First-principles lattice energy calculation of urea and hexamine crystals by a combination of periodic DFT and MP2 two-body interaction energy calculations

Journal of Physical Chemistry B

Volumn 114, Issue 20, 2010, Pages 6799-6805

  Tsuzuki, Seiji ^a   Orita, Hideo ^a   Honda, Kazumasa ^a   Mikami, Masuhiro ^a  

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSIONS; HYDROGEN BONDS; METABOLISM; MOLECULAR CRYSTALS; SULFUR COMPOUNDS; UREA;

DFT AND MP2 CALCULATIONS; DFT CALCULATION; DISPERSION CONTRIBUTION; DISPERSION INTERACTION; EXPERIMENTAL VALUES; FIRST-PRINCIPLES; HEXAMINES; INTERACTION ENERGIES; ISOLATED MOLECULES; LATTICE ENERGIES; LATTICE ENERGY CALCULATIONS; NEIGHBORING MOLECULES; PERIODIC DFT; PERIODIC DFT CALCULATION; STABILIZATION ENERGY; SUBLIMATION ENERGY;

MOLECULES;

EID: 77952724729     PISSN: 15206106     EISSN: 15205207     Source Type: Journal    
DOI: 10.1021/jp912028q     Document Type: Article

References (70)

1. Fogassy, E.; Nogradi, M.; Kozma, D.; Egri, G.; Palovics, E.; Kiss, V. Org. Biomol. Chem. 2006, 4, 3011
2. Karamertzanis, P. G.; Anandamanoharan, P. R.; Fernandes, P.; Cains, P. W.; Vickers, M.; Tocher, D. A.; Florence, A. J.; Price, S. L. J. Phys. Chem. B 2007, 111, 5326
3. Gourlay, M. D.; Kendrick, J.; Leusen, F. J. J. Cryst. Growth Des. 2007, 7, 56
4. Price, S. L. Adv. Drug Delivery Rev. 2004, 56, 301
5. Evans, O. R.; Lin, W. B. Acc. Chem. Res. 2002, 35, 511
6. Roesky, H. W.; Andruh, M. Coord. Chem. Rev. 2003, 236, 91
7. Kwon, O.-P.; Ruiz, B.; Choubye, A.; Mutter, L.; Schneider, A; Jazbinesek, M.; Gramlich, V.; Gunter, P. Chem. Mater. 2006, 18, 4049
8. Day, G. M.; Price, S. L. J. Am. Chem. Soc. 2003, 125, 16434
9. Day, G. M.; Chisholm, J.; Shan, N.; Motherwell, W. D. S.; Jones, W. Cryst. Growth. Des. 2004, 4, 1327
10. Dunitz, J. D.; Gavezzotti, A. Angew. Chem., Int. Ed. 2005, 44, 1766
11. Dunitz, J. D.; Gavezzotti, A. Cryst. Growth Des. 2005, 5, 2180
12. Welch, G. W. A.; Karamertzanis, P. G.; Misquitta, A. J.; Stone, A. J.; Price, S. L. J. Chem. Theory Comput. 2008, 4, 522
13. Asmadi, A.; Neumann, M. A.; Kendrick, J.; Girard, P.; Perrin, M.-A.; Leusen, F. J. J. J. Phys. Chem. B 2009, 113, 16303
14. Day, G. M.; Cooper, T. G.; Cruz-Cabeza, A. J.; Hejczyk, K. E.; Ammon, H. L.; Boerrigter, S. X. M.; Tan, J. S.; Valle, R. G. D.; Venuti, E.; Jose, J.; Gadre, S. R.; Desiraju, G. R.; Thakur, T. S.; van Eijck, B. P.; Facelli, J. C.; Bazterra, V. E.; Ferrano, M. B.; Hofmann, D. W. M.; Neumann, M. A.; Leusen, F. J. J.; Kendrick, J.; Price, S. L.; Misquitta, A. J.; Karamertzanis, P. G.; Welch, G. W. A.; Scheraga, H. A.; Arnautova, Y. A.; Schmidt, M. U.; van de Streek, J.; Wolf, A. K.; Shweizer, B. Acta Crystallogr. B 2009, 65, 107
15. Dan C. Sorescu, D. C.; Boatz, J. A.; Thompson, D. L. J. Phys. Chem. A 2001, 105, 5010
16. Fau, S.; Wilson, K. J.; Bartlett, R. J. J. Phys. Chem. A 2002, 106, 4639
17. Morrison, C. A.; Siddick, M. M. Chem.-Eur. J. 2003, 9, 628
18. Fortes, A. D.; Brodholt, J. P.; Wood, I. G.; Vocadlo, L. J. Chem. Phys. 2003, 118, 5987
19. Ju, X.-H.; Xiao, H.-M.; Chen, L.-T. Int. J. Quantum Chem. 2005, 102, 224
20. Rivera, S. A.; Allis, D. G.; Hudson, B. S. Cryst. Growth Des. 2008, 8, 3905
21. Lo Presti, L.; Ellern, A.; Destro, R.; Lunelli, B. J. Phys. Chem. A 2009, 113, 3186
22. Hobza, P.; Spooner, J.; Reschel, T. J. Comput. Chem. 1995, 16, 1315
23. Meijer, E. J.; Sprik, M. J. Chem. Phys. 1996, 105, 8684
24. Tsuzuki, S.; Luthi, H. P. J. Chem. Phys. 2001, 114, 3949
25. Stone, A. J.; Tsuzuki, S. J. Phys. Chem. B 1997, 101, 10178
26. Civalleri, B.; Doll, K.; Zicovich-Wilson, C. M. J. Phys. Chem. B 2007, 111, 26
27. Chickos, J. S.; Acree, W. E. A., Jr. J. Phys. Chem. Ref. Data 2002, 31, 537
28. Suzuki, K.; Onishi, S.; Koide, T.; Seki, S. Bull. Chem. Soc. Jpn. 1956, 29, 127
29. Ritter Sutter, J. Ph.D. Thesis, Tulane University, New Orleans, LA, 1959.
30. De Wit, H. G. M.; Van Miltenburg, J. C.; De Kruif, C. G. J. Chem. Thermodyn. 1983, 15, 651
31. Trimble, L. E.; Voorhoeve, R. J. J. Analyst 1978, 103, 759
32. Ferro, D.; Barone, G.; Gatta, G. D.; Piacente, V. J. Chem. Thermodyn. 1987, 19, 915
33. Neumann, M. A.; Perrin, M.-A. J. Phys. Chem. B 2005, 109, 15531
34. Feng, S.; Li, T. J. Chem. Theor. Comput. 2006, 2, 149
35. Civalleri, B.; Zicovich-Wilson, C. M; Valenzano, L.; Ugliengo, P. Cryst. Eng. Commun. 2008, 10, 405
36. The MP2-level interaction energy is not always close to the CCSD(T)-level interaction energy. (24, 37) For example, the MP2 calculations overestimate the attraction between aromatic molecules compared with the CCSD(T) calculations. However, the MP2-level interaction energies for many molecular clusters (hydrogen-bonded clusters and saturated hydrocarbon dimers) are close to the CCSD(T) values. (24)
37. Tkatchenko, A.; DiStasio, R. A., Jr.; Head-Gordon, M.; Sheffler, M. J. Chem. Phys. 2009, 131, 094106
38. Alfredsson, M.; Ojamae, L.; Hermansson, K. G. Int. J. Qunatum Chem. 1996, 60, 767
39. Ikeda, T.; Nagayoshi, K.; Kitaura, K. Chem. Phys. Lett. 2003, 370, 218
40. Ringer, A. L.; Sherrill, C. D. Chem.-Eur. J. 2008, 14, 2542
41. Podeszwa, R.; Rice, B. M.; Szalewicz, K. Phys. Rev. Lett. 2008, 101, 115503
42. The dipole moments of organic molecules obtained by DFT calculations using a basis set with polarization functions are close to the experimental values. This shows that the electrostatic interactions with well-separated molecules calculated by the DFT method do not have large errors.
43. Delley, B. J. Chem. Phys. 1990, 92, 508
44. Delley, B. J. Phys. Chem. 1996, 100, 6106
45. Delley, B. J. Chem. Phys. 2000, 113, 7756
46. Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244
47. Swaminathan, S.; Craven, B. M.; McMullan, R. K. Acta Crystallogr. B 1984, 40, 300
48. Kampermann, S. P.; Sabine, T. M.; Craven, B. M.; McMullan, R. K. Acta Crystallogr. A 1995, 51, 489
49. The lattice parameters for urea crystal were taken from experimental measurements at 12 K. Those for hexamine crystal were taken from experimental measurements at 15 K.
50. The interaction energy between the nearest urea molecules in the crystal (Figure 1S, Supporting Information) were calculated using the aug-cc-pVTZ basis set. The HF- and MP2-level interaction energies calculated for the dimer using the optimized geometry of the crystal by periodic DFT calculations are-8.87 and-10.76 kcal/mol, respectively. Those obtained using the crystal structure are-8.65 and-10.47 kcal/mol. The geometry optimization increases the attraction calculated at the HF and MP2 levels only slightly (by-0.22 and-0.29 kcal/mol, respectively). The electron correlation contribution to the interaction energy (the difference between the MP2- and HF-level interaction energies, which is mainly dispersion energy) obtained using the optimized geometry (-1.89 kcal/mol) is close to that obtained using the crystal structure (-1.82 kcal/mol). The effects of geometry optimization on the calculated interaction energies between urea molecules are not large. Probably, the very accurate hydrogen atom positions in the crystal reported from the neutron diffraction measurements are the cause of the negligible effects of the geometry optimization. However, it is well known that accurate determination of the positions of hydrogen nuclei by XRD is extremely difficult, and consequently, the positions of the hydrogen atoms in an XRD structure often have large errors. The geometry optimization of the position of atoms in the unit cell often changes the hydrogen-bonding energy significantly. Our previous study on the intermolecular interactions between α-(trifluoromethyl)lactic acid in the crystal showed that the hydrogen-bonding energy between the nearest molecules in the crystal calculated using the XRD structure (-5.03 kcal/mol) is significantly smaller (less negative) than that calculated using the optimized geometry (-8.37 kcal/mol). (51) The calculations showed that the geometry of crystal must be optimized with great care, if one wants to evaluate the lattice energy of the crystal accurately.
51. Tsuzuki, S.; Orita, H.; Ueki, H.; Soloshonok, V. A. J. Fluorine Chem. 2010, 131, 461
52. Müller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618
53. Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503
54. min = 10 Å). The MP2-level interaction energy at the basis-set limit can be estimated by an extrapolation from the MP2-level interaction energies calculated using the cc-pVDZ and cc-pVTZ basis sets. (55) The MP2/cc-pVTZ-level calculation of a hexamine dimer requires a few hours using the same computer. The computational time required for the calculation of the interaction energy of a urea dimer is much lower than that for the calculation of the hexamine dimer.
55. Tsuzuki, S.; Honda, K.; Uchimaru, T.; Mikami, M. J. Chem. Phys. 2006, 124, 114304
56. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Wallingford, CT, 2004.
57. Ransil, B. J. J. Chem. Phys. 1961, 34, 2109
58. Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553
59. Various different correction models have been discussed in the literature; (27) 2 RT is only one possibility. We could apply other models, such as 6 RT. The values of 2 RT and 6 RT are 1.2 and 3.6 kcal/mol, respectively, at 298 K. The difference is as much as 2.4 kcal/mol. This shows that the calculated sublimation enthalpy has an error (about 2 kcal/mol) associated with the choice of correction model. Several experimental values have been reported for the sublimation enthalpy of urea crystal (20.9-23.6 kcal/mol). The deviations of the experimental values are larger than the error associated with the correction model. Therefore, we believe that the choice of the correction model is not a serious problem in comparing the calculated sublimation enthalpy of the urea crystal with experimental values. It can be concluded that the calculated sublimation enthalpy of urea agrees with the experimental value within the experimental error. On the other hand, the experimental sublimation enthalpies of hexamine crystal (17.7-18.8 kcal/mol) have smaller deviations. Therefore, the choice of correction model is more important in this case. The sublimation enthalpy calculated for hexamine crystal is 17.8 kcal/mol, if 6 RT is used for the correction. This value is closer to the experimental values than that obtained using 2 RT (20.0 kcal/mol). The 6 RT correction model might be better than the 2 RT correction model in this case.
60. Dovesi, R.; Causa, M.; Orlando, R.; Roetti, C.; Saunders, V. R. J. Chem. Phys. 1990, 92, 7402
61. Ayala, P. Y.; Scuseria, G. E. J. Comput. Chem. 2000, 21, 1524
62. Gora, R. W.; Bartkowiak, W.; Roszak, S.; Leszcznski, J. J. Chem. Phys. 2002, 117, 1031
63. Klipping, V. G.; Stranski, I. N. Z. Anorg. Allg. Chem. 1958, 297, 23
64. Budurov, S. Izv. Khim. Inst. Bulg. Akad. Nauk 1960, 7, 281
65. Wada, T.; Kishida, E.; Tomiie, Y.; Suga, H.; Seki, S.; Nitta, I. Bull. Chem. Soc. Jpn. 1960, 33, 1317
66. Stephenson, R. M.; Malanowski, S. Handbook of the Thermodynamics of Organic Compounds; Elsevier: New York, 1987.
67. lattice(DFT+MP2) value calculated for the crystal (-23.4 kcal/mol) was close to that calculated using the TNP basis set.
68. lattice(DFT) was calculated by subtracting the energy of the fully optimized geometry of an isolated molecule from the energy of a unit cell per molecule. The mixing of rotamers can contribute to the average enthalpy of an isolated molecule if the molecule has large conformational flexibility. This effect was not considered in this work, because urea and hexamine are rigid molecules. The lattice energy calculation does not include the contributions of vibrational states, phonons, and other terms. These terms might be the sources of the errors of calculated lattice energies.
69. Dunning, T. H., Jr. J. Phys. Chem. A 2000, 104, 9062
70. The interaction energies between the nearest urea molecules in the crystal (Figure 1S, Supporting Information) calculated by the MP2 method using the 6-31G, 6-311G, 6-311G, cc-pVDZ, cc-pVTZ, and aug-cc-pVDZ basis sets are-9.47,-9.25,-9.14,-8.67,-9.98, and-10.18 kcal/mol, respectively. These values are close to those calculated by the CCSD(T) method using the same basis sets (-9.43, -9.25, -9.20, -8.70, -10.04, and-10.27 kcal/mol, respectively). The interaction energies between the nearest hexamine molecules in the crystal (Figure 2S, Supporting Information) calculated by the MP2 and CCSD(T) methods using the 6-31G* basis set are-2.38 and-2.13 kcal/mol, respectively.