.3.2. Integral Equation Theoretical Studies. It is interesting to notice that in comparison with the total volume of literature on the structure of liquid acetonitrile, the ratio of works presenting purely statistical mechanical considerations is exceptionally high: at least 5 publications from various research groups over a time period of about 20 years have appeared.334,379,380,385 Necessary input data for these calculations are interparticle potentials: in the simplest case, these are hard-sphere diameters of the constituents of the molecule.229,379 On the basis of this input, integral equation theories (in their numerical and, necessarily, approximative versions) are applied to calculate correlation functions (for textbooks on statistical theories of liquids, see, e.g., Hansen and McDonald421 and Gray and Gubbins398,422). The main reason why these, by now, somewhat obsolete studies are mentioned here is that in the early work of Hsu and Chandler,379 in 1978, all of the measured (X-ray and neutron diffraction) total scattering structure factors have been calculated (cf. Figure 4 of ref 379), and moreover, the agreement between (this time, really pure!) theory and experiments is remarkably good, at least of semiquantitative quality. (Note that no computer simulation studies have provided such a complete comparison.) It is rather instructive to look at the PRDFs that are the realspace counterparts of the calculated TSSFs: all of them display unphysically sharp features, cusps, that, according to the authors, appear due to the “interference between intramolecular and intermolecular lengths”. Since the particular version of the theory these authors used (RISM228) allows the calculation of angle-dependent pair distribution functions from the site−site AM


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Table 14. Experimental Studies of Liquids with Molecules of Symmetry C2v (formula) CX2Y2 bond lengths (Å) system

first author, year

ref

diffraction method

Qmax (Å−1)

CH2F2

Mort, 2000 Morita, 2006 Orton, 1977 Jung, 1989 Georgiou, 2006 Bálint, 2007 Pothoczki, 2010

423 424 217 425 426 131 427

CH2Br2

Pothoczki, 2010

427

CH2I2

Pothoczki, 2010

427

CBr2Cl2 CCl2F2

Pothoczki, 2012 Hall, 1991

351 297

neutron X-ray X-ray neutron X-ray X-ray neutron X-ray neutron X-ray neutron X-ray neutron neutron

30 0.122 10 17 7.6 16.06 9 14.5 8 14.5 6 13.5 23 40

CH2Cl2

center−ligandX

center−ligandY

1.14

1.32

1.07

1.77 1.76

1.09 1.08(10)

1.77 1.76(10)

1.07(6)

1.92(6)

1.01(6)

2.13(6)

1.95 1.755(1)

1.77 1.326(2)

remarks 153 K small angle, supercritical H/D isotope substitution time-resolved

153 K and for CDClF2

Table 15. Simulation/Theoretical Studies of Liquids with Molecules of Symmetry C2v (formula) CX2Y2 system

first author, year

ref

remarks

CH2F2

Lisal, 1996 Higashi, 1997 Potter, 1997 Jedlovszky, 1999 Myers, 1952 Evans, 1982 Ferrario, 1982 Ferrario, 1982 Ferrario, 1982 Böhm, 1984 Böhm, 1985 Evans, 1985 Kneller, 1989 Jedlovszky, 1997 Fox, 1998 Richardi, 1998 Torii, 2005 Georgiou, 2006 Bálint, 2007 Pothoczki, 2010 Pothoczki, 2010 Almásy, 2011 Levy, 1937 Chadwick, 1975 Pothoczki, 2010 Pothoczki, 2010 Pothoczki, 2010 Pothoczki, 2010 Pothoczki, 2012 Pothoczki, 2013

428 429 194 430 431 432 433 434 435 384 329 436 437 438 246 439 338 426 131 427 127 440 400 441 427 127 427 127 351 272

MD MD MD MC μ-wave spectra, dipole moment, molecular structure MD MD MD MD ab initio calculation, intermolecular potential MD MD, far-infrared spectrum MD RMC MD, force-field parameters hypernetted chain approximation of Ornstein−Zernike theory ab initio molecular orbital, MC, MD MD MD RMC RMC ab initio calculation molecular structure molecular structure RMC RMC RMC RMC MD,RMC orientational correlations in liquid compared to plastic phase

CH2Cl2

CH2Br2

CH2I2 CBr2Cl2


5.4. Molecules with C2v Symmetry: Methylene Chloride and Its Derivatives

Mort,423 2000

Jung,425 1989 Jung,425 1989; Orton,217 1977

Georgiou,426 2006 Jung,425 1989; Bálint,131 2007 Pothoczki,427 2010 Pothoczki,427 2010

Pothoczki,427 Pothoczki,427 Pothoczki,427 Pothoczki,427 Pothoczki,351 Pothoczki,351

2010 2010 2010 2010 2012 2012

Experimental and computer simulation investigations for these systems are summarized in Tables 14 and 15, respectively. 5.4.1. Liquid Methylene Chloride, CH2Cl2. 5.4.1.1. Diffraction Experiments. The first diffraction experiment on this liquid was performed by Orton et al.,217 who determined the TSSF by X-ray diffraction in 1977 (together with that of liquid CCl4 and CHCl3). Even though the data looked perfectly sensible, no further attempts were made to interpret them in terms of the microscopic structure. The next measurement was a carefully planned and executed isotopic substitution neutron

Molecules of these liquids contain two types of ligands connected to the common center, two pieces of each (that is, they most frequently (in this review, 100% of them) contain 5 atoms). Similarly to the tetrahedral molecules with C3v symmetry, these molecules generally possess a dipole moment. Liquid methylene chloride is a well-known solvent in the chemistry lab as well as in industry, and perhaps this why this material has been the best studied in this group. AN


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diffraction, published by Jung et al.425 in 1989. The authors considered four mixtures of CH2Cl2 and its heavy version, CD2Cl2, with molar ratios of the latter constituent as 0, 0.36 (thus providing no coherent scattering from the hydrogen sites), 0.5, and 1.0. Although the reliability of data from the 1Hcontaining samples was (and is) of concern (see the MD study of Kneller et al.437), these data still represent the most complete set of diffraction experiments on this three-component system. Next, nearly 20 years later, Bálint et al.131 measured the TSSF by means of a modern laboratory X-ray diffractometer; the data were an integral part of a combined quantum chemical and molecular dynamics study (see below for more details). Finally, the latest set of diffraction data, consisting of one neutron and one (synchrotron) X-ray TSSF, was published in 2010,427 in conjunction with an extensive reverse Monte Carlo investigation on three methylene halides (chloride, bromide, iodide). To complete the set of experiments, the highly nonstandard approach of Georgiu et al.426 must be mentioned: they used time-resolved X-ray diffraction with a time resolution of 100 ps for the study of effects of fast heating (for instance, by the X-ray beam itself) on the structure. Even though structure factors were produced, they were not (yet) made use of for revealing features of the microscopic structure. 5.4.1.2. Computer Simulations. The first known computer simulation on methylene chloride was the MD calculation of Evans,432 who compared a 3-site (CH2− and two Cls) and a 5site (all-atom) model of the molecule; unfortunately, only dynamic properties were mentioned in this short communication. In a series of publications, Ferrario and Evans433−435 applied the two (3- and 5-site) interatomic potentials for a fairly exhaustive investigation of the liquid; only one of these papers433 concerned structural properties and calculated the partial radial distribution functions for the 5-site potential (with and without partial charges). Böhm et al.384 reported on a systematic potential development effort, within which new interatomic potentials were introduced in 1984, based on ab initio and experimental data (for about 10 molecular liquids consisting of molecules of methane derivatives). One later, the same author applied the previously developed (5-site) potential functions for a detailed molecular dynamics study of liquid CH2Cl2. Among other properties, PRDFs were calculated along with the intermolecular part of a neutron-weighted experimental structure factor that was compared with the first (then unpublished) piece (sample CD2Cl2) of the data set reported later by Jung et al.425 The comparison was favorable, so that the PRDFs now had a more solid basis than previously, even though no further analyses of the structure took place. Still, in the mid 1980s, Evans 436 produced yet another MD investigation of dynamical/spectral properties, based on their 3-site potential model;432 the structure was not mentioned at all this time. Following quickly the landmark neutron diffraction experiments of Jung et al.,425 Kneller et al. devoted a thorough MD simulation investigation to the structure (and another one442 to the dynamics) of liquid methylene chloride. All four intermolecular total neutron scattering structure factors (determined for four samples of varying H/D ratios) were calculated and compared with the experimental data for two different 5-site potential models. More interestingly, the reciprocal space information was also calculated via two different routes from the particle coordinates: (1) the standard method is to combine PRDFs to composite RDFs with the appropriate weights425 and then perform numerical Fourier

transformation; (b) the crystallographic method, in which particle position vectors are directly combined with the permitted reciprocal space vectors and summed up (similarly to what is done in one version of the reverse Monte Carlo algorithm for crystals, called RMCPOW288). The two methods of calculating the intermolecular TSSFs coincided. Although no attempt was made to characterize orientational correlations, a large chunk of the work dealt with thoughtful analyses of the possible sources of errors/uncertainties that plague the data measured from samples containing a significant amount of 1H. Another decade later, Fox et al.246 meticulously parametrized interatomic potentials for a number of organic solvents; for methylene chloride, they obtained good agreement with numerous thermodynamic properties but the structure was not considered. In the same year (of 1998), Richardi et al.439 performed integral equation-based theoretical calculations. These authors presented no PRDFs, only some geometrical arrangements of dimers that, supposedly, possess importance in forming the bulk structure; in terms of the Rey groups (see ref 133), these arrangements appear to be of the 3:3, 2:3, and 2:2 types. The mid-2000s have brought up three important computer simulation investigations131,338,426 that, actually, appear to have been the last ones published for liquid methylene chloride. Torii338 scrutinized the role and influence of electrostatic terms, particularly of the quadrupolar one, on the microscopic properties of liquid CH2Cl2 (and CHCl3). PRDFs for four different potential parametrizations were shown; it was the C− C and C−H partials that proved to be most sensitive to changing the electrostatic potential parameters. Bálint et al.131 used three types of potentials338,350,433 in their MD calculations that accompanied their X-ray diffraction measurement discussed earlier. Intermolecular parts of their X-ray data as well some neutron TSSFs from Jung et al.425 could be reproduced in both the reciprocal and the real spaces at a precision better than semiquantitative. Analyses concerning the orientational structure suggested that neighbors that are in contact “...slightly prefer an antiparallel, tail-to-tail orientation...”, whereas above 4 Å, parallel dipoles are preferred. Interestingly, in their dimerbased quantum chemical calculations, Almásy et al.440 could not find the dominance of antiparallel arrangements, even though one can see visual agreement between the two dimer-related calculations.131,440 Georgiu et al.426 exploited (with success) the MD methodology to follow their time-resolved X-ray diffraction experiments as closely as possible; the orientation of molecules was not considered in this methodology-oriented publication. Reverse Monte Carlo modeling found its applications for liquid methylene chloride too. The first such study438 modeled intermolecular parts of neutron425 and X-ray217 TSSFs. It appeared that the quality of the fit to the latter type of data was sacrificed in order to be able to reproduce the, rather featureless, functions of ref 425. This work found that the mutual orientations of the dipoles of molecular neighbors tend to be preferentially parallel or antiparallel. Thirteen years later, in 2010, Pothoczki et al.127 in their RMC calculations considered the total scattering structure factors (thus modeling the intramolecular contributions as well), with which perfect agreement could be achieved (see Figure 11). Their PRDFs show an overall satisfactory agreement with earlier MD and RMC investigations but not with those resulting from the hardsphere reference models of the same author.427 From a comparison with the hard-sphere reference structure, “Clear, AO


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analyzed interactions between nearest neighbors; hydrogen bonding via F···H bridges was visioned. The same year (1997), Potter et al. applied their ab initio-based interatomic potentials for a series of MD simulations (between roughly 200 and 300 K); the emphasis was placed heavily on thermodynamics. Still, structural properties were mentioned, and further, preliminary results from the neutron diffraction study of Mort et al.423 were compared to the prediction of the MD simulation. While good agreement with experiment was found for CHF3, considered in the same work as CH2F2,194 somewhat surprisingly, the methylene fluoride composite RDF appeared to be rather different from the corresponding experimental function. Potter et al. tried to modify potential parameters, but the discrepancies persisted; considering all circumstances (a good description of a very similar material by using essentially the same potential parameters; difficulties with processing neutron data for hydrogenous materials), it might also be these particular diffraction data that may need some reanalyses. One more set of simulations, the Monte Carlo study of Jedlovszky et al.430 from 1999, needs to be reported here in detail. These authors also obtained the neutron data of Mort et al.423 prior to publication so that comparison with experimental intermolecular composite RDF could be made. A reasonable match (better than that of Potter et al.194 but somewhat inferior to that of Higashi et al.429) was reported. Jedlovszky et al.430 performed an extensive study of short-range mutual molecular orientations and showed, as a key finding, that a parallel headto-tail arrangement is preferred. As they also note, this is, indeed, somewhat unusual among methane derivatives; on the other hand, in liquid CH2Cl2, a similar438 or even stronger127 such preference was detected. In summary, considering the practical importance of difluoromethane, a more extensive set of experimental data (e.g., synchrotron X-ray diffraction; neutron diffraction on the deuterated specimen) would be desirable; however, computer simulations with potentials developed just before the millennium appear to be capable of describing structural and thermodynamic properties over a wide range of state points. 5.4.2.2. Methylene Bromide (Dibromomethane), CH2Br2. In spite of small ambiguities about gas-phase electron diffraction results,400 the molecular structure of this material could be clarified (to a precision of 0.001 of an Angstrom) by the mid-1970s441 by microwave spectroscopy. To our knowledge, only one set of diffraction experiments has been reported, by Pothoczki et al.,427 consisting of TSSFs from one neutron (on CD2Br2) and one X-ray diffraction measurement. These data have been modeled by reverse Monte Carlo, a procedure which was able to reproduce the measured data (in the reciprocal space) within experimental uncertainties; on the other hand, the hard-sphere reference system could not predict the X-ray-weighted TSSF (even though the match with the neutron data is good). PRDFs from RMC modeling (in full consistency with diffraction results) were shown in ref 427; unfortunately, there are no theoretical/simulation results to compare with, apart from again the hard-sphere Monte Carlo predictions that failed to produce reliable C−Br and Br−Br partials (cf. Figure 5 of ref 427). Orientational correlations were analyzed extensively;127 the main characteristics are that, similarly to liquid CH2Cl2 and CH2F2,430 the head-to-tail arrangement has a significant presence, although not at the contact distance, where one of the T-shaped configurations appears with the highest probability.

Figure 11. Normalized total scattering structure factors from neutron (deuterated forms, left) and X-ray (middle) diffraction on liquid CH2Cl2 (top) and CH2I2 (bottom). Red (neutron) and blue (X-ray) solid lines represent the experimental data,427 whereas black solid lines denote the corresponding hard-sphere reference models. Orientational correlation functions127 from Rey analyses (right), as well schematic drawings of the molecules (right, inset). Color coding to Rey groups (different kinds of ligands are not distinguished): black (1:1); red (1:2); dark green (2:2); turquoise (1:3); dark blue (2:3); magenta (3:3).

although not very strong, dipolar ordering could be detected upon the introduction of diffraction data.” This kind of ordering manifested in the formation of head-to-tail and Tshaped arrangements. Such ordering can be seen on the dipole−dipole correlation map (Figure 8 of ref 127) and on the Rey groups too (see Figure 11). 5.4.2. Liquid Methylene Halides CH2F2, CH2Br2, CH2I2, and CBr2Cl2. 5.4.2.1. Methylene Fluoride (Difluoromethane), CH2F2. This important industrial coolant/refrigerant is a gas at room temperature and pressure, and therefore, the first (and, to our knowledge, only) diffraction experiment was performed at 153 K at a pulsed neutron source by Mort et al.423 quite recently in 2000. Unfortunately, the deuterated compound was not available, so that the difficulties with data corrections could not avoided; perhaps this fact is reflected by the unexpected (and unexplained) rise of the structure factor toward Q = 0 Å−1 (somewhat similar to a small angle scattering signal). Intra- and intermolecular contributions were separated, and from the latter, it was concluded that the shortest intermolecular H···F distance would be too long for a hydrogen bond (this idea, somewhat surprisingly, was around that time429). (There is one more experiment, using small-angle X-ray scattering, reported on the industrially relevant supercritical states of methylene fluoride;424 no information on the microscopic structure was provided though.) Computer simulation studies are more abundant, and interestingly, they all preceded the neutron diffraction experiment, that is, their findings may be considered as predictions. The potential functions applied have been of the Lennard− Jones plus point charges type; Lisal et al.428 used also a 14-7 form for describing the dispersion part (to be contrasted with the 12-6 form of LJ), with no appreciable differences in terms of thermodynamic and structural properties. These authors calculated the PRDFs and speculated on the mutual orientations of neighbors on the basis of peak positions: the suggestion was interlocking “in a gear-like fashion”. Higashi et al.429 showed qualitatively similar PRDFs from their molecular dynamics simulations (at subcritical temperatures) and AP


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5.4.2.3. Methylene Iodide (Diiodomethane), CH2I2. Only the combined diffraction/RMC study of Pothoczki et al.427 on methylene halides followed by a detailed investigation of the orientational structure127 are available for this liquid. Due to some unknown problems, the Q range of the neutron diffraction TSSF had to be shortened if a satisfactory reproduction was required by RMC. One noteworthy point is that the hard-sphere reference model predicts both the X-rayand the neutron-weighted TSSFs to within errors (cf. Figure 3 of ref 427). This dominance of steric effects (density, molecular shape, and packing fraction) is also reflected by characteristics of Rey groups. In terms of the specific orientational correlations, the sudden increase of the probability of tail-totail (i.e., CH2−CH2) arrangements at the contact distance could be detected, but in general, head-to-tail and T-shaped dimers are the most frequent, in agreement with other methylene halides. 5.4.2.4. Dibromodichloromethane, CBr2Cl2. This particular combination of Br and Cl ligands has caught some attention due to the existence of an easily reachable plastic crystalline phase that appear upon cooling the (room temperature) liquid down to around the freezing point of water. The liquid phase was studied by neutron diffraction, followed by MD simulations and RMC modeling, by Pothoczki et al.,351 whereas a comparison with the plastic crystalline phase is provided by ref 272. Molecular dynamics was able to yield an extremely good initial guess for the TSSF of the liquid in the reciprocal space, so that RMC had to act only as refinement (cf. Figure 1 of ref 351). Concerning mutual orientations of neighbors (as well as, in fact, the total scattering structure factors, cf. Figure 1 of ref 272), the liquid and plastic crystalline phases were found to be nearly identical:272 at the contact distance, face-to-face (3:3) arrangements dominate and then with increasing C−C distance edge-to-face (2:3) and edge-to-edge (2:2) follow. A plausible explanation for this behavior, involving the competition between steric and electrostatic effects, could be provided in ref 351.

to predict the structure correctly, a statement that has been validated via comparisons with reverse Monte Carlo models that were in full consistency with diffraction data.123,124 There are only a few individual cases (liquid GeBr4, P4) that need further structural modeling for a full understanding of their microscopic structure, including orientations, but this is only a matter of time and willingness. With deteriorating molecular symmetry, orientational correlations become harder to reveal, as exemplified in Figures 7, 8, and 11. Another manifestation of this notion is provided by Figure 12, where the bivariate representation of Pardo139 is

Figure 12. Positional ordering, as calculated from RMC models, according to the bivariate formalism.139 Color code scales the probability from low (blue) to high (red). (Top left) Liquid CBr4; (top right) liquid CD3I; (bottom left) liquid CHCl3; (bottom right) definition of the angles confined.

applied to liquid CBr4 (particle coordinates from Temleitner160), CHCl3 (particle coordinates from Pothoczki128), and CD3I (particle coordinates from Pothoczki300). Whereas the picture for liquids containing perfect tetrahedral molecules is clear (see, e.g., refs 6 and 139), the graphs corresponding to molecules of distorted tetrahedral shape are less transparent (e.g., large angular regions are unavailable, etc., see Figure 12). It would be most desirable to develop computational tools that would be able to provide more clear-cut interpretations for such systems as well. As the symmetry of the molecules deteriorates, the issue of the structure is becoming more and more open: a single diffraction experiment is provenly insufficient for a reliable structure determination any longer for the overwhelming majority of such liquids (cf. ref 300). In some cases, notably of chloroform, even an exceptionally large amount of experimental information (e.g., the presence of 6 independent experimental TSSFs for this three-component system) has not been ample to clarify the issue of orientational correlations (cf. refs 128 and 295). On the other hand, in the family of PX3 liquids, one still finds examples for which even the hard-sphere reference system can provide an adequate description of the structure: see the case of phosphorus trichloride;115 note that such cases are very much the exception rather than the rule in this family! We think it is of utmost importance to state that molecular dynamics simulation results have consistently been found to be spectacularly good predictions of the structure (many times, also in the reciprocal space) of molecular liquids discussed in

6. SUMMARY AND CONCLUDING REMARKS We described the structure of about 35 neat molecular liquids consisting of molecules of the shape of (perfect and nearly) tetrahedra to the detail that is allowed by the available experimental and theoretical evidence. At least one set of (either X-ray or neutron) diffraction data is available for each liquid that has been complemented by, sometimes a rather large, a number of theoretical/simulation/structural modeling studies. In each case, we tried to provide a simple, plausible characterization of the mutual arrangements of neighboring molecules; the success rate of this activity has been heavily influenced by (a) the nature of the actual material (see below) and (b) the available volume and quality of relevant literature. Concerning liquids of perfect tetrahedral molecules, including carbon tetrachloride, the evidence listed in the relevant sections allows us to claim that our present understanding of details of the microscopic structure in these liquids, including details of the orientational correlations, is well established and adequate. Note that these materials are easy and grateful subjects nowadays: one set of diffraction data is most frequently sufficient (see, e.g., ref 124) since the positions of the 4 identical ligands determine the position of the center, and this piece of information can be exploited fully by using various computer modeling techniques. It has been shown, for instance, that modern classical MD simulations133,136 are able AQ


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this review. This statement is based on countless cross-checks between reverse Monte Carlo and MD structures: RMC, in most cases, would only be needed as refinement to the MD result. This finding is extremely encouraging for future investigations of more complex molecular liquids. A short outlook toward studies of disorder in crystals consisting of tetrahedral molecules has been provided using the examples of the plastic crystalline phases of CCl4−xBrx. It could be revealed that the corresponding liquids and plastic crystals possess nearly identical mutual orientational correlations at short range. Except for these recent investigations,6,8,9,159,271,272 this area may be considered as terra incognita, whose exploration could provide even more detailed information on the local (partially disordered) structure of both phases. An important extension to our knowledge of these liquids would be a more systematic coverage of the temperature and pressure range where their liquid/fluid phases exist; at present, only sporadic examples (e.g., on phosphorus169 and carbon tetrachloride223) are available. As a closing remark, as well as an outlook toward desired/ possible future studies, a short list of important tetrahedral liquids is given here for which open questions related to the structure do still very much exist: chloroform, fluoroform, acetonitrile, methylene chloride and fluoride, and most of all liquid ammonia.

László Temleitner received his Ph.D. degree in 2007 at the BUTE (Hungary). Since 2003, he has worked at the WRCP (formerly RISSPO) of the HAS. In 2009, he was granted a 2 year postdoctoral fellowship of the Japan Society for the Promotion of Science to work at the Japan Synchrotron Radiation Research Institute (SPring-8) under the supervision of Dr. Shinji Kohara. Since 2012, he has been first instrument scientist on the MTEST neutron diffractometer at the WRCP (Budapest, Hungary). He has acquired experience in both neutron and X-ray diffraction measurements and data evaluation. Also, he contributed as a program developer of RMC programs and configuration analysis. His main focus at present is structural disorder in crystalline materials.

AUTHOR INFORMATION Corresponding Author

*Phone: +36 (06)1 3922589. Fax: +36 (06)1 3922589. E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies

László Pusztai graduated in 1987 at the Eötvös University, Budapest, Hungary, with his M.Sc. degree in Chemistry. Before his Ph.D. studies (Chemistry, 1992, HAS, Budapest, Hungary), he worked at the Clarendon Laboratory, University of Oxford, under the supervision of Prof. Robert McGreevy, on the development and early applications of reverse Monte Carlo modeling. While working permanently at the Eötvös University, he has stayed as a postdoctoral researcher at the Technical University of Delft (The Netherlands) and at the Studsvik Neutron Research Laboratory, Univesity of Uppsala (Sweden). He joined the RISSPO of the HAS in 1999 as Head of the Department of Neutron Physics; when this department was merged with other units in the newly formed WRCP (in 2012), he became the leader of the Liquid Structure research group. His main focus has been, and is, placed on the structure of molecular liquids.

Szilvia Pothoczki received her M.S. degree in Engineering Physics and her Ph.D. degree in Physics at the Budapest University of Technology and Economics (BUTE, Hungary) in 2006 and 2010, respectively. During her Ph.D. studies she worked at the Research Institute for Solid State Physics and Optics (RISSPO), Hungarian Academy of Sciences (HAS). In 2010 she started her postdoctoral work in the group of Professor Joseph Lluis Tamarit at the Universitat Politecnica de Catalunya in Barcelona. In 2012, she returned to Hungary as a postdoctoral researcher. She has since been working in the Department of Complex Fluids of the Wigner Research Centre for Physics (WRCP), HAS, focusing on atomic level computer simulations of disordered systems, especially in their liquid state.

ACKNOWLEDGMENTS We thank all colleagues who have contributed to our efforts aimed at understanding the structure of tetrahedral liquids, in particular Dr. P. Jóvári (Wigner RCP, Hungary), Dr. S. Kohara(NIMS, previously JASRI/SPring-8, Japan), Dr. L. C. Pardo and Professor J. Ll. Tamarit (Politecnica de Catalunya, AR


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Spain), Prof. Robert L. McGreevy (STFC/ISIS, UK). The authors acknowledge financial support from the former Hungarian Basic Research Fund (OTKA), via grant no. 083529, and from the National Research, Development and Innovation Office of Hungary (NKFIH), grant no. SNN 116198.

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