Evaluation of the Lattice Energy of the Two-Component Molecular

Article pubs.acs.org/crystal

Evaluation of the Lattice Energy of the Two-Component Molecular Crystals Using Solid-State Density Functional Theory Published as part of the Crystal Growth & Design Mikhail Antipin Memorial virtual special issue Mikhail V. Vener,*,† Elena O. Levina,†,⊥ Oleg A. Koloskov,†,⊥ Alexey A. Rykounov,‡ Alexander P. Voronin,§ and Vladimir G. Tsirelson† †

D. I. Mendeleev University of Chemical Technology, Moscow, Russia Russian Federal Nuclear Center − All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk Region, Russia § G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia ‡

S Supporting Information *

ABSTRACT: The lattice energy Elatt of the two-component crystals (three co-crystals, a salt, and a hydrate) is evaluated using two schemes. The first one is based on the total energy of the crystal and its components computed using the solid-state density functional theory method with the plane-wave basis set. The second approach explores intermolecular energies estimated using the bond critical point parameters obtained from the Bader analysis of crystalline electron density or the pairwise potentials. The Elatt values of two-component crystals are found to be lower or equal to the sum of the absolute sublimation enthalpies of the pure components. The computed energies of the supramolecular synthons vary from ∼80 to ∼30 kJ/mol and decrease in the following order: acid−amide > acid− pyridine > hydroxyl−acid > amide−amide > hydroxyl−pyridine. The contributions from different types of noncovalent interactions to the Elatt value are analyzed. We found that at least 50% of the lattice energy comes from the heterosynthon and a few relatively strong H-bonds between the heterodimer and the adjacent molecules.

1. INTRODUCTION Two-component crystals are currently recognized as the best alternatives for optimizing different properties of active pharmaceutical ingredients without chemical modification of the drug substance.1 Their stability is one of the target properties. Several theoretical methods have been suggested in the literature for assessment of this property: an approach based on crystal structure prediction with anisotropic potential,2,3 quick methods of energy estimation based on molecular electrostatic potential surfaces,4 and quantitative structure−property relationships with an additional descriptor taking into account molecular structural similarity.5 Here, the density functional theory (DFT) methods with periodic boundary conditions (solid-state DFT) are used for evaluation of the lattice energy of the two-component crystals Elatt. These methods are time-consuming in comparison to the above-mentioned approaches; however, the essential feature of the solid-state DFT computations is their ability to evaluate the IR spectral characteristics, inelastic neutron scattering spectra6−8 and the NMR parameters of the two-component crystals.9 These experimental methods are widely used for investigations of the H-bonds in condensed phases, e.g., see refs 10 and 11, and comparison of theoretical predictions with experiments makes us confident about the general conclusions. © 2014 American Chemical Society

Moreover, the solid-state DFT methods combined with the Bader analysis of the periodic electron density give a unique possibility to distinguish the noncovalent interactions according to different types and strength in crystals and describe quantitatively the contributions of these interactions to the lattice energy; e.g., see refs 12 and 13. The characteristics of energy contributions of different interaction types along with CSD data mining14 can be used further in crystal engineering, which is especially desirable for commercially applicable multicomponent crystals.15 The aim of the study is 3-fold: (1) to compare the Elatt values evaluated using different theoretical approaches with the available literature data, (2) to reveal the contributions of different types of the noncovalent (intermolecular) interactions to the lattice energy of the two-component crystals, (3) to study the performance of different exchange-correlational functionals and basis-set types on the Elatt value. Received: April 15, 2014 Revised: August 22, 2014 Published: September 5, 2014 4997

dx.doi.org/10.1021/cg5005243 | Cryst. Growth Des. 2014, 14, 4997−5003

Crystal Growth & Design

Article

2. TWO-COMPONENT CRYSTALS: THE TRAINING SET A characteristic feature of the two-component molecular crystals is the presence of short (strong) O−H···O/N−H···O bonds with the O···O/N···O distance lower than 2.6/2.65 Å16−21 and the energies higher than 40 kJ/mol.22,23 Short (strong) H-bonds correspond to an intermediate (transit) region separating the shared (covalent) and closed-shell (van der Waals) interactions.24 In contrast to moderate and weak Hbonds which belong to the pure closed-shell interactions, the strong H-bonds require accounting for the partial covalent character of the interaction.24b In the present study, we consider five two-component crystals: the 1:1 complex of 3-hydroxypyridine and benzoic acid (the salt),14 hydrate of N-(4-nitrophenyl)-N′-(3-hydroxyphenyl)-urea (the hydrate),25 the 1:1 complex of salicylic acid and benzamide (cocrystal I),26 2-((2,6-dichlorophenyl)amino)phenyl)acetic acid isonicotinamide (cocrystal II),27 1:1 cocrystal of 3-hydroxybenzoic acid and 4,4′-bipyridine (cocrystal III).14 These crystals are taken for the following reasons: (i) Different types of hetero- and homosynthons exist in the systems; see Scheme 1. (ii) They are characterized by the

Table 1. Performance of Various Functionals with the Different-Type Basis Sets in Assessment of the Elatt Values of the Salta functional/method of computation PBE BLYP B3LYP

DFT/6-31G**, eq 2c c

d

200.7 (158.4 ; 198.5 ) 184.9 (267.9; 358.7) 186.2 (222.9; 300.6)

DFT/110 Ry, eq 1 153.3 (158.7; 199.1) 82.0 (269.4; 360.0) 167.2 (224.5; 302.2)

a

The dispersion energy valuesb (for the heterodimer) are given in parentheses. The units are kJ/mol. bDispersion corrections have been calculated for both CRYSTAL and CPMD results assuming energy cutoff 110 Ry using Grimme dftd3 code. cSingle-point dispersion energy (for the heterodimer) of the partially optimized structure computed with the D3 correction;44 dSingle-point dispersion energy (for the heterodimer) of the partially optimized structure computed with the D3(BJ) correction.45 PBE-D methods used to calculate the intermolecular distances and cell volume of the ethyl acetate crystal yield results that differ significantly from the experiment.38 Empirical corrections increase sharply (∼250 kJ/mol) the lattice energies of the DMSO solvates of 2-(4fluorophenylamino)-5-(2,4-dihydroxybenzeno)-1,3,4-thiadiazole. 39 3.1. Solid-State DFT Computations. Two different codes are used in the present study: CRYSTAL0940 and CPMD.41 The CPMD calculations are done with the B3LYP, PBE, and BLYP functionals using Troullier-Martins pseudopotentials for core electrons.42 The kinetic energy cutoff for the plane wave basis set is 110 Ry. This value of the kinetic energy cutoff gives reasonable results for molecular crystals containing hydrogen and first-row elements.43 k-Space sampling is limited to the Γ point. Criterion on the maximum energy gradient component controlling the optimization process is set to 5 × 10−6 hartree/bohr. Tolerance on energy controlling the self-consistent field convergence for geometry optimization is set to 5 × 10−7 hartree. The stable minimum-energy structures have been confirmed by numerical calculating (using step length in a finite difference run of 0.03 bohr) the harmonic frequencies. Different empirical dispersion corrections44,45 are used in the CPMD computations. In the CRYSTAL09 calculations, the B3LYP, PBE, and BLYP functionals employed with an all-electron Gaussian-type localized orbital basis sets. The 6-31G** basis set provides reliable and consistent results in studying the intermolecular (noncovalent) interactions in crystals, in particular, the electron-density features of the intermolecular H-bonds of different strength.46 Therefore, it is used below. The default CRYSTAL09 computational options are used to achieve an appropriate level of accuracy in evaluating the Coulomb and Hartree−Fock exchange integrals and the exchange-correlation contribution. Tolerance on energy controlling the self-consistent field convergence for the partial geometry optimizations and frequencies computations is set to 1 × 10−8 and 1 × 10−9 hartree, respectively. The shrinking factor, reflecting the density of the k-points grid in the reciprocal space, is set to 3. Frequencies of normal vibrational modes have been calculated within the harmonic approximation by numerical differentiation of the analytical gradient of the potential energy with respect to atomic position47 to control the minimum attainment on the potential energy surface. The space groups and unit cell parameters of the considered twocomponent crystals obtained in the single-crystal X-ray studies were fixed, and structural relaxations are limited to the positional parameters of atoms. This approximation yields a reasonable description of different properties of molecular crystals.48 The atomic positions from experiment are used as the starting point in the solid-state DFT computations. All the optimized structures correspond to the minimum point on the potential energy surface. 3.2. Lattice Energy Evaluation. There are several theoretical approaches to assess the lattice energy in crystalline materials. The first one is based on phenomenological models (see ref 49 for examples). The considerable potency of this approach is demonstrated for in silico screening of cocrystals, as well as their relative solubility. At the same

Scheme 1. Supramolecular Synthons Considered in the Present Study: 1 - Acid−Amide; 2 - Acid−Pyridine; 3 Amide−Amide; - Diphenylurea Hydrate; 5 - Hydroxyl−Acid; 6 - Hydroxyl−Pyridine

1:1 ratio of the components in the asymmetric unit with Z′ = 1. (iii) There are three co-crystals, a salt and hydrate among them. (iv) There are short (strong) intermolecular H-bonds in the salt,14 cocrystal I,26 and cocrystal II.27

3. COMPUTATIONAL METHODS The PBE and B3LYP functionals are widely used in assessment of the lattice energy in van der Waals and H-bonded molecular crystals.28−30 In the past, a lot of attention was paid to the different empirical corrections31,32 needed for an adequate description of the dispersive interactions.33 PBE and B3LYP with three empirical corrections give a mean absolute deviation of the sublimation energy of the benchmark set X23 of about 2 kcal/mol (Table 1 in ref 30). The point is that this set for noncovalent interactions in solids29,34 does not contain the short (strong) H-bonds. Succinic and acetic acid crystals are characterized by the strongest intermolecular H-bonds in the benchmark set X23. H-bond energy in these crystals is less than 40 kJ/mol.35,36 To our best knowledge, influence of different empirical dispersion corrections on the structure and lattice energy of crystals with the Hbonds of different types and strength has not been studied yet. According to ref 13, the Grimme dispersion correction37 does not provide a simultaneous description of C−H···O interactions and strong H-bonds in the picolinic acid N-oxide crystal. B3LYP-D and 4998



Article

time, it is based on simplified thermodynamic arguments, the physical meaning of which is vague.50 In the second approach Elatt is evaluated using the total energy of the unit cell, E(bulk), and relaxed energies of the A and B molecules, E(A) and E(B), forming a supramolecular heterodimer: E latt = E(bulk)/ Z − E(A) − E(B)

with short (strong) H-bonds, the Elatt value of the salt crystal is computed by B3LYP, BLYP, PBE, and various dispersion corrections. The salt is chosen due to the following reasons. (i) The acid-pyridine moiety is a persistent H-bond motif in twocomponent crystals.64 (ii) Corresponding crystal is small (54 atoms per unit cell); see Figure 1. (iii) The salt is characterized

(1)

Z is the number of heterodimers in the unit cell. If the localized basis set is used in solid-state computations, the basis set superposition error (BSSE) has to be additionally evaluated. This can be done using the MOLEBSSE option of the CRYSTAL09 package.40 However, its applicability to the BSSE evaluation in two-component crystals is not straightforward.39 If the plane-wave basis set is used, eq 1 is the BSSEfree. The E(bulk), E(A), and E(B) values are computed with CPMD41 at the B3LYP/110 Ry level of approximation. The isolated molecules are optimized in a cubic cell with an edge length of 24 Å. The third approach views the lattice energy as a sum of the energies of intermolecular (noncovalent) pairwise interactions between the considered molecule and its neighbors:51

E latt =

∑ ∑ Eint,j ,i j

j acid‐pyridine > hydroxyl‐acid > amide ‐amide > hydroxyl‐pyridine

Arranging the energies of supramolecular synthons presenting in our crystal structures, one could mention that they are in a reasonable agreement with their frequencies in CSD (for data mining results, see, e.g., Scheme 1 in ref 15b): heterosynthons with higher energy (e.g., acid−amide or acid−pyridine) are more likely to form than those with lower energy. The supramolecular synthon energies evaluated by the QTAIMC approach are compared with the interaction energies between molecules forming the synthon obtained by the PIXEL model63 in Table 3. The QTAIMC and PIXEL energies are in a satisfactory agreement with the best matching of urea hydrate synthon, as no another interaction except the heterosynthon exists between the molecules of water and substituted urea. Table 3 shows that the PIXEL interaction energy tends to be significantly lower than that one estimated by QTAIMC in several cases. This is caused by the paradigm difference of both approaches, putting different interaction types on the first place. The PIXEL approach mostly deals with nonspecific van der Waals forces and may be less suitable to the crystals with short (strong) H-bonds. The Bader charge density analysis, in its turn, is concerned with finding critical points indicating primarily H-bonds and has almost no means to quantitatively describe the weak nondirected dispersion interaction. The latter is integrated in the coefficient in eq 3 considered proportional to electronic kinetic energy density at critical point. In the case of heterodimers formed by relatively large molecules, the divergence in calculated energies increases, as the PIXEL pair interaction energy counts not only H-bonds of the specific synthon but also weak C−H···O(N) contacts and van der Waals interaction between the selected molecules. For instance, the energy of the acid−pyridine synthon in cocrystal II evaluated by PIXEL is 8.4 kJ/mol lower than that by QTAIMC and vice versa for cocrystal III. There is still a little correlation between the interaction energies evaluated for crystal structures and gas-phase dimers of model compounds (Table 3). It may be caused by the presence of additional substituents and environmental effects. Hits were obtained only for the acid−amide (cocrystal I) and acid−acid (propionic acid) synthons calculated by PIXEL in the crystal and gas phase36 and the hydroxyl−pyridine synthon (cocrystal II) calculated by QTAIMC and CCSD(T)/CBS.71 In the first two cases the selected synthons give the major contribution to the Elatt value (so the interaction energy is nearly equal to dimer energy regardless the method). The QTAIMC approach seems to mimic the ab initio hydroxyl−pyridine synthon energy pretty well.

E latt = (A···B) + [∑ (A···B′) +

∑ (B···A′) + (1/2) ∑ (A···A′) + (1/2) ∑ (B···B′)]

(4)

Here, A′ and B′ represent molecules interacting with A···B heterodimer by noncovalent interactions of various types (relatively strong H-bonds, weak H-bonds, and van der Waals interaction). The energy of the relatively strong H-bonds is ∼50 to ∼90% of the lattice energy of the considered crystals, cf. Tables 4 and 2. There are only a few (from 1 to 3) relatively strong H-bonds formed by the heterosynthon with the adjacent molecules (Table 4). Obtained results may be interpreted in terms of the concept of primary and secondary synthons.64 In the salt (1:1 complex of 3-hydroxypyridine and benzoic acid), the O···H−N bonds correspond to primary interactions, while the O···H−O bonds can be treated as secondary interactions (Figure 3). On the other hand, weak H-bonds and van der Waals interactions significantly contribute to the Elatt energy (Table 4). Their unambiguous identification requires knowledge of the periodic electron density computed using the solid-state DFT73 or derived from precise X-ray diffraction experiments.74

5. CONCLUSIONS Theoretical values of the lattice energies of the considered cocrystals are found to be lower than the sum of the absolute sublimation enthalpies of the pure components. Not less than 50% of the lattice energy is caused by the heterosynthon and a few relatively strong H-bonds between the heterodimer and the adjacent molecules. Existing theoretical approaches lead to different Elatt values. Therefore, influence of various functional and different empirical corrections on the structure and lattice energy of crystals with the H-bonds of different types and strength has to be studied. To be on the safe side, the benchmark set X23 has 5001



■

to be enlarged by inclusion the crystals with short (strong) intermolecular H-bonds of different types. According to computations, the energy of the considered supramolecular synthons varies from ∼80 to ∼30 kJ/mol and decreases in the following order: acid−amide > acid−pyridine > hydroxyl−acid > amide−amide > hydroxyl−pyridine in accordance with their frequencies in CSD. The energy of the acid−pyridine supramolecular synthon on salts is expected to be ∼10 kJ/mol larger than in cocrystals due to proton transfer. Very recently Dunitz et al.75 extended the CLP/PIXEL approach to ionic crystals. We are planning to test their approach on our compounds.

ASSOCIATED CONTENT

S Supporting Information *

Geometrical and electron density parameters, and the energy of the noncovalent interactions in the considered two-component crystals (Tables S1−S5, Figures S1−S5). This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

(1) Vishweshwar, P.; McMahon, J. A.; Bis, J. A.; Zaworotko, M. J. J. Pharm. Sci. 2006, 95, 499−516. (2) Issa, N.; Karamertzanis, P.; Wellch, G.; Price, S. Cryst. Growth Des. 2009, 9, 442−453. (3) Karamertzanis, P.; Kazantsev, A.; Issa, N.; Welch, G. W. A.; Adjiman, G. C.; Pantelides, C.; Price, S. J. Chem. Theory Comput. 2009, 5, 1432−1448. (4) Musumeci, D.; Hunter, C.; Prohens, R.; Scuderi, S.; McCabe, F. Chem. Sci. 2011, 2, 883−890. (5) Perlovich, G.; Raevsky, O. Cryst. Growth Des. 2010, 10, 2707− 2712. (6) Vener, M. V.; Manaev, A. V.; Hadži, D.; Tsirelson, V. G. Z. Phys. Chem. 2008, 222, 1349−1358. (7) Katsyuba, S. A.; Vener, M. V.; Zvereva, E. E.; Fei, Z.; Scopelliti, R.; Laurenczy, G.; Yan, N.; Paunescu, E.; Dyson, P. J. Phys. Chem. B 2013, 117, 9094−9105. (8) Molčanov, K.; Stare, J.; Vener, M. V.; Kojić-Prodić, B.; Mali, G.; Grdadolnik, J.; Mohaček-Grošev, V. Phys. Chem. Chem. Phys. 2014, 16, 998−1007. (9) Rachocki, A.; Pogorzelec-Glaser, K.; Ławniczak, P.; PugaczowaMichalska, M.; Łapiński, A.; Hilczer, B.; Matczak, M.; Pietraszko, A. Cryst. Growth Des. 2014, 14, 1211−1220. (10) (a) Rozenberg, M.; Shoham, G.; Reva, I.; Fausto, R. A. Phys. Chem. Chem. Phys. 2005, 7, 2376−2383. (b) Zakharov, B. A.; Kolesov, B. A.; Boldyreva, E. V. Phys. Chem. Chem. Phys. 2011, 13, 13106− 13116. (11) Lorente, P.; Shenderovich, I. G.; Golubev, N. S.; Denisov, G. S.; Buntkowsky, G.; Limbach, H.-H. Magn. Reson. Chem. 2001, 39, S18− S29. (12) Shishkina, A. V.; Stash, A. I.; Civalleri, B.; Ellern, A.; Tsirelson, V. G. Mendeleev Commun. 2010, 20, 161−164. (13) 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. (14) Shattock, T. R.; Arora, K. K.; Vishweshwar, P.; Zaworotko, M. J. Cryst. Growth Des. 2008, 8, 4533−4545. (15) (a) Babu, N. J.; Reddy, N. S.; Nangia, A. Mol. Pharmaceutics 2007, 4 (3), 417−434. (b) Childs, S. L.; Wood, P. A.; RodríguezHornedo, N.; Reddy, L. S.; Hardcastle, K. I. Cryst. Growth Des. 2009, 9, 1869−1888. (16) Hosseini, M. W. Coord. Chem. Rev. 2003, 240, 157−166 and references therein. (17) (a) Aaker"y, C. B.; Fasulo, M. E.; Desper, J. Mol. Pharmaceutics 2007, 4, 317−322. (b) Bucar, D.-K.; Henry, R. F.; Lou, X.; Duerst, R. W.; Borchardt, T. B.; MacGillivray, L. R.; Zhang, G. G. Z. Mol. Pharmaceutics 2007, 4, 339−346. (18) Ward, M. D. Struct. Bonding (Berlin) 2009, 32, 1−23 and references therein. (19) Das, B.; Baruah, J. D. Cryst. Growth Des. 2011, 11, 5522−5532. (20) (a) Lie, S.; Maris, T.; Malveau, C.; Beaudoin, D.; Helzy, F.; Wuest, J. D. Cryst. Growth Des. 2013, 13, 1872−1877. (b) Bolla, G.; Sanphui, P.; Nangia, A. Cryst. Growth Des. 2013, 13, 1988−2003. (c) Tilborg, A.; Leyssens, T.; Norberg, B.; Wouters, J. Cryst. Growth Des. 2013, 13, 2373−2389. (21) Harriss, B. I.; Vella-Zarb, L.; Wilson, C.; Evans, I. R. Cryst. Growth Des. 2014, 14, 783−781. (22) Babu, N. J.; Reddy, L. S.; Nangia, A. Mol. Pharmaceutics 2007, 4, 417−434. (23) Steiner, T. Angew. Chem., Int. Ed. 2002, 41, 48−76. (24) (a) Gatti, C. Z. Kristallogr. 2005, 220, 399−457. (b) Vener, M. V.; Manaev, A. V.; Egorova, A. N.; Tsirelson, V. G. J. Phys. Chem. A 2007, 111, 1155−1162. (25) Reddy, L. S.; Chandran, S. K.; George, S.; Babu, N. J.; Nangia, A. Cryst. Growth Des. 2007, 7, 2675−2690. (26) Seaton, C. C.; Parkin, A. Cryst. Growth Des. 2011, 11, 1502− 1511. (27) Bathori, N. B.; Lemmerer, A.; Venter, G. A.; Bourne, S. A.; Caira, M. R. Cryst. Growth Des. 2011, 11, 75−87.

Figure 3. Fragment of the 3-hydroxypyridine−benzoic acid crystal. Hbonds are denoted by dotted lines. Their energy values are given in kJ/ mol. See the captions of Figure 1 for the color coding.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions ⊥

E.O.L. and O.A.K. contributed equally.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This study is supported by the Federal Program for Supporting Science and Innovation (No. 02.740.11.0857), grant of the President of the Russian Federation for Young Scientists (MK67.2014.3) and by the Russian Foundation for Basic Research (Grant 14-03-01031). M.V.V. thanks Dr. A. A. Korlukov for help in numerical calculations and Dr. A. V. Shishkina for useful discussion.

■

DEDICATION We devote this paper to memory of our friend Professor Michail Antipin. 5002



Article

(28) (a) Feng, S.; Li, T. J. Chem. Theory Comput. 2006, 2, 149−156. (b) Civalleri, B.; Zicovich-Wilson, C. M.; Valenzano, L.; Ugliengo, P. CrystEngComm 2008, 10, 405−410. (29) (a) Otero-de-la-Roza, A.; Johnson, E. R. J. Chem. Phys. 2012, 137, 054103. (b) Reilly, A. M.; Tkatchenko, A. J. Chem. Phys. 2013, 139, 024705. (30) Brandenburg, J. G.; Alessio, M.; Civalleri, B.; Peintinger, M. F.; Bredow, T.; Grimme, S. J. Phys. Chem. A 2013, 117, 9282−9292. (31) Tkatchenko, A.; Scheffler, M. Phys. Rev. Lett. 2009, 102, 073005. (32) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A. J. Chem. Phys. 2010, 132, 154104. (33) Hesselmann, A. J. Phys. Chem. A 2011, 115, 11321−11330. (34) Reilly, A. M.; Tkatchenko, A. J. Phys. Chem. Lett. 2013, 4, 1028− 1033. (35) Hagler, A. T.; Dauber, P.; Lifson, S. J. Am. Chem. Soc. 1979, 101, 5131−5141. (36) Dunitz, J. D.; Gavezzotti, A. Cryst. Growth Des. 2012, 12, 5873− 5877. (37) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (38) Boese, A. D.; Kirchner, M.; Echeverria, G. A.; Boese, R. ChemPhysChem 2013, 14, 799−804. (39) Hoser, A. A.; Kamiński, D. M.; Matwijczuk, A.; Niewiadomy, A.; Gagos, M.; Woźniak, K. CrystEngComm 2013, 15, 1978−1988. (40) Dovesi, R.; Saunders, V. R.; Roetti, R.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; et al. M. CRYSTAL09; CRYSTAL09 User’s Manual; University of Torino: Torino, 2009. (41) CPMD 3.17.1, http://www.cpmd.org/, IBM Corp 1990−2008, MPI für Festkörperforschung Stuttgart 1997−2001. (42) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993−2006. (43) Tosoni, S.; Tuma, C.; Sauer, J.; Civalleri, B.; Ugliengo, P. J. Chem. Phys. 2007, 127, 154102. (44) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (45) Grimme, S.; Ehrlich, S.; Goerigk, L. J. Comput. Chem. 2011, 32, 1456−1465. (46) (a) Oddershede, J.; Larsen, S. J. Phys. Chem. A 2004, 108, 1057−1063. (b) Munshi, H.; Guru Row, T. N. J. Phys. Chem. A 2005, 109, 659−672. (c) Munshi, H.; Thakur, T. S.; Guru Row, T. N.; Desiraju, G. R. Acta Crystallogr. B 2006, 62, 118−127. (d) Munshi, H.; Guru Row, T. N. Acta Crystallogr. B 2006, 62, 612−626. (47) Pascale, F.; Zicovich-Wilson, C. M.; Gejo, F. L.; Civalleri, B.; Orlando, R.; Dovesi, R. J. Comput. Chem. 2004, 25, 888−897. (48) (a) Vener, M. V.; Sauer, J. Phys. Chem. Chem. Phys. 2005, 7, 258−263. (b) Jezierska, A.; Panek, J. J.; Koll, A.; Mavri, J. J. Chem. Phys. 2007, 126, 205101. (c) Vener, M. V.; Manaev, A. V.; Tsirelson, V. G. J. Phys. Chem. A 2008, 112, 13628−13632. (d) King, M. D.; Korter, T. M. J. Phys. Chem. A 2010, 114, 7127−7138. (e) Brela, M.; Stare, J.; Pirc, G.; Sollner-Dolenc, M.; Boczar, M.; Wojcik, M. J.; Mavri, J. J. Phys. Chem. B 2012, 116, 4510−4518. (49) Kuleshova, L. N.; Hofmann, D. W. M.; Boese, R. Chem. Phys. Lett. 2013, 564, 26−32. (50) Manin, A. N.; Voronin, A. P.; Manin, N. G.; Vener, M. V.; Shishkina, A. V.; Lermontov, A. S.; Perlovich, G. L. J. Phys. Chem. B 2014, 118, 6803−6814. (51) Dominiak, P. M.; Espinosa, E.; Á ngyán, J. In Modern Charge Density Analysis; Gatti, C., Macchi, P., Eds.; Springer, Heidelberg, 2012; pp 387−433. (52) (a) Gavezzotti, A. Model. Simul. Mater. Sci. Eng. 2002, 10, R1− R29. (b) Day, G. M. Crystallogr. Rev. 2011, 17, 3−52 and references therein. (53) Vener, M. V.; Egorova, A. N.; Churakov, A. V.; Tsirelson, V. G. J. Comput. Chem. 2012, 33, 2303−2309. (54) Ouvrard, C.; Mitchell, J. B. O. Acta Crystallogr. B 2003, 59, 676−685. (55) Chickos, J. S.; Acree, W. E. J. Phys. Chem. Ref. Data 2002, 31, 537−698.

(56) Saunders, V. R.; Dovesi, R.; Roetti, C.; Causa, M.; Harrison, N. M.; Orlando, R.; Zikovich-Wilson, C. M. CRYSTAL 98 User’s Manual; Universita di Torino: Torino, 1998. (57) (a) Bader, R. F. W. Atoms in Molecules - A Quantum Theory; Oxford University Press: Oxford, 1990. (b) Tsirelson, V. G. In The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design; Matta, C., Boyd, R., Eds.; Wiley-VCH: New York, 2007; Chapter 10. (58) Gatti, C. TOPOND98 User’s Manual; CNR-CSRSRC: Milano, Italy, 1999. (59) (a) Bertini, L.; Cargnoni, F.; Gatti, C. Theor. Chem. Acc. 2007, 117, 847−884. (b) Churakov, A. V.; Prikhodchenko, P. V.; Lev, O.; Medvedev, A. G.; Tripol’skaya, T. A.; Vener, M. V. J. Chem. Phys. 2010, 133, 164506. (c) Vener, M. V.; Medvedev, A. G.; Churakov, A. V.; Prikhodchenko, P. V.; Tripol’skaya, T. A.; Lev, O. J. Phys. Chem. A 2011, 115, 13657−13663. (60) Mata, I.; Alkorta, I.; Espinosa, E.; Molins, E. Chem. Phys. Lett. 2011, 507, 185−189. (61) Vener, M. V.; Shishkina, A. V.; Rykounov, A. A.; Tsirelson, V. G. J. Phys. Chem. A 2013, 117, 8459−8467. (62) Gavezzotti, A. New J. Chem. 2011, 35, 1360−1368. (63) Gavezzotti, A. J. Phys. Chem. B 2003, B107, 2344−2353. (64) Mukherjee, A.; Desiraju, G. R. Cryst. Growth Des. 2014, 14, 1375−1385. (65) Tuma, C.; Boese, A. D.; Handy, N. C. Phys. Chem. Chem. Phys. 1999, 1, 3939−3947. (66) Vener, M. V.; Rozanska, X.; Sauer, J. Phys. Chem. Chem. Phys. 2009, 11, 1702−1712. (67) Vener, M. V.; Egorova, A. N.; Tsirelson, V. G. Chem. Phys. Lett. 2010, 500, 272−276. (68) Perlovich, G. L.; Volkova, T. V.; Bauer-Brandl, A. J. Pharm. Sci. 2006, 95, 1448−1458. (69) Brandenburg, J. G.; Grimme, S. Theor. Chem. Acc. 2013, 132, 1− 6. (70) Warshel, A.; Weiss, R. M. J. Am. Chem. Soc. 1980, 102, 6218− 6226. (71) Rezac, J.; Riley, K. E.; Hobza, P. J. Chem. Theory Comput. 2011, 7, 2427−2438. (72) Bruno, G.; Randaccio, L. Acta Crystallogr. B 1980, 36, 1711− 1712. (73) (a) Aubert, E.; Lebegue, S.; Marsman, M.; Bui, T. T. T.; Jelsch, C.; Dahaoui, S.; Espinosa, E.; Á ngyán, J. G. J. Phys. Chem. A 2011, 115, 14484−14494. (b) Brezgunova, M. E.; Aubert, E.; Dahaoui, S.; Fertey, P.; Lebègue, S.; Jelsch, C.; Á ngyán, J. G.; Espinosa, E. Cryst. Growth Des. 2012, 12, 5373−5386. (74) (a) Suponitsky, K. Y.; Tsirelson, V. G.; Feil, D. Acta Crystallogr., Sect. A 1999, 55, 821−827. (b) Morrison, C. A.; Siddick, M. M. Chem.Eur. J. 2003, 9, 628−634. (c) Vishweshwar, P.; Babu, N. J.; Nangia, A.; Mason, S. A.; Puschmann, H.; Mondal, R.; Howard, J. A. K. J. Phys. Chem. A 2004, 108, 9406−9416. (d) Schmidtmann, M.; Farrugia, L. J.; Middlemiss, D. S.; Gutmann, M. J.; McIntyre, G. J.; Wilson, C. C. J. Phys. Chem. A 2009, 113, 13985−13997. (e) Dittrich, B.; Weber, M.; Kalinowski, R.; Grabowsky, S.; Hubschle, C. B.; Luger, P. Acta Crystallogr., Sect. B 2009, 65, 749−756. (f) Hathwar, V. R.; Guru Row, T. N. Cryst. Growth Des. 2011, 11, 1338−1346. (g) Krawczuk, A.; Stadnicka, K. J. Phys. Chem. A 2012, 116, 9759− 9768. (75) Dunitz, J. D.; Gavezzotti, A.; Rizzato, S. Cryst. Growth Des. 2014, 14, 357−366.

5003


Evaluation of the Lattice Energy of the Two-Component Molecular

Recommend Documents