Liquid-State Structure via Very High-Field Nuclear Magnetic

Letter pubs.acs.org/JPCL

Liquid-State Structure via Very High-Field Nuclear Magnetic Resonance Discriminates among Force Fields Edward T. Samulski,*,† Chi-Duen Poon,† Leah M. Heist,† and Demetri J. Photinos*,‡ †

Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States Department of Materials Science, University of Patras, Patras 26110, Greece

‡

S Supporting Information *

ABSTRACT: Deuterium nuclear magnetic resonance (2H NMR) spectra of labeled molecular liquids obtained at high fields, for example, |B| = 22.3 T (950 MHz proton NMR), exhibit resolved quadrupolar splittings that reflect the average orientation of the molecules relative to B. Those residual nuclear spin interactions exhibited by benzene and chloroform provide an experimental determination of the leading tensor component of the pair correlation function for these two molecular liquids. In this way, very high-field 2H NMR may be used to extract unambiguous information about liquid-state structure. Additionally, replicating the experimentally derived pair correlation function using molecular dynamics simulations provides a critical test of simulation force fields.

A

tensor component of the angular pair correlation function between molecules of the same or different species in a binary mixture. We also demonstrate that this component is a sensitive indicator of structure in molecular liquids that when calculated, using molecular dynamics simulations, yields a critical assessment of the simulation force field. Residual quadrupolar interactions cause a small splitting Δν (∼1 Hz in a 22.3 T magnetic field) of the deuterium resonance and its carbon-13 satellite lines in the 2H NMR spectra of liquid benzene-d6 (Figure 1a) and chloroform-d1 (Figure 1b). The apparent lower resolution spectrum of benzene is due to the unresolved fine structure; the direct dipole−dipole interactions are negligible.15 The observed Δν may be precisely measured and is proportional to the incompletely averaged electric field gradient (EFG) tensor V⃡ at the deuterium nucleus. That nonzero average stems from the slight orientational bias that the molecule’s CD bonds experience relative to the spectrometer magnetic field B. The bias derives from the orientation-dependent magnetic energy contribution,−(1/2) B·χ⃡ ·B, with χ⃡ denoting the molecular magnetizability anisotropy tensor. The small magnetic-field-induced quadrupole splitting may be readily extracted from VHF-NMR spectra and in general form is given by16

fter early geometrical models of liquid-state structure were proposed,1 the theory of liquids progressed rapidly.2,3 Significant understandings have come from computer simulations,4,5 but simulations are only as reliable as the force fieldthe partial charge values, force constants and excluded volume parametersdescribing pairwise atomistic interactions. Mistakenly assumed to be transferable, irrespective of the simulation environment, and usually devoid of many-body interactions,6 the force field is typically generated and optimized by fitting it to a limited set of experimental data (e.g., density, heat of vaporization, self-diffusion, X-ray, and neutron scattering) or results from quantum calculations. Here we show that very high-field nuclear magnetic resonance (VHFNMR) yields an experimental determination of the leading tensor component of the pair correlation function that, in turn, provides an additional experimental parameter that may be used to validate force fields. While the influence of a magnetic field B on molecular liquids is usually negligibly small,7 there is a measurable effect: a high field perturbs molecular reorientation, revealing incompletely averaged, anisotropic NMR interactions.8 As a result, VHF-NMR in conjunction with liquid-state simulations can be used to discriminate among simulation models of molecular liquids. Herein we employ the prototypical molecular liquids benzene and chloroform to demonstrate this. Magnetic fieldinduced orientation has been previously reported for both of these liquids, albeit at a lower NMR field strength (|B| ≈ 14 T),9,10 and both liquids have been extensively modeled;11−14 however, the liquid-state structure inferred from previous NMR studieslocal molecular orientational correlationswas described in a phenomenological manner. Herein we show that deuterium NMR (2H NMR) studies of perdeuterated benzene (C6D6) and chloroform (CDCl3) at magnetic field strength |B| = 22.3 T provide an experimental determination of the leading © 2015 American Chemical Society

Δν =

η 3 ⎡3 1 νQ ⎢ ⟨(B̂ ·z)̂ 2 ⟩ − + EFG {⟨(B̂ ·x)̂ 2 ⟩ ⎣ 2 2 2 2 ⎤ − ⟨(B̂ ·y )̂ 2 ⟩}⎥ ⎦

(1)

Received: August 8, 2015 Accepted: August 31, 2015 Published: August 31, 2015 3626

DOI: 10.1021/acs.jpclett.5b01737 J. Phys. Chem. Lett. 2015, 6, 3626−3631

Letter

The Journal of Physical Chemistry Letters

Figure 1. 2H NMR spectra recorded at |B| = 22.3 T (Bruker Avance III 950 MHz proton NMR spectrometer at temperature, T = 303 K). (a) Benzene-d6 and (b) chloroform-d1. The molecule-fixed frame specifies the angle θ that the magnetic field B makes with the symmetry axes of the molecules (y axis of C6D6, and z axis of CDCl3). Both the primary central resonance and the flanking C-13 satellite resonances show quadrupolar splittings (Δν = 1.04 Hz for C6D6,15 and Δν = 0.524 Hz for CDCl3).

where νQ is the deuterium quadrupole coupling constant, the unit vector B̂ denotes the direction of the magnetic field, and x̂, ŷ, and ẑ are the principal axes of the EFG tensor. These axes are assigned so that Vzz is the largest component; that is, x̂ is identified with the C−D bond direction and the Vyy is the smallest component; that is, the asymmetry parameter of the EFG tensor ηEFG = (Vxx − Vyy)/Vzz is positive. The angular brackets indicate a motional average. Because of the axial symmetry of the benzene and chloroform molecules, the average can be expressed in terms of the motionally averaged orientation of the molecular symmetry axes relative to the direction of the magnetic field and is typically described by an order parameter S = ⟨3 cos2 θ − 1⟩/2

axes of the A and B molecular species and cA (= NA/N) and cB (= 1 − cA) are the respective molecular concentrations in a binary mixture having a total number of molecules N = NA + NB occupying a volume V. The orientational correlation factors (2) g(2) A ̅ −A and gA̅ −B between A−A and A−B pairs of molecules are radial integrals of the second rank function g(220;r) of the wellknown tensor expansion2 of the pair correlation function for axially symmetric molecules g (ω1ω2 r) =

* (ω) Yl2m2(ω2)Y lm

3 νQ Sclfm 2

g A̅ (2) = −J

χ(p) A

N 4π 2V

∫V gA−J (2, 2, 0, r) dr

(6)

and depend on both temperature and concentration. It follows from eqs 1, 2, and 4 that the 2H NMR study of the binary mixture at different temperatures and concentrations provides an experimental determination of the integrated second rank components gA−J(2,2,0,r) of the pair correlation functions for the species pairs A−A and A−B given the principal values of the molecular magnetizability anisotropy of each species. Previously, the influence of molecular correlations on the order parameter has been introduced (see, for example, refs 8−10) through the Kirkwood g2 factor by defining an effective (p) (p) magnetizability anisotropy as χ(p) eff = g2χmol, where χmol is the molecular (“gas-phase”) value; however, the result in eq 4 does not rely on the introduction of effective magnetizabilities and provides, for a binary mixture, a rigorous expression for g2 and its explicit dependence on concentration in terms of the (p) molecular magnetizabilities χ(p) A and χB and the correlation (2) (p) factors g(2) and g , namely, g = 1 + cAg(2) A A 2;A A ̅ −A ̅ −B ̅ −A + (1 − cA)(χB / (p) (2) χA )gA̅ −B. In the following we present the results from the study of two mixtures where (i) the deuteriated molecular species is benzene-d6 (A = benz) and the diluent molecular species is tetramethylsilane (B = TMS); (ii) the deuteriated molecular species is chloroform-d1 (A = clfm) and the diluent species is again TMS (B = TMS). In both cases, due to the symmetric,

(3)

(3′)

At room temperature (for the magnetic field strengths and the magnetic anisotropies involved), the orientation-dependent magnetic potential energy of a molecule is on the order of 10−4kT or smaller. Consequently, starting from the formal statistical mechanics definition of the motional averaging in eq 2, the order parameter SA of an axially symmetric molecule of species A in a liquid mixture with another molecular species B, having axial symmetry or higher, can be expressed as ⎛ |B|2 ⎞ (p) (2) (p) (2) SA = ⎜ ⎟(χ (1 + cAg A̅ − A ) + cBχB g A̅ − B ) ⎝ 10kT ⎠ A

(5)

where C(l1l2l;m1m2m) denotes the Clebsch−Gordan coefficients and Ylm is the spherical harmonics. Specifically, the pair correlation factors g(2) A ̅ −J, with J = A or B, are given by

(2)

For the chloroform molecules, where the C3 axis corresponds to the ẑ molecular axis (C−D bond direction), the symmetry imposed relations yield Δνclfm =

g (l1l 2l ; r )C(l1l 2l ; m1m2m)Yl1m1(ω1)

l1l 2l m1m2m

where θ is the instantaneous angle between the symmetry axis and the magnetic field. Thus, in the case of benzene, where the C6 axis corresponds to the ŷ molecular axis (ring normal), symmetry imposes the relation ⟨(B̂ ·x̂)2⟩ = ⟨(B̂ ·ẑ)2⟩ = ⟨1 − (B̂ · ŷ)2⟩/2, by which eq1 leads to the expression 3 Δνbenz = − νQ S benz(1 + ηEFG) 4

∑ ∑

(4)

χ(p) B

Here and are the principal values of the molecular magnetizability anisotropy tensors along the axial symmetry 3627


Letter


ν0;benz(T) = −(3/20)νQ((|B|2χyy benz)/(2kT))(1 + ηEFG) to obtain ν0;benz(T = T0)calc = 1.25 Hz, with νQ = 187 ± 0.4 kHz,17 ηEFG = −28 0.054,18 and χyy JT−2 (see Supporting benz = −7.1 × 10 Information). This is in excellent agreement with experiment (i.e., Δν/ν0 extrapolates to 1.0 in Figure 2). Using eq7 at the other concentration extreme, x = 1, one obtains from the measured splitting of neat benzene (Δνbenz(T = T0, x = 1) = 1.04 ± 0.01 Hz), the value gn̅ eat = −0.16 ± 0.01. It is noted that the splitting measured here for neat benzene, when scaled to the magnetic field strength (|B| = 14.09T) and temperature (T = 296 K) of the previous measurements in ref 9 is reduced to 0.43 Hz, in good agreement with the value of 0.41 Hz reported there. The concentration dependence of the splitting throughout the entire concentration range (x = 0 to 1) shows a slight but clear deviation from linearity, which is adequately conveyed by eq 8 (see solid line in Figure 2) with g′̅ = −0.21 ± 0.07; g″̅ is too small to be evaluated at the experimental resolution of the data points. Next, we compare the experimentally determined neat benzene value of gn̅ eat = −0.16 with the value of g ̅ directly obtained from computer simulations by numerically integrating the simulated spatial distribution function according to

tetrahedral structure of the TMS molecule and, therefore, its magnetic isotropy, the magnetizability anisotropy χ(p) B in the expression of eq 4 is set to zero, and the correlation factor g(2) A ̅ −B between the deuteriated and diluent molecules does not appear in the expression for the order parameter of the deuteriated species. In other words, for these mixtures, the magnetically relevant g(2) A ̅ −A (i.e., benzene−benzene or chloroform-chloroform) correlations are simply attenuated by the TMS diluent. Accordingly, combining eqs 3 and 3′ with eq 4 we obtain for both mixtures the following expression for the quadrupolar splittings of the deuteriated species at temperature T and the mole fraction cA = x Δν(T , x) = ν0(T )(1 + xg ̅ (T , x))

(7)

−(3/20)νQ((|B|2χyy benz)/ χzz benz representing the

Here, according to eq 3, ν0;benz(T) = (2kT))(1 + ηEFG) for benzene, with principal value of the magnetizability anisotropy tensor along the C6 axis of the benzene molecule. Similarly, we obtain from eq 3′ ν0;clfm(T) = (3/10)νQ((|B|2χzz clfm)/(2kT)) for chloroform, where χzz clfm is the respective principal value along the C−D bond (C3 axis) of the chloroform molecule. The correlation function g(T,x) represents, in abbreviated notation, the ̅ correlation factors g2A̅ −A(T,cA) of eq 6 for the benzene−benzene and chloroform−chloroform molecular pair correlations in the respective mixtures. The concentration dependence of g ̅ is expected because, in principle, the correlations between a pair of species A molecules depend on whether or not this pair is surrounded predominantly by species A or TMS diluent molecules. The magnitude of the concentration dependence of g ̅ would, according to eq 7, be reflected directly in the extent of the observed nonlinearity of the concentration dependence of Δν versus x. As shown in Figure 2, the concentration

g̅ ≡

2πN V

∫0

∞

r 2 dr

1

∫−1 d cos θ1,2(P2(cos θ1,2)g (̃ r ; θ1,2)) (9)

where g̃(r;θ1,2) is the scaled integral of the benzene−benzene pair correlation g(ω 1 ω 2 r) over the direction of the intermolecular vector, with θ1,2 denoting the angle between the C6 symmetry axes of pairs of molecules and r their intermolecular distance. In Table 1 we show the calculated Table 1. Calculated Radial Integral of Leading Tensor Component of g(ω1ω2r) ΔHvap (kcal/mol)a,c

force field

AMOEBA19 DANG20 OPLS-AA22 CHARM2223 MM324

C6 D 6 CDCl3 C6 D 6 CDCl3 C6 D 6 CDCl3 C6 D 6 CDCl3 C6 D 6 CDCl3 C6 D 6 CDCl3

7.89 7.50 7.91 7.48 7.91 7.52 7.82 7.53 7.91 7.78 7.45

21

density (g/cm3)b 0.874 1.489 0.879 1.489 0.878 1.480 0.870 1.487 0.872 0.873 1.496

17

D (10−5 cm2 s−1)

gb̅

2.27 2.45 1.74 2.17 1.64 2.63 1.82 2.52 1.92

−0.16d +0.15d −0.14 +0.15 −0.15 +0.07 +0.08 +0.19 +0.15

2.68 2.76

+0.37 +0.14

Figure 2. Observed Δν/ν0 versus x, the mole fraction of C6D6, and CDCl3 in the diluent tetramethylsilane (TMS); the respective lines are fits of eq8 to the data.

a

dependence is rather moderate and can be quite adequately represented by a simple Taylor expansion about the values for the neat liquids (x = 1), that is 1 2 g ̅ (x) ≈ gneat ̅ + (1 − x)g ̅ ′ + 2 (1 − x) g ̅ ″ (8) We consider in detail benzene and chloroform separately, starting with the benzene−TMS mixture. According to eq7, for vanishing concentration of benzene, the measured splitting extrapolates to Δv(T,x → 0) = ν0(T). One can readily compute ν0;benz at the experimental temperature T0 = 303K using

values at T = 298 K and P = 1 atm for benzene using five force fields. For benzene only the AMOEBA19 and DANG20 force fields exhibit a negative sign for g ̅ in agreement with experiment; notably, these are the only force fields that employ many body polarization effects. The negative sign of g ̅ for neat benzene indicates that the correlations between pairs of benzene molecules result in the weakening of the magnetic alignment. This is in qualitative accord with trends obtained from simulations of the spatial distribution function (Figure 3a), where g̃(r;θ1,2) is evaluated using the AMOEBA force field. It is apparent from the 3-D plot

NVT simulations. bNPT simulations. cΔHvap = Egas − Eliq + RT. Experiment (this work)

d

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enhance the orientational order relative to the order observed for an isolated molecule, Δνclfm(T = T0,x = 1) = 0.524 ± 0.010 Hz. This value of the splitting, when scaled to a magnetic field strength (|B| = 14.35T) and temperature (T = 296 K), is reduced to 0.222 Hz, which confirms the value (0.223 ± 0.003) Hz previously reported.10 Contrary to the benzene−TMS case, the concentration dependence of the chloroform splitting in TMS shows no appreciable deviation from linearity (see Figure 2), and application of eq 8 yields values within the experimental error for g′(≈ − 0.03 ± 0.06) and g″(≈ 0). A more pronounced ̅ ̅ difference between the two mixtures is reflected in the opposite slopes of the splittings versus concentration, yielding opposite signs for g.̅ In contrast with benzene, the positive sign of g ̅ for chloroform indicates that the correlations between pairs of chloroform molecules enhance the magnetic alignment. A positive g ̅ value implies that the relative molecular dispositions that bring the molecular symmetry axes into a parallel or an antiparallel configuration (thus favoring the simultaneous alignment of the molecular pair along the magnetic field) are, in total, more probable than those configurations having the symmetry axes orthogonal (for which a simultaneously favorable alignment cannot be obtained for the two molecules). This is in agreement with the calculated spatial distribution function g̃(r;θ1,2) obtained from simulations using the AMOEBA force field. In Figure 3b, g̃(r;θ1,2) shows maxima for the parallel and antiparallel chloroform dimer dispositions, around θ1,2 = 0° and θ1,2 = 180°, respectively. Electrostatic considerations would suggest that the latter dimer with θ1,2 = 180° does not have the chloroform symmetry axes collinear, merely antiparallel; see Figure 3b. Contrary to previous reports,13 our findings suggest that chloroform is an associated liquid. The results of the comparison between the experimentally determined value gn̅ eat = +0.15 ± 0.02 and the values of g ̅ obtained directly from computer simulations of the chloroform−chloroform pairs according to eq 9 for different force fields are presented in Table 1. The data show that the calculated g ̅ values for chloroform from both AMOEBA and MM3 force fields, for example, are almost identical, +0.15 and +0.14, respectively. This is because for both force fields the parallel and antiparallel pair configurations are much more probable than the orthogonal ones. Comparable results are obtained for the vaporization enthalpies and the densities (Table 1), but the diffusion constants are considerably different and deviate in opposite directions; the AMOEBA diffusion constant (2.28 × 10−5 cm2 s−1) is smaller and the MM3 value (2.76 × 10−5 cm2 s−1) is larger than the experimental value (2.45 × 10−5 cm2 s−1). A quantitative comparison of calculated D values with experiment suggests that the many-body AMOEBA force field is best, and that is corroborated by traditional metrics, for example, a comparison of the MM3- and AMEOBA-calculated radial distribution functions with experiment. (See Figure SI-3.) Computer simulations of benzene and chloroform continue to serve as benchmarks for probing liquid-state structure and evaluating force fields. For example, Fu and Tian recently compared several force fields using MD simulations of benzene.28 They concluded from fits to experimental radial distribution functions and thermodynamic data that the OPLSAA force field best described the microstructures of benzene. However, their traditional evaluation does not adequately discriminate among force fields: When one contrasts computed radial distribution functions (from numerical integrations of

Figure 3. Spatial distribution functions of neat liquids (a) C6D6 with parallel ring planes (P) and perpendicular ring planes (T) dimers θ1,2 = 0 and 90°, respectively. (b) CDCl3 with coparallel (θ1,2 = 0°) and antiparallel (θ1,2 = 180°) dimer configurations.

that the most probable dimer is one wherein the two ring planes are mutually perpendicular (T) in agreement with ab initio calculations;25 the dominance of the T dimer in neat benzene was also inferred from incompletely averaged dipolar couplings.26 Such T dimers sample orientations in the magnetic field that do not have both rings simultaneously in low magnetic-energy orientations, that is, with both of the C6 axes perpendicular to the field. As a result, some T dimer orientations correspond to higher magnetic potential energy and therefore, reduce the observed Sbenz of the benzene C6 axis. Hence adding the magnetically inert TMS diluent to liquid benzene results in a decrease in the probability of realizing Tshaped benzene−benzene pair correlations. The disruption of those correlations, in turn, causes an elevation of the order parameter Sbenz, apparent from the increased quadrupolar splittingfrom 1.04 Hz at x = 1 to 1.25 Hz for x → 0. The latter value yields the order parameter of the C6 axis for a single “uncorrelated” benzene molecule in the 22.3T magnetic field (Sbenz = −2ν0;benz/νQ(1 + ηEFG) ≈ −1.3 × 10−5). Now we consider the chloroform−TMS mixture. From eq 3′ we calculate ν0;clfm(T = T0)calc = 0.456 Hz using ν0;clfm(T) = (3/ 10)νQ((|B|2χzz clfm)/(2kT)) with νQ = 167 ± 0.6 kHz (derived −28 from liquid crystal studies27) and χzz JT−2 (see clfm = 1.5 × 10 SI). This is in excellent agreement with the measurement (i.e., Δν/ν0 extrapolates to 1.0; see dotted line in Figure 2) indicating that liquid environmental effects on νQ are insignificant. For neat chloroform, the measured splitting is larger than ν0;clfm(T = T0), suggesting that pair correlations 3629


Letter

The Journal of Physical Chemistry Letters g̃(r;θ1,2) in eq 9 over θ1,2) with experimental data, the differences are barely perceptible. (See Figure SI-1.) By contrast, comparing experimental values of g ̅ for benzene with simulated values (see Figure SI-2) suggests that faithful computer replication of liquid-state structure requires more sophisticated force fields, ones that include many body polarizability effects. Alternately, if we were to look at just the chloroform results in Table 1, we would then conclude that both MM3 and AMEOBA force fields are equally good (or bad); however, things change dramatically when we bring benzene into the picture because then we see that the two force fields give different signs for g ̅ (with the densities and vaporization enthalpies remaining in reasonable agreement and again finding that the calculated diffusion constants deviate significantly and in opposite directions from the experimental value). Hence, contrasting all of the results in Table 1 we can say unequivocally that AMOEBA is overall the best force field. Lastly, the NMR method for extracting the leading second rank tensor component g(2,2,0;r) is robust and may be readily extended to liquids with lower molecular symmetry. The methodology is also sensitive to mixtures with specific electrostatic interactions such as hydrogen bonding or quadrupole−quadrupole interactions, for example, benzene− hexafluorobenzene (unpublished results). Higher field NMR spectrometers (1.2 GHz) are currently being manufactured,29 thus enabling the method to provide a critical assessment tool for force fields and a facile way to explore subtle aspects of liquid-state structure.

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(6) Frenkel, D. Simulations: The Dark Side. Eur. Phys. J. Plus 2013, 128, 10. (7) Buckingham, A. D.; McLauchlan, K. A. High Resolution Nuclear Magnetic Resonance in Partially Oriented Molecules. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 2, 63−109. (8) Bastiaan, E. W.; Maclean, C. Molecular Orientation in High-Field High-Resolution NMR. In NMR at Very High Field; Robert, J. B., Ed.; Springer-Verlag: Berlin, 1991; pp 17−43. (9) Van Zijl, P. C. M.; MacLean, C.; Bothner-By, A. A. Angular Correlation and Diamagnetic Susceptibilities Studied by High Field NMR. J. Chem. Phys. 1985, 83, 4410. (10) Bothner-By, A. A.; Dadok, J.; Mishra, P. K.; Van Zijl, P. C. M. High-Field NMR Determination of Magnetic Susceptibility Tensors and Angular Correlation Factors of Halomethanes. J. Am. Chem. Soc. 1987, 109, 4180−4184. (11) Claessens, M.; Ferrario, M.; Ryckaert, J.-P. The Structure of Liquid Benzene. Mol. Phys. 1983, 50, 217−227. (12) Baker, C. M.; Grant, G. H. The Structure of Liquid Benzene. J. Chem. Theory Comput. 2006, 2, 947−955. (13) Hsu, C. S.; Chandler, D. RISM Calculation of the Structure of Liquid Chloroform. Mol. Phys. 1979, 37, 299−301. (14) Yin, C.-C.; Li, A. H.-T.; Chao, S. D. Liquid Chloroform Structure from Computer Simulation with a Full Ab Initio Intermolecular Interaction Potential. J. Chem. Phys. 2013, 139, 194501. (15) Heist, L. M.; Poon, C.-D.; Samulski, E. T.; Photinos, D. J.; Jokisaari, J.; Vaara, J.; Emsley, J. W.; Mamone, S.; Lelli, M. Benzene at 1 GHz. Magnetic Field-Induced Fine Structure. J. Magn. Reson. 2015, 258, 17−24. (16) Emsley, J. W. Nuclear Magnetic Resonance of Liquid Crystals; NATO ASI Series: Mathematical and Physical Sciences 141; Published in cooperation with NATO Scientific Affairs Division by D. Reidel Pub. Co.: Boston, 1985. (17) Kantola, A. M.; Ahola, S.; Vaara, J.; Saunavaara, J.; Jokisaari, J. Experimental and Quantum-Chemical Determination of the (2)H Quadrupole Coupling Tensor in Deuterated Benzenes. Phys. Chem. Chem. Phys. 2007, 9, 481−490. (18) Pyykkö, P.; Elmi, F. Deuteron Quadrupole Coupling in Benzene: Librational Corrections Using a Temperature-Dependent Einstein Model, and Summary. The Symmetries of Electric Field Gradients and Conditions for H = 1. Phys. Chem. Chem. Phys. 2008, 10, 3867−3871. (19) Ren, P.; Wu, C.; Ponder, J. W. Polarizable Atomic MultipoleBased Molecular Mechanics for Organic Molecules. J. Chem. Theory Comput. 2011, 7, 3143−3161. (20) Dang, L. X. Molecular Dynamics Study of Benzene−benzene and Benzene−potassium Ion Interactions Using Polarizable Potential Models. J. Chem. Phys. 2000, 113, 266. (21) ASTM Committee D-2 on Petroleum Products and Lubricants. Physical Constants of Hydrocarbons C1 to C10; ASTM STP 109A; American Society for Testing & Materials, 1963. (22) Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. L. Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides †. J. Phys. Chem. B 2001, 105, 6474−6487. (23) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; et al. All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. J. Phys. Chem. B 1998, 102, 3586−3616. (24) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. Molecular Mechanics. The MM3 Force Field for Hydrocarbons. 1. J. Am. Chem. Soc. 1989, 111, 8551−8566. (25) DiStasio, R. A.; von Helden, G.; Steele, R. P.; Head-Gordon, M. On the T-Shaped Structures of the Benzene Dimer. Chem. Phys. Lett. 2007, 437, 277−283. (26) Laatikainen, R.; Santa, H.; Hiltunen, Y.; Lounila, J. Dipolar Couplings in Strong Magnetic Field as Indicators of AromaticAromatic Interactions in Benzene-Benzene, Benzene-Hexafluorobenzene, and Benzene-2,6-Dichlorobenzaldehyde Systems. J. Magn. Reson., Ser. A 1993, 104, 238−241.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.5b01737. Experimental and computation methods. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (E.T.S.). *E-mail: [email protected] (D.J.P.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Szilvia Pothoczki for the experimental scattering data on CHCl3, colleagues Lee Pedersen, Max Berkowitz, and John Papanikolas for suggestions, Dr. Kevin Knagge (David H. Murdock Research Institute) for help securing the 950 MHz data, the Cary Boshamer Professorship fund for partial support of D.J.P. and E.T.S., and NSF MIRT (DMR 1122483) for L.M.H..

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REFERENCES

(1) Bernal, J. D. A Geometrical Approach to the Structure Of Liquids. Nature 1959, 183, 141−147. (2) Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids: Fundamentals; International Series of Monographs on Chemistry; Clarendon Press: New York, 1984. (3) Barrat, J. L.; Hansen, J. P. Basic Concepts for Simple and Complex Liquids; Cambridge University Press: Cambridge, U.K., 2003. (4) Allen, P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: New York, 1989. (5) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Academic Press: San Diego, CA, 2002. 3630


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The Journal of Physical Chemistry Letters (27) Jokisaari, J.; Hiltunen, Y. Deuteron Quadrupole Coupling Constants of Methyl Iodide and Chloroform Determined by NMR in Liquid-Crystalline Phases. J. Magn. Reson. 1984, 60, 307−319. (28) Fu, C.-F.; Tian, S. X. A Comparative Study for Molecular Dynamics Simulations of Liquid Benzene. J. Chem. Theory Comput. 2011, 7, 2240−2252. (29) Council, N. R. High Magnetic Field Science and Its Application in the United States: Current Status and Future Directions; The National Academies Press: Washington, DC, 2013.

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Liquid-State Structure via Very High-Field Nuclear Magnetic

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