Quantifying the Inter- and Intramolecular Interactions in Crystalline

Article pubs.acs.org/crystal

Quantifying the Inter- and Intramolecular Interactions in Crystalline Phthalic Acid Published as part of the Crystal Growth & Design Mikhail Antipin Memorial virtual special issue Vladimir V. Zhurov and A. Alan Pinkerton* University of Toledo, Toledo, Ohio 43606, United States S Supporting Information *

ABSTRACT: All inter- and intramolecular interactions in the crystals of phthalic acid have been quantified from the topology of the electron density distribution obtained from low temperature (20 K) X-ray diffraction data and from theoretical calculations. Using the Quantum Theory of Atoms in Molecules (QTAIM) approach, all covalent bonds have been characterized by the electronic properties at their (3, −1) bond critical points as well as all noncovalent bonds of the type O···H (both strong and weak), C···C, O···O, O···C, and H···H. Integrated atomic charges and the derived molecular dipole moment are reported. Differentiation of the two faces of the pyramidalized sp2 carbon atoms is investigated via the electrostatic potential projected onto the molecular surface.

1. INTRODUCTION

potential for characterizing C···C, O···O, O···C, and H···H interactions was recognized. Although perhaps not relevant to crystal engineering, the phthalic acid molecule exhibits pyramidalization of two sp2 hybridized carbon atoms.10 This is a common observation in strained organic molecules, for example, in norbornene derivatives, and affects the stereoselectivity of their chemistry.11,12 Hence, we also have the opportunity to examine the impact of pyramidalization on the electron density distribution and the derived electrostatic potential.

The field of crystal engineering is largely based on identifying or predicting the strength and directionality of intermolecular interactions.1 By far the most important among them is the hydrogen bond, and the literature describing structural motifs that are determined by the geometry allowed by hydrogen bonds is vast.2 However, it is becoming clear that there are other types of noncovalent interactions that also have the potential to guide the organization of molecules in the solid state, although rarely of the same magnitude as hydrogen bonds. As stated by Aakeröy,1 “an improved understanding of the strength, directional behaviour, structural inf luence, in short, the very essence of non-covalent forces, becomes the underlying focus for initial research into crystal engineering.” Hence, in order to have an appreciation of the strength of such noncovalent bonds, it is informative to estimate their interaction energies from the topological analysis of the electron density using the quantum theory of atoms in molecules (QTAIM) approach.3 For every pair of atoms linked by a bond path, the energy of these closed shell interactions may be estimated from the potential energy density at the bond critical point,4 which in turn is calculated from the electron density (ρ(r)), and its first and second derivatives (∇ρ(r) and ∇2ρ(r)).5−8 The values for ρ(r), ∇ρ(r), and ∇2ρ(r) may be obtained from careful low temperature Xray diffraction experiments or from theoretical calculations with periodic boundary conditions.9 We have chosen to determine the electron density distribution in phthalic acid crystals because the known structure suggested that we would be able to quantify both classical carboxylic acid hydrogen bonding, as well as weaker CH···O bonds. In addition, based only on distances, the © XXXX American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Data Collection and Reduction. A colorless, single crystal of phthalic acid (0.33 × 0.23 × 0.14 mm3) was chosen from those grown by slow evaporation from single drops of a 2:1 water/methanol solution on a paraffin film. This crystal was mounted in oil on a capillary with a thin nylon loop and cooled to 20 K using an open flow, liquid helium device.13 The intensity data were collected on a Rigaku diffractometer comprising an ULTRAX-18 rotating anode (Mo, graphite monochromator) generator operating at 50 kV and 300 mA, and a RAPID cylindrical image plate detector.14 Data were collected using 100 s, 6° omega oscillations with 3° of overlap in 12 runs covering 180° each. The goniometer angles for the runs were set to χ = 0° (φ = 0, 180°), χ = 40° (φ = 0, 90, 180, 270°) thus ensuring adequate data redundancy. Indexing was carried out with HKL2000,15 and integrated intensities determined using VIIPP applying background and reflection profiles averaged over the complete data set as previously described.16,17 Scaling and merging of the data was carried out with the program SORTAV.18 Received: July 1, 2014 Revised: September 12, 2014

A

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2.2. Electron Density Model Refinement. The structure was initially resolved and refined using the SHELXTL suite.19 This independent atom model was then used as the starting point for refinement of the electron density using the Hansen-Coppens multipole formalism20 implemented in the program XD2006.21 In the multipole model, we represent the total electron density in the crystal as a superposition of individual aspherical atoms, whose electron density is calculated according to l

4

ρ(r) = Pcρc (r ) + Pvκs3ρv (κsr ) +

refinement is shown in Figure 1. The quality of the data and refinement model was confirmed with a normal probability plot, a scale factor plot with respect to resolution, and fractal analysis24 of the residual density. The corresponding plots have been deposited as well as tables of observed and calculated structure factors. The total electron density as well as its derivatives were calculated from the refined multipole parameters. A static deformation map is shown in Figure 2. The topology of the total electron density was analyzed, in particular to characterize all of the bond critical points, both intra- and intermolecular using the program WinXPRO.26 Derived values are reported in Table 2a. Using the local virial theorem and the DFT formulas, the kinetic (gb) and potential (νb) energy densities at the bond critical points were calculated from the electron density and its derivatives for all interactions. As has been previously suggested,4 the energy of weak, closed shell interactions may be estimated as Eint = −νb/2, and these values are included in Table 2b. Although this empirical relationship was originally determined for hydrogen bonds, it has been extrapolated to give reasonable values for all closed shell, weak interactions. Integrated properties (atomic volumes and charges) for all atomic basins (delimited by zero flux surfaces) have also been determined and are reported in Table 3. 2.3. Theoretical Calculations. A density functional theory (DFT) calculation with periodic boundary conditions was carried out with the CRYSTAL09 package27 using the B3LYP functional. The (8s)(411sp)-(1d1d) and (6s)-(311sp)-(1d1d) basis sets28 were chosen for oxygen and carbon atoms, respectively, and the more common 6311G** basis was used for hydrogen atoms. No geometry optimization was performed, i.e., the unit cell and atomic coordinates were fixed to those obtained from the experiment and the final multipole refinement. Topological analysis of the resulting electron density distribution was carried out with TOPOND.29 Static theoretical structure factors were then calculated corresponding to the same (sin θ/λ)max as for the experimental data set, and used as a basis for a similar multipole refinement with the scale factor fixed to unity and all ADP’s fixed to zero. Unlike for the experimental refinement, the κ0 − κ4 were allowed to refine separately within a single atom type. The topological analysis of the resulting electron density was carried out as for the experimental results.

∑ κl3Rl(κlr) ∑ Plm ±ylm ± (r/r) l=0

m=0

where ρc and ρv are spherical core and valence densities normalized to one electron. In the last term, which accounts for the aspherical deformation, Rl are normalized Slater-type radial functions, ylm± are density normalized real angular spherical harmonics. The parameters κs and κl allow contraction/expansion of the spherical and aspherical valence parts, respectively. Refinement was on F over all merged data with I/σ(I) > 3 using the VM databank. In the initial cycles of refinement a variety of chemical and symmetry constraints were applied. These were gradually released and the final model only constrained κ0 − κ4 to common values by atom type (C, O), κs, and κ0 − κ4 for hydrogen being set to 1.2. Thus, all multipoles up to hexadecapoles were refined for C and O atoms, and three dipoles and the P20 quadrupole for hydrogens. As previously shown,17 including two monopole terms, Pv and P00, for C and O in the refinement improves the fit in the core region. All atoms were refined with anisotropic displacement parameters, and at such a low temperature (20 K), there was no apparent anharmonic contribution to the ADP’s. The data quality was sufficient such that both the position and the anisotropic displacement parameters were cleanly refined for the hydrogen atoms. The viability of this approach was previously demonstrated by a comparison of X-ray and neutron diffraction experiments in the explosive RDX.22 Additional justification for this refinement here is provided by comparison of the experimental ADP’s with those obtained from SHADE.23 The results have been deposited. The electroneutrality constraint was maintained throughout the refinement. A crystallographic summary is reported in Table 1, and full details have been deposited. A plot of the molecule from the final

3. RESULTS Phthalic acid is known to crystallize in space group C2/c with four molecules per unit cell, each molecule having twofold symmetry.10 As previously noted, the carboxylic acid groups are not coplanar with the aromatic ring, the rotation about C(1)− C(2) being approximately 35°. This distortion is also reflected in the observed pyramidalization of C(2), the corresponding C(1)−C(2)−C(2a)−C(1a) torsion angle being 20.5°, as well as in the slight lengthening of the C(2)−C(2a) bond by 0.014 Å compared to the other aromatic C−C bonds. The molecules are linked into chains by classical cyclic carboxylic acid hydrogen bonded motifs (Figure 1).30 We note that all C−H bond distances are in good agreement with those anticipated from neutron diffraction studies; however, the O−H distance appears to be ∼0.1 Å short. Despite this, as there is no evidence for unmodeled electron density around the hydrogen position, we believe the model to be adequate. The following analysis of the electron density distribution will be organized as follows: First, the properties of the molecule and its strongly covalent bonds will be discussed. Then, the integrated atomic properties will be presented coupled with the estimation of the molecular dipole moment. The electrostatic potential on the molecular surface will be discussed in relation to the pyramidalization of the aromatic carbon atoms carrying the carboxylic acid groups. Finally, the weaker interactions, both intra- and intermolecular, will be analyzed. Discussion will be mainly provided using the

Table 1. Crystallographic Data for Phthalic Acid Chemical formula Space group a (Å) b (Å) c (Å) β (deg) Volume (Å3), Z T (K) Wavelength λ (Å) Crystal size (mm) (sin θ/ λ)max (Å−1) Reflections integrated Rint/average data multiplicity Completeness: sin θ/λ < 1.00 Å−1, all data (%) Independent reflections Observed reflections (I > 3σ) Spherical atom refinement R1, wR2, GOF Δρmin/max e Å−3 Multipole refinement R1, wR2, GOF Weighting scheme: a, ba Δρmin/max e Å−3 all data, sin θ/λ < 1.0 Å−1 a

C8H6O4 C2/c 4.9917(2) 14.1715(5) 9.5119(4) 94.629(3) 670.68(5), 4 20.0(1) 0.71073 0.33 × 0.23 × 0.14 1.32 63075 0.016/10.2 99.4, 94.2 6159 5040 0.0276, 0.0818, 1.094 −0.38/0.63 0.0159, 0.0140, 0.9865 0.01, 0.01 −0.188/0.216, −0.083/0.089

w2 = 1/{σ2(F2) + (ap)2 + bp}, p = 03333F2obs + 0.6667F2calc B

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Figure 1. (a) Phthalic acid, 99% probability ellipsoids,25 (b) hydrogen bonded chains drawn perpendicular to a,25 (c) unique intramolecular bond critical points shown as yellow spheres.26

Figure 2. (a) Experimental static deformation map in the plane of the aromatic ring, (b) experimental static deformation map in the plane of the carboxylate group, (c) experimental residual density map in the plane of the aromatic ring (data to sin θ/λ ≤ 1.0 Å−1). Contours are 0.10 e Å−3 for (a), (b), and 0.05 e Å−3 for (c).

parameters derived from the experimental data; however, the agreement with theory is typically very good. The tabulated values of the properties of the covalent bond critical points (Table 2a) are organized with three lines per atom, results from the experimental multipole values, the same values obtained by refining against theoretical structure factors, and the results from pure theory. Similar information for the noncovalent, weak interactions is reported in Table 2b. Throughout this paper, when such numerical comparisons are made, they will be in the same order, and color coded red, blue, and magenta as in Table 2a and b. 3.1. Molecular Properties. Static deformation maps in the aromatic plane and in that of the carboxylate group are shown in Figure 2, along with a residual density map. Equivalent maps for results from pure theory or from refinements against theoretical structure factors are very similar and have been deposited. All covalent bonds are represented by accumulation of electron density, and there are two clearly defined lone pairs on the carboxyl oxygen atom. In contrast, the two lone pairs on the OH group expected from our previous work on phenolic compounds31 are not distinguished, the corresponding electron density being smoothly distributed in the plane perpendicular to the C−O−H plane (Figure 3) as has been previously observed for other OH groups.32

The strength of the covalent bonds can be inferred from the electron density and its Laplacian at the bond critical points. The most elegant way to make this comparison is via determination of the topological bond order, ntopo, as suggested by Howard and Lamarche.33 ntopo = a + bλ3 + c(λ1 + λ 2) + dρb

Values of the coefficients for the various bond types have been previously published.34 All aromatic C−C bonds have ntopo = 1.295−1.356, the lowest corresponding to the slightly extended C(2)−C(2a) bond, with a concomitant strengthening of the C(4)−C(4a) bond. The lack of conjugation of the carboxylate to the aromatic ring is confirmed by ntopo = 0.999 for C(1)−C(2). The impact of hydrogen bonding on the acid group is manifested by a weakening of O−H bond (ntopo = 0.383) and the CO double bond (ntopo = 1.465). The complete set of bond orders is listed in Table 2. Atomic charges obtained from integration of the electron density of the volume elements delimited by the zero flux surfaces are reported in Table 3. Again, the agreement between theory and experiment is very good. Both oxygens carry significant negative charges; the carboxylate carbon atom is highly positive, whereas the other carbons are essentially C

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Table 2. Properties of the (a) Covalent and (b) Noncovalent Bond Critical Pointsa

First line (red) from the multipole fit to experimental data, second line (blue) from the multipole fit to theoretical structure factors, third line (magenta) directly from theory. a

D

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torsion angles. This magnitude of O···O interaction energy is modest for an intramolecular interaction. Values of 19.6 and 20.4 kJ mol−1 have been previously observed for the dinitramide anion,8,37 and values up to 13.9 kJ mol−1 have been calculated for the enol form of cis-β-diketones.38 In contrast, similar intermolecular interactions are known to be weaker, and range from 1.3 to 6.6 kJ mol−1.17,39 Of the intermolecular interactions, clearly the most important is the hydrogen bond that links the carboxylate groups in pairs (Figure 5a), and is responsible for the ribbon formation shown in Figure 1. With an estimated interaction energy of 65.1 kJ mol−1 per hydrogen bond, this is well within the normal range for such interactions (50.8−73.8 kJ mol−1).41 The hydrogen bonded ribbons are joined together by a series of weaker O···H, O···O, O···C, C···C, and H···H interactions. These have been separated into groups in Figure 5 for clarity. It is not unusual to attribute the bond paths perpendicular to the aromatic rings to π···π interactions; however, we note that the bond paths clearly terminate at the carbon atoms. The bifurcated hydrogen bond (CH···O and CH···H) observed in Figure 5a is an unusual motif. Although the crystal packing is largely dominated by the hydrogen bond linking the carboxylate groups, in terms of both the energy and the directionality of the interaction, the stabilization provided by the additional 11 weaker interactions represents an additional 37.1 kJ mol−1, albeit with much less directional preference. None of the individual energies listed in Table 2 for these weak intermolecular interactions are unusual. We have previously observed values for O···H (1.4−11.3 kJ mol−1), O···C (2.6−8.7 kJ mol−1), C···C (3.4−4.5 kJ mol−1), and H···H (1.3−5.2 kJ mol−1).17,22,31,39,42 However, together they provide sufficient energy to modify any prediction of crystal packing based on hydrogen bonded motifs alone.

Table 3. Integrated Atomic Charges and Volumes from Experiment (columns 2, 3), Theoretical Structure Factors (columns 4, 5), and Theory (columns 6, 7)

neutral. The acidic hydrogen is strongly positive, while the aromatic hydrogens carry minimal charge. The molecular dipole moment derived from either the atomic multipole parameters, 4.22 (expt.), 3.57 (theory) D, or from the integrated atomic charges and dipole moments, 4.97 (expt.), 4.50 (theory) D, may be compared with the experimental values of 2.30 or 2.599 D reported in dioxane solution.35,36 As discussed above, due to the torsion about the C(2)− C(2a) bond, these sp2 hybridized carbon atoms are significantly pyramidalized. Any impact of pyramidalization on the reaction chemistry should be reflected in an asymmetry in the electrostatic potential. From the experimental result in Figure 4a, there does indeed appear to be a loss of mirror symmetry (left to right) across the aromatic ring. The left to right twofold symmetry is maintained due to the space group. However, we are reluctant to draw conclusions from this rather subtle effect on the electrostatic potential as there are significant differences between the results obtained from experimental and theoretical structure factors (Figure 4b). 3.2. Noncovalent Interactions. Traditionally one would attribute the distortion of the carboxylic acid groups from coplanarity with the aromatic ring to steric repulsion of the neighboring oxygen atoms O(1) and O(1a). However, this is not the whole story, as shown by the presence of a bond path between these two atoms. Assuming the validity of the Espinosa et al. correlation4 for this weak, closed shell, noncovalent interaction, at the equilibrium geometry there is a stabilization of ∼9.4 kJ mol−1, which would be lost at higher or lower

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CONCLUSION We have presented the results of a combined charge density analysis from a low temperature (20 K) X-ray experiment and theoretical calculations with periodic boundary conditions for crystalline phthalic acid. All intra- and intermolecular interactions together with integrated charge density properties have been characterized based on QTAIM analysis. From consideration of the topological bond orders within the aromatic ring we see that the C(2)-C(2a) bond is weakened by ∼0.03, and the opposite C(4)-C(4a) bond strengthened by

Figure 3. (a) Deformation density isosurface (0.2 e Å−3) for the OH oxygen atom showing the extended lone pair region to the left, the O−H bond to the right, and the O−C bond down; (b) deformation map through the lone pair region, contour level 0.10 e Å−3. E

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Figure 4. Electrostatic potential (−0.12 to 0.12 eÅ−1) mapped onto the molecular surface (0.001 au = 0.00675 eÅ−3) obtained from (a) experiment and (b) solid state theory calculations.40

Figure 5. Bond paths (blue) and bond critical points (yellow): (a) unique intramolecular interactions, strong intermolecular carboxylate hydrogen bonds, weak CH···O and H···H interactions, (b) weak interactions involving O(2) or C(3), (c) weak interactions involving O(1), (d) weak interactions involving H(4).26

fractal dimension plot, hydrogen bonded ribbons, observed and calculated structure factors, summary intensity statistics from SORTAV, comparison of refined hydrogen ADP’s and SHADE calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

approximately the same amount, compared to bond orders of 1.322 for the other aromatic C−C bonds. The lack of conjugation of the carboxylate group to the aromatic ring is confirmed by an observed bond order of 0.999. The crystal packing is largely dominated by the hydrogen bonds (65.1 kJ mol−1), but this is supplemented by C···C (2.8 kJ mol−1 ave.), O···O (3.0 kJ mol−1 ave.), H···H (2.45 kJ mol−1), CH···O (4.5 kJ mol−1 ave.), and O···C (2.9 kJ mol−1) weaker interactions, which sum to 35.4 kJ mol−1 per asymmetric unit. The stabilization effect of the O(1)···O(1a) intramolecular bond on the molecular geometry has been discussed, as well as the pyramidalization of the C(2) carbon atom.

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AUTHOR INFORMATION

Corresponding Author

*Tel. (419) 530-4580, fax (419)530-4033, e-mail a.pinkerton@ utoledo.edu. Author Contributions

The manuscript was written through equal contributions of all authors. All authors have given approval to the final version of the manuscript.

ASSOCIATED CONTENT

S Supporting Information *

Crystallographic information file (CIF) including full multipole refinement for phthalic acid, residual Fourier maps, deformation density maps, normal probability plot and scale factor plot,

Funding

This work was supported by the National Science Foundation (grant NSF-CHE-1213329). F

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Notes

(29) Gatti, C. TOPOND-98: An Electron Density Topological Program for Systems Periodic in N (N=0−3) Dimensions. User’s Manual; CNRISTM: Milano, 1999. (30) Leiserowitz, L. Acta Crystallogr. 1976, B32, 775−802. (31) (a) Zhurova, E. A.; Matta, C. F.; Wu, N.; Zhurov, V. V.; Pinkerton, A. A. J. Am. Chem. Soc. 2006, 128, 8849−8861. (b) Parrish, D.; Zhurova, E. A.; Kirschbaum, K.; Pinkerton, A. A. J. Phys. Chem. B 2006, 110, 26442−26447. (c) Yearley, E. J.; Zhurova, E. A.; Zhurov, V. V.; Pinkerton, A. A. J. Am. Chem. Soc. 2007, 129, 15013−15021. (d) Yearley, E. J.; Zhurova, E. A.; Zhurov, V. V.; Pinkerton, A. A. J. Mol. Struct. 2008, 890, 240−248. (e) Zhurova, E. A.; Zhurov, V. V.; Chopra, D.; Stash, A. I.; Pinkerton, A. A. J. Am. Chem. Soc. 2009, 131, 17260−17269. (32) Nassour, A.; Kubicki, M.; Wright, J.; Borowiak, T.; Dutkiewicz, G.; Lecomte, C.; Jelsch, C. Acta Crystallogr. 2014, B70, 197−211. (33) Howard, S. T.; Lamarche, O. J. Phys. Org. Chem. 2003, 16, 133− 141. (34) (a) Tsirelson, V. G.; Stash, A. I.; Potemkin, V. A.; Rykounov, A. A.; Shutalev, A. D.; Zhurova, E. A.; Zhurov, V. V.; Pinkerton, A. A.; Gurskaya, G. V.; Zavodnik, V. E. Acta Crystallogr. 2006, B62, 676−688. (b) Tsirelson, V. G.; Bartashevich, E. V.; Stash, A. I.; Potemkin, V. A. Acta Crystallogr. 2007, B63, 142−150. (c) Bartashevich, E. V.; Nikulov, D. K.; Vener, M. V.; Tsirelson, V. G. Comp. Theor. Chem. 2011, 973, 33−39. (35) Narisimhan, P. T. J. Ind. Inst. Sci. 1955, 37A, 35−38. (36) Yaws, C. L. Thermophysical Properties of Chemicals and Hydrocarbons, electronic ed.; Knovel, 2010; p 678. (37) Zhurova, E. A.; Tsirelson, V. G.; Stash, A. I.; Pinkerton, A. A. J. Am. Chem. Soc. 2002, 124, 4574−4575. (38) Pakiari, A. H.; Eskandari, K. J. Mol. Struc. THEOCHEM 2007, 806, 1−7. (39) (a) Zhurova, E. A.; Stash, A. I.; Tsirelson, V. G.; Zhurov, V. V.; Bartashevich, E. V.; Potemkin, V. A.; Pinkerton, A. A. J. Am. Chem. Soc. 2006, 128, 14728−14734. (b) Chen, Y.-S.; Stash, A. I.; Pinkerton, A. A. Acta Crystallogr. 2007, B63, 309−318. (c) Zhurova, E. A.; Zhurov, V. V.; Pinkerton, A. A. J. Am. Chem. Soc. 2007, 129, 13887−13893. (d) Piccoli, P. M. B.; Koetzle, T. F.; Schultz, A. J.; Zhurova, E. A.; Stare, J.; Pinkerton, A. A.; Eckert, J.; Hadzi, D. J. Phys. Chem. B 2008, 112, 6667−6677. (40) Hübschle, C. B.; Luger, P. J. Appl. Crystallogr. 2006, 39, 901− 904. (41) (a) Bach, A.; Lentz, D.; Luger, P. J. Phys. Chem. A 2001, 105, 7405−7412. (b) Munshi, P.; Guru Row, T. N. Acta Crystallogr. 2006, B62, 612−626. (c) Howard, J. A. K.; Mahon, M. F.; Raithby, P. R.; Sparkes, H. A. Acta Crystallogr. 2009, B65, 230−237. (d) Hathwar, V. R.; Thakur, T. S.; Guru Row, T. N.; Desiraju, G. R. Cryst. Growth Des. 2011, 11, 616−623. (e) Hathwar, V. R.; Guru Row, T. N. Cryst. Growth Des. 2011, 11, 1338−1346. (f) Hathwar, V. R.; Thakur, T. S.; Dubey, R.; Pavan, M. S.; Guru Row, T. N.; Desiraju, G. R. J. Phys. Chem. A 2011, 115, 12852−12863. (g) Arputharaj, D. S.; Hathwar, V. R.; Guru Row, T. N.; Kumaradhas, P. Cryst. Growth Des. 2012, 12, 4357−4366. (42) (a) Zhurova, E. A.; Tsirelson, V. G.; Zhurov, V. V.; Stash, A. I.; Pinkerton, A. A. Acta Crystallogr. 2006, B62, 513−520. (b) Chopra, D.; Zhurov, V. V.; Zhurova, E. A.; Pinkerton, A. A. J. Org. Chem. 2009, 74, 2389−2395. (c) Shishkina, A. V.; Zhurov, V. V.; Stash, A. I.; Vener, M. V.; Pinkerton, A. A.; Tsirelson, V. G. Cryst. Growth Des. 2013, 13, 816−828.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. C. Gatti for providing a preliminary Windows version of TOPOND, and for helpful discussions. REFERENCES

(1) Aakeröy, C. B. Acta Crystallogr. 1997, B53, 569−586. (2) Galek, P. T. A.; Chisholm, J. A.; Pidcock, E.; Wood, P. A. Acta Crystallogr. 2014, B70, 91−105. (3) Bader, R. F. W. Atoms in Molecules: A Quantum Theory. The International Series of Monographs of Chemistry, No.22; Clarendon Press: Oxford, 1990. (4) Espinosa, E.; Molins, E.; Lecomte, C. Chem. Phys. Lett. 1998, 285, 170−173. (5) Abramov, Yu. Acta Crystallogr. 1997, A53, 264−272. (6) Tsirelson, V. G. Acta Crystallogr. 2002, B58, 632−639. (7) Tsirelson, V. G.; Stash, A. I. Acta Crystallogr. 2004, A60, 418− 426. (8) Zhurova, E. A.; Tsirelson, V. G.; Stash, A. I.; Yakovlev, M. V.; Pinkerton, A. A. J. Phys. Chem. B 2004, 108, 20173−20179. (9) Coppens, P. X-ray Charge Densities and Chemical Bonding; Oxford University Press: Oxford, U.K., 1997. (10) Ermer, O. Helv. Chim. Acta 1981, 64, 1902−1909. (11) Pinkerton, A. A.; Schwarzenbach, D.; Stibbard, J. H. A.; Carrupt, P. A.; Vogel, P. J. Am. Chem. Soc. 1981, 103, 2095−2096. (12) Pinkerton, A. A.; Schwarzenbach, D.; Birbaum, J.-L.; Carrupt, P.A.; Schwager, L.; Vogel, P. Helv. Chim. Acta 1984, 67, 1136−1153. (13) (a) Hardie, M. J.; Kirschbaum, K.; Martin, A.; Pinkerton, A. A. J. Appl. Crystallogr. 1998, 31, 815−817. (b) Kirschbaum, K.; Martin, A.; Parrish, D. A.; Pinkerton, A. A. J. Phys.: Condens. Matter 1999, 11, 4483−4490. (14) Zhurov, V. V.; Zhurova, E. A.; Pinkerton, A. A. J. Appl. Crystallogr. 2008, 41, 340−349. (15) Otwinowski, Z.; Minor, W. Methods Enzymol. 1997, 276, 307− 326. (16) (a) Zhurova, E.; Zhurov, V. V.; Tanaka, K. Acta Crystallogr. 1999, B55, 917−922. (b) Zhurov, V. V.; Zhurova, E. A.; Pinkerton, A. A. J. Appl. Crystallogr. 2008, 41, 340−349. (17) Zhurov, V. V.; Pinkerton, A. A. Z. Anorg. Allg. Chem. 2013, 639, 1969−1978. (18) (a) Blessing, R. H. Acta Crystallogr. 1995, A51, 33−38. (b) Blessing, R. H. J. Appl. Crystallogr. 1997, 30, 421−426. (19) Sheldrick, G. M. Acta Crystallogr. 2008, A64, 112−122. (20) Hansen, N. K.; Coppens, P. Acta Crystallogr. 1978, A34, 909− 921. (21) Volkov, A.; Macchi, P.; Farrugia, L. J.; Gatti, C.; Mallinson, P.; Richter, T.; Koritsanszky, T. XD2006, rev. 5.34; University at Buffalo, State University of New York; Buffalo, NY, USA, 2006. (22) Zhurov, V. V.; Zhurova, E. A.; Stash, A. I.; Pinkerton, A. A. Acta Crystallogr. 2011, A67, 160−173. (23) Madsen, A. Ø. J. Appl. Crystallogr. 2006, 39, 757−758. (24) Meindl, K.; Henn, J. Acta Crystallogr. 2008, A64, 404−418. (25) Macrae, C. F.; Bruno, I. J.; Chisholm, J. A.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Rodriguez-Monge, L.; Taylor, R.; van de Streek, J.; Wood, P. A. J. Appl. Crystallogr. 2008, 41, 466. (26) (a) Stash, A. I.; Tsirelson, V. G. J. Appl. Crystallogr. 2002, 35, 371−373. (b) Stash, A. I.; Tsirelson, V. G. Crystallogr. Rep. 2005, 50, 177−184. (27) (a) Dovesi, R.; Orlando, R.; Civalleri, B.; Roetti, C.; Saunders, V. R.; Zicovich-Wilson, C. M. Z. Kristallogr. 2005, 220, 571. (b) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, T.; Zicovich-Wilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, Ph.; Llunell, M. CRYSTAL09 User’s Manual; University of Torino: Torino, 2009. (28) Valenzano, L.; Torres, F. J.; Doll, K.; Pascale, F.; ZicovichWilson, C. M.; Dovesi, R. Z. Phys. Chem. 2006, 220, 893−912. G

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