The Most Loose Crystals of Organic Compounds - The Journal of

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The Most Loose Crystals of Organic Compounds Michał Kaźmierczak and Andrzej Katrusiak* Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland S Supporting Information *

ABSTRACT: Crystal structures of organic compounds with all intermolecular contacts longer than the sum of van der Waals radii can be classified as a loose state of solids. The survey of Cambridge Structural Database (CSD) revealed about 450 of such crystals. Specific features responsible for the loose arrangement are low magnitudes of electrostatic potential on the molecular surface and the concentric distribution of net atomic charges, reducing the contribution of electrostatic forces to the crystal cohesion interactions. Additionally, in the loose structures a partial mismatch between the requirement of molecular close-packing with electrostatic and specific directional interactions has been observed. Consequently, the cohesion forces are dominated by dispersion interactions, and their contribution is much larger compared to Coulombic and polarization energy. In the most loose compound presently deposited in the CSD, bis(trichlorosilyl)acetylene, the shortest of all contacts is by 0.256 Å longer than the sum of van der Waals radii, according to Bondi.

1. INTRODUCTION Density is one of the most basic characteristics of all compounds. It directly depends on the chemical composition, structure, and interactions. The density of compounds can be significant technologically; however, the main scientific interest is connected to the interplay of shape and interactions of molecules with their ability to efficiently aggregate and fill the space in crystals. Applications of general rules governing the molecular aggregation in crystals are countless, particularly in pharmaceutical and chemical practice.1−3 Kitaigorodskii postulated the close-packing rule for molecular aggregation in crystals.4 The molecular surface for these considerations was associated with the van der Waals (vdW) radii of atoms. On the other hand, it was demonstrated by Desiraju5,6 and others7,8 that the molecular aggregation in crystals is controlled by specific types of weak interactions. These interactions, associated with electrostatic potential distribution on the surface of functional groups, are directional, like weak hydrogen bonds CH···O and halogen···halogen contacts. Recently, Dance9−11 indicated that energy minima associated with interatomic contacts are considerably (about 0.4 Å) longer than the sums of vdW contacts, as determined by Bondi,12 Pauling,13 Kitaigorodski,4 and others.14,15 It was also found that there are crystal structures where all intermolecular contacts are longer than sums of vdW radii, for example 1,1-dichloroethane,16 1,1,1-trichloroethane,17 and benzene.18 In our study, the intermolecular contacts and molecular aggregation have been characterized by a contact parameter δ, defined as the shortest of all intermolecular contacts calculated as the difference of distance dij from atom i to atom j and their vdW radii δ = min(dij − vdWi − vdW) j © 2012 American Chemical Society

where min is the minimum function of all intermolecular contacts in the crystal, described as the arguments in the parentheses. The structures for which δ is positive (larger than 0 Å) will be termed loosely packed or loose crystals. High pressures of about 1 GPa are required before the δ parameter in 1,1dichloroethane and 1,1,1-trichloroethane are compressed to zero. An analogous crystal, chloroethane, crystallizes as either the loose or the closely packed phase depending on pressure.19 In crystalline benzene the contact parameter δ remains positive in the temperature range below the melting point and 150 K, while at 296 K pressure of about 0.2 GPa reduces δ to below 0 Å (Figure 1). The occurrence of loose structures can be interpreted as either (i) an underestimation of the vdW radii for some atoms, in certain molecules at least, for example to their librational vibrations, or (ii) that some kinds of molecules aggregate in crystals more loosely than others. Presently, we report the results of the Cambridge Structural Database (CSD) search aimed at retrieving all deposited structures where the shortest intermolecular contacts are longer than or equal to the sum of vdW radii. It was our intention to establish how common the loosely packed crystals are, if such crystals are specific for certain groups of substances, and if low-density phases can be considered as a state of condensed matter different than the closely packed state, where intermolecular contacts are equal to or shorter than the sums of vdW radii (e.g., δ < 0 Å). The compounds for which the loose arrangement has been evidenced until now are either liquid or gaseous at normal conditions. We intended to check if loose solids exist also at Received: November 19, 2012 Published: December 22, 2012

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Figure 2. Cumulant of structures as the function of distance δ (eq 1): orange bars represent structures retrieved automatically from CSD using ConQuest according to criteria 1−5 after covalent bonds of H atoms were normalized (C−H 1.089 Å, N−H 1.015 Å, O−H 0.993 Å);30 the solid line represents the structures left after criteria 1−5 have been checked manually, for all retrieved structures with δ ≥ 0.1 Å (navy-blue line) and for representative groups (of 10% structures retrieved automatically) in the 0 ≤ δ < 0.1 Å range (light-blue line).

Figure 1. Contact parameter δ in the function of temperature (at ambient pressure) and pressure (in room temperature) determined for benzene phase I (δI) and phase II (δII).18,20−24 The insets show the Hirshfeld surfaces of benzene molecules decorated with the color map of intermolecular distances scaled to the van der Waals radii of C and H according to Bondi.25

location of H atoms was scrutinized because X-rays are scattered by electrons, and X-ray diffraction experiments usually yield models with H atoms located too close to their carriers, as shown by neutron-diffraction measurements.29 This treatment of the structural models also corrected the positions of H atoms, located less precisely than other atoms. The normalization of H-positions was performed by using the bond length determined by neutron diffraction.27 The structures with positive contact parameter δ have been thoroughly inspected. In the first stage of this survey all 126 structures with δ ≥ 0.3 Å have been checked “manually” one by one. It occurred that each of these structures was either inconsistent with at least one of criteria 1−5 or contained apparent errors. The following main reasons of excluding the structural models can be listed: 1 The ConQuest search assumes that in framework organometallic structures (MOF’s), polymers (COF’s), or catenas, all the crystal is built of one (infinite) molecule, which has no intermolecular contacts at all, and thus these structures fulfill criteria 1−5 independently of the δ magnitude. In fact, an additional criterion (6) could be applied, that at least one intermolecular contact must be present. 2 Some structural models are incomplete due to missing H atoms. Another type of incompleteness is missing molecules or symmetry elements. For example, the structure of tetrakis(N-(p-tolyl)tetrachlorophthalimide) o-xylene (the REFCODE of the CSD entry: BAVVEZ) is described as triclinic, space group P1, Z = 8, but only one of eight independent molecules has its coordinates specified and, moreover, even two solvent molecules are missing. 31 In another structural deposit of triiodoheptakis(triphenylphosphine)undecagold (CAGCAO), all triphenylphosphine substitents are absent in the structural model.32 3 In several structures short contacts were not found by the ConQuest search, but they were found by program

normal conditions and if the energy of intermolecular interactions in loose solids is characteristic and different than in closely packed crystals. These questions are fundamental for understanding the rules governing molecular aggregation. In this study, the isotropic vdW radii have been applied as a reference criterion for analyzing intermolecular contacts at the first stage of survey, and in the further stages also anisotropic vdW radii26 have been used for halogen atoms, too.

2. EXPERIMENTAL SECTION The CSD (version 5.33 released in Nov 2011,27 ConQuest version 1.1428) has been searched for the structures fulfilling the following criteria: (1) The structural model must be complete, with 3-dimentional coordinates for all non-H atoms. (2) The structures must be ordered. (3) No structural errors can be present. (4) In the structures of compounds containing H atoms, at least one of them is determined. (5) There are no intermolecular distances dij between any atoms shorter than their vdW radii sum plus predefined distance δ. In other words, δ is the shortest of all intermolecular interatomic distances, after subtracting the vdW radii of the atoms in contact: Λ(d ij ∈ D) (dij < vdWi + vdWj + δ)

(2)

where dij are intermolecular distances between atoms i and j, D is the set of all intermolecular contacts between atoms, vdWi(j) is the van der Waals radius of atom i (j), and δ is the contact parameter. It was intended to obtain a histogram of structures as the function of the minimum δ magnitude. The histogram obtained for the retrieved from CSD structures fulfilling criteria 1−5 is shown in Figure 2. Multiple entries for the same structure (reinterpretations and redeterminations) have been excluded in order to avoid biased statistics due to the significance and interest in some compounds. When multiple entries were retrieved for a compound, the structure with the largest δ value was retained, unless errors in its determination were found. The 1442

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Mercury.33 We have noticed that this deficiency of ConQuest occurs for elongated triclinic or monoclinic and strongly oblique unit cells. For example, this type of disagreement between ConQuest and Mercury occurred for the structure of bis(μ4-oxo)tetrakis(μ3-trimethylacetato-O,O,O′)hexakis(μ2-trimethylacetato-O,O′)-tris(η1trimethylacetic acid)(η1-ethanol)tetrairon(II),diiron(III) trimethylacetic acid solvate (QEXZID). This crystal is triclinic, with the unit-cell dimensions a = 13.3719(14) Å, b = 15.7318(15) Å, c = 25.019(2) Å, α = 73.259(3)°, β = 79.599(4)°, and γ = 65.903(3)°.34 Similar problems occurred when the listed atoms were located away from the origin. 4 Despite specified option “not disordered” in the ConQuest search, some disordered structures sneaked into the hitlist (e.g., in 1,3,5-trichloro-2,4,6-trimethylbenzene, ZEPDAZ02). There are nine disordered atoms, each assuming at least two positions.35 Because of the reasons listed above, all but one of the 125 structures found for parameter δ ≥ 0.3 Å have been eliminated. This one remaining structure of hexamethylenetetramine (urotropine) determined at 296 K (HXMTAM2236) had the contact δ value of 0.314 Å. In fact, urotropine was thoroughly studied by X-rays and neutron diffraction in the function of temperature, and no phase transition was reported in this compound. There are 24 urotropine structures deposited in CSD. Their contact distance function δ(T) plotted in Figure 3

the structures with positive contact parameter are characteristic of specific types of chemical compounds. We have also calculated the contact parameter δ for the contacts involving halogen atoms by applying their anisotropic vdW radii.26 These calculations have been performed for all structures with δ larger than 0.1 Å, and the results are listed in Table S2. The contacts parameters based on anisotropic vdW radii are denoted δa. The δa magnitudes are generally similar to δ, and in most cases δa is larger than δ. The δa calculation included the Y−X′···X and X′···X−Y′ (X = halogen atom) angles, and they revealed that most of the halogen contacts in the loose crystals significantly divert from the favored type I and type II geometries37 (Table S2).

3. DISCUSSION The survey of CSD deposits (Figure 2) shows that there are only about 450 structures with parameter δ ≥ 0 Å. The number of structures quickly decreases for larger δ magnitudes, and there are only 21 structures with δ ≥ 0.14 Å and only seven structures with δ ≥ 0.2 Å. Almost all the compounds with δ ≥ 0 Å are molecular crystals; the only confirmed exception is tetraphenylphosphonium tetraiodomolybdate38 (YUCHOT, δ = 0.015 Å). All 67 crystals with δ ≥ 0.1 Å have been listed in Table S1 of the Supporting Information. All of them are single-component, molecular crystals. The inspection of these 67 crystals allows their most frequently represented features to be distinguished. There are 33 compounds with large bulky terminal substituents, like bis(trichlorosilyl)acetylene39 (WILWUJ, δ = 0.256 Å) and bis((μ2-di-tert-butylarsenido)divinylgallium)40 (NUJYUM, δ = 0.112 Å); 25 chlorine and fluorine derivatives, for example perchloro(4)radialene41 (CLMCBU10, δ = 0.114 Å) and cisdichlorofumaronitrile42 (DCFUMN, δ = 0.131 Å); 10 carbohydrates of various sizes, for example n-octadecane43 (NOCTDC, δ = 0.149 Å), and acetylene44 (ACETYL, δ = 0.203 Å); 3 arenes, for example hexaethynylbenzene45 (DODXEZ, δ = 0.13 Å); 13 complexes of transition metals, like bis(hexafluoroacetylacetonato)bis(tetrahydrofuran)nickel(II)46 (JILVEF, δ = 0.224 Å) and pentacarbonyliron47 (FOJBOV02, δ = 0.112 Å); 5 highly symmetric bulky polycyclic molecules, such as hexamethylenetetramine36 (HXMTAM17, δ = 0.129 Å, molecular symmetry Td) and cubane48 (CUBANE, δ = 0.183 Å, molecular symmetry Oh). The most loose crystal presently found in the CSD is bis(trichlorosilyl)acetylene (WILWUJ,39 Scheme 1), where the closest intermolecular distance δ of 0.256 Å is between two chlorine atoms. The Si−Cl···Cl and Cl···Cl−Si angles are 130.84° and 97.73°, respectively, which are incompatible with neither type I nor type II halogen···halogen interaction.37 In the second most loose crystal, tris(tert-butyl)boron49 (JAZGEX), the closest distance δ = 0.235 Å is for H···H contacts, then bis(hexafluoroacetylacetonato)−bis(tetrahydrofuran)nickel(II)46 (JILVEF) with δ = 0.224 Å is for a F···H contact, and in 1,1,1-trichloroethane14 (MECHLF12) δ = 0.213 Å for Cl···Cl contacts. The fifth and sixth most loose crystals (2-(1-(ptolylimino)ethyl)ferrocenyl)chloro(pyridine-N)palladium50 (CIDRUD) and acetylene44 (ACETYL) have the same δ = 0.203 Å, and in both these structures the shortest contacts (relative to the vdW radii) involve H···C atoms. In the crystal of 1,1-dichloroethane, for which it was noticed that all contacts can be longer than the sums of vdW radii, the contact parameter δ is 0.075 Å.

Figure 3. Contact parameter δ in the function of temperature determined for 24 urotropine structures retrieved from the CSD. Green arrows indicate the δ magnitude of HXMTAM22 before (the red point, δ = 0.314 Å) and after correction (0.127 Å). The urotropine molecule is shown in the inset.

reveals that the δ value of 0.314 Å is an outlier. It is not only an outlier off the δ(T) trend line but also an outlier over 2.5 times larger than 14 urotropine structures measured at a similar temperature close to 296 K. Then it occurred that H atoms in CSD deposit HXMTAM22 had wrong positions due to confused H-coordinates signs in the original paper.36 After correcting this error, the recalculated δ fitted well with the trend line, and the HXMTAM22 structure has been retained in the list of loose structures, but with the δ parameter equal to 0.127 Å. It can be argued that similar outliers exist also among other structures with 0 ≥ Å. However, it can be shown for the structures determined at various conditions that δ magnitudes consistently change with pressure and temperature, as shown for benzene (Figure 1) and urotropine (Figure 3). Moreover, 1443

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Scheme 1. Six Most Loose Crystals Deposited in the CSD, Their REFCODES, and δ Values

Figure 5. Electrostatic potential distribution on the molecular isosurface (defined at 0.001 au electron density calculated by Gaussian 03W, Version 6.1, at the b3lyp/3-21g level of theory) for bis(trichlorosilyl)acetylene (WILWUJ), tri-tert-butylboron (JAZGEX), acetylene (ACETYL), and benzene (BENZEN18) (cf. Scheme 1). The common color scale of electrostatic potential has been applied.51

are arranged according to the match of opposite electrostatic potentials on the molecular surface, but in the loose crystals there are also unfavorable contacts between electrostatic potentials of the same sign that reduce the electrostatic attraction. Owing to the loose arrangement and increased intermolecular distances, the electrostatic repulsion is reduced, too, and the cohesion forces are dominated by dispersion interactions, as it has been shown by theoretical energy calculations presented below. The contacts with mismatched electrostatic potential of the same sign can disappear when molecules change their mutual orientation. This type of molecular rearrangement take place at the phase transitions of benzene18 and chloroethane.17 In the only ionic loose crystal, tetraphenylphosphonium tetraiodomolybdate38 (YUCHOT, δ = 0.015 Å), the cations are large and highly symmetric (pseudo T-symmetric point group), which reduces the magnitudes of electrostatic potential on the surface of the ions. The lattice energy of the most loose crystals have been calculated by Gaussian W03 at the MP2/6-31G** level of theory and CLP Program suite applying the PIXEL approach.48 The lattice energy (Elatt) is decomposed in this program into Columbic (ECoul), polarization (Epol), dispersion (Edisp), and repulsions (Erep) contributions (Table 1). It is characteristic of the loose crystals that their ECoul and Epol components are small and that Edisp is the largest negative contribution. In this respect the loose structures resemble the molecular crystals of naphthoquinone and anthracene. However, in the hydrogenbonded crystals of sucrose and urea the ECoul and Edisp are much more significant, and the contribution of Edisp is much smaller. Also, the Erep component is much larger in (+)-sucrose and urea, which is connected with shorter intermolecular distances in the closely packed crystal.

It is characteristic of majority of loose structures that they are molecular crystals with highly symmetric bulky molecules and the electric dipole moment close to or equal to zero. The only exception indicated above, YUCHOT, is built of large highly symmetric ions. The highly symmetric crystallographic systems among loose crystals are more frequent than among all structures deposited in CSD (Figure 4). Many of loose crystals

Figure 4. Distribution of all structures grouped according to crystallographic systems, for all structures in CSD (red line), and among the loosely packed crystals (δ ≥ 0 Å, blue line).

have a characteristic charge distribution which can be described as a centric one. For example, in benzene the negative electrostatic potential at the center of the ring is counterbalanced by positive potential on the molecular surface surrounding the hydrogen atoms. This feature of electrostatic potential distribution has been illustrated for the molecules of WILWUJ, JAZGEX, ACETYL, and BENZEN18 in Figure 5. In most structures the molecules arrange their packing just to avoid counterposition of the same sign charges; however, in many of the loose structures such a counterposition of charges cannot be avoided. Thus, most of the intermolecular contacts

4. CONCLUSIONS The survey of CSD confirms that there are crystals considerably more loosely packed than others. When referred to atomic vdW radii, in about 0.075% of all CSD entries no contacts are 1444

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Table 1. Crystal Lattice Energy (Elatt) Decomposed into Coulombic (ECoul), Polarization (Epol), Dispersion (Edisp), and Repulsion (Erep) Components, Computed by Program Suite CLP52 for the Most Loose Crystalsa compd

ECoul

Epol

Edisp

Erep

Elatt

ACETYL BENZEN18 CUBANE HXMTAM17 JAZGEX NOCTDC WILWUJ anthracene naphthoquinone urea (+)-sucrose

−12.2 −13.8 −13.6 −37.3 −3.0 −21.9 −20.9 −26.1 −36.7 −97.6 −324.1

−7.2 −5.1 −5.2 −12.0 −1.0 −8.0 −8.9 −12.3 −11.4 −32.3 −134.4

−17.3 −57.7 −70.0 −85.9 −71.6 −165.5 −132.3 −115.9 −105.9 −41.5 −196.9

9.3 27.7 42.5 46.3 13.8 76.6 65.6 68.4 51.8 75.0 356.7

−27.4 −48.9 −43.7 −89.0 −61.8 −118.8 −86.5 −85.9 −102.2 −96.4 −298.7

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ASSOCIATED CONTENT

* Supporting Information S

List of crystal structures with δ ≥ 0.1 Å and their melting points; contact parameter δ recalculated according to anisotropic van der Waals radii. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by The Foundation for Polish Science, Team Programme, Grant 2009-4/6.

a

The loose crystals have been listed with their REFCODES. The energies for anthracene,53 naphthoquinone,53 urea,53 and (+)-sucrose have been also indicated for a reference to the structures with negative contact paramter δ. All energy magnitudes are expressed in kJ mol−1, so they depend on the size of molecules.

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REFERENCES

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formed between molecules (e.g., the contact parameter δ is positive). We found that loose crystals are not necessarily stable only at low temperature, as of 37 entries for which δ ≥ 0.1 Å and the mp was available, 6 have their mp above 500 K, and 18 crystals melt above 400 K (Table S1). However, there are also loose crystals that melt at low temperature, and it appears that the CSD can be biased in this respect that loose structures are under-represented due to their low melting point and usually more complex experimental procedures required for measuring diffractometric data. The common features of loose crystals are weak cohesion forces and directional preferences of specific interactions inconsistent with requirements of crystal packing. This features can be illustrated by the structures of isomeric chloroethanes, for example, 1,2-dichloroethane54 and 1,1dichloroethane,16 or 1,1,2-trichloroethane,55 and 1,1,1-trichloroethane.17 Small electrostatic and polar contributions to the cohesion forces in loose crystals, compared to the dispersion interactions, are due to low net atomic charges and their centric distribution in molecules, while the energy of repulsive interactions is also relatively low owing to the long intermolecular distances. The effect of pressure on loose structures is either a monotonic compression (like in 1,1dichloroethane and 1,1,1-trichloroethane) or a transition to closely packed phase (chloroethane, benzene II). There are considerable differences between loose crystals in the magnitudes of pressure necessary for compressing the contact parameter δ to 0 Å. In this context the concept of loose crystals can be valuable and useful for characterizing the interplay of intermolecular interactions, molecular arrangement, and thermodynamic conditions. Furthermore, the loose association may be particularly relevant to the amorphous and liquid state and may also be associated with parts of crystal structures, as opposed to fully loose crystals, where δ ≥ 0 Å. These aspects of the loose association are still under study. Noteworthy, more than 70 years after the concept of van der Waals radii was successfully applied as a basic reference for investigating intermolecular interactions in crystals,56 it affords a new application in identifying the chemical features of loosely aggregating compounds. 1445

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dx.doi.org/10.1021/jp311403k | J. Phys. Chem. C 2013, 117, 1441−1446