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Why divide by two? This question may occur to readers unfamiliar with the bookkeeping of lattice energy. For simplicity, consider a cluster of N monatomic molecules. Each molecule interacts with all the others, so there are N(N, 1)/2 separate interactions, each of which contributes to the total cohesive energy of the cluster. If this energy is to be expressed in molar units, e.g, kJ mol-1, then the sum over the cluster has to be divided by N, the number of molecules in the cluster. For an extended crystal, where all molecules can be regarded as equivalent, the same result is obtained by choosing an arbitrary reference molecule, summing over the N, 1 interactions with the remaining molecules, and then dividing by 2. If the molecules in the crystal are not equivalent, e.g, if Z′ > 1 or in a cocrystal, then the matter becomes more complicated
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-1, then the sum over the cluster has to be divided by N, the number of molecules in the cluster. For an extended crystal, where all molecules can be regarded as equivalent, the same result is obtained by choosing an arbitrary reference molecule, summing over the N - 1 interactions with the remaining molecules, and then dividing by 2. If the molecules in the crystal are not equivalent, e.g., if Z′ > 1 or in a cocrystal, then the matter becomes more complicated.
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17044375934
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Dunitz, J. D.; Gavezzotti, A. Angew. Chem., Int. Ed. 2005, 44, 1766-1787.
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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, 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-La
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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.; 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.; W. Gill, P. M.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004.
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This information can be conveniently recovered from the Cambridge Structural Database (CSD, distributed by the Cambridge Crystallographic Data Centre, Cambridge, England , under the refcode BENZEN01
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This information can be conveniently recovered from the Cambridge Structural Database (CSD), distributed by the Cambridge Crystallographic Data Centre, Cambridge, England (www.ccdc.cam.ac.uk), under the refcode BENZEN01.
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In the four Pixel calculations Table 2, the dispersion contribution to the binding energy is dominant and remains nearly constant. The largest energy changes occur in the repulsion contribution, which increases with the expansion of the basis set
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In the four Pixel calculations (Table 2), the dispersion contribution to the binding energy is dominant and remains nearly constant. The largest energy changes occur in the repulsion contribution, which increases with the expansion of the basis set.
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