von Neumann Entropies Analysis in Hilbert Space for the Dissociation Processes of Homonuclear and Heteronuclear Diatomic Molecules
DOI:
https://doi.org/10.29356/jmcs.v52i1.1042Keywords:
Quantum Information Theory, entanglement, diatomic molecules, Ab initio calculationsAbstract
Quantum Information Theory is a new field with potential implications for the conceptual foundations of Quantum Mechanics through density matrices. In particular, information entropies in Hilbert space representation are highly advantageous in contrast with the ones in phase space representation since they can be easily calculated for large systems. In this work, novel von Neumann conditional, mutual, and joint entropies are employed to analyze the dissociation process of small molecules, Cl2 and HCl, by using the spectral decomposition of the first reduced density matrix in natural atomic orbital-based representation which allows us to assure rotational invariance, N- and v-representability in the Atoms-in-Molecules (AIM) scheme. Quantum information entropies permit to analyze the dissociation process through quantum mechanics concepts such as electron correlation and entanglement, showing interesting critical points which are not present in the energy profile, such as charge depletion and accumulation, along with bond breaking regions.
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References
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2. Bouwmeester, D.; Pan, J.-W.; Mattle, K.; Eibl, M.; Weinfurter, H.; Zeilinger, A. Nature 1997, 390, 575-579.
3. Boschi, D.; Branca, S.; De Martini, F.; Hardy, L.; Popescu S. Phys. Rev. Lett. 1998, 80, 1121-1125.
4. Braunstein, S. L.; Kimble, H. J. Nature 1998, 394, 841-841.
5. Bouwmeester, D.; Mattle, K.; Pan, J.-W.; Weinfurter, H.; Zeilinger, A.; Zukowski, M. Appl. Phys. B 1998, 67, 749-752.
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10. Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833-1840.
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13. Bader, R. F. W. and T. T. Nguyen-Dang. Adv. Quantum Chem. 1981, 14, 63-124.
14. Hirshfeld, F. L. Theor. Chim. Acta 1977 44, 129-138.
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16. Parr, R. G. Int. J. Quantum Chem. 1984, 26, 687-692.
17. Rychlewski, J.; Parr, R. G. J. Chem. Phys. 1986, 84, 1696-1703.
18. Li, L.; Parr, R. G. J. Chem. Phys. 1986, 84, 1704-1711.
19. Cedillo, A.; Chattaraj, P. K.; Parr, R. G. Int. J. Quantum Chem. 2000, 77, 403-407.
20. Ayers, P. J. Chem. Phys., 2000, 113, 10886-10898.
21. Esquivel, R. O.; Rodríguez, A. L.; Sagar, R. P.; Ho, M.; Smith Jr., V. H. Phys. Rev. A 1996, 54, 259-265.
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24. Guevara, N. L.; Sagar, R. P.; Esquivel, R. O. Phys. Rev. A 2003, 67, 012507-1 – 012507-6.
25. Guevara, N. L.; Sagar, R. P.; Esquivel, R. O. J. Chem. Phys. 2005, 122, 084101-1 – 084101-8.
26. Sen, K. D.; Antolin, J.; Angulo, J. C. Phys. Rev. A 2007, 76, 032502-1 – 032502-7.
27. Sen, K. D.; Panos, C. P.; Chatsisavvas, K. Ch.; Moustakidis, Ch. C. Phys. Lett. A 2007, 364, 286-290.
28. Amovilli, C.; March, N. H. Phys. Rev. A 2004, 69, 054302-1 - 054302-4.
29. Huang, Z.; Kais, S. Chem. Phys. Lett. 2005, 413, 1-5
30. Huang Z; Wang H; Kais, S. J. Mod. Op. 2006, 53, 2543-2558.
31. Esquivel, R. O.; Flores-Gallegos, N. Phys. Rev. A (to be published).
32. Flores-Gallegos, N.; Esquivel, R. O. J. Comp. App. Math. (to be published).
33. Carrera, E.; Flores-Gallegos, N.; Esquivel; R. O. J. Comp. App. Math. in press, 2008.
34. Shannon, C. E.; Weaver, W. 1949, The Mathematical Theory of Communication (University of Illinois, Urbana, IL).
35. Kullback, S.; Leibler, R. A. Ann. Math. Stat. 1951, 22, 79-86.
36. For an earliest application of Kullback-Leibler measure see Raju K.B.K., Nair P. &V. and Sen K.D. Chem. Phys. Lett. 1990, 170, 89-93.
37. Einstein, A.; Podolsky, B; Rosen, N. Phys. Rev. 1935, 47, 777-780.
38. Bell, J., Speakable and Unspeakable in Quantum Mechanics 1987 (Cambridge University, Cambridge).
39. von Neumann, J., Mathematical Foundations of Quantum Mechanics, 1955 translated from the German ed. by R. T. Beyer (Princeton University, Princeton).
40. Wehrl, A. Rev. Mod. Phys. 1978, 50, 221-260.
41. Vedral, V. Rev Mod. Phys. 2002, 74, 197-234.
42. Araki, H.; Lieb, E. H. Commun. Math. Phys. 1970, 18, 160-170.
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44. Reed, A. E.; Weinhold, F. J. Chem. Phys. 1983, 78, 4066-4073.
45. Davidson, E. R. J. Chem. Phys. 1967, 46, 3320-3324.
46. Reed, A. E.; Weinstock, R. B; Weinhold, F. J. Chem. Phys. 1985, 83, 735-746.
47. Bruhn, G.; Davidson, E. R.; Mayer, I..; Clark, A. E. Int. J. Quantum Chem. 2006, 106, 2065-2072.
48. Nalewajski, R. F. Chem. Phys. Lett. 2003, 372, 28-34.
49. Rajagopal, A. K.; Rendell, R. W. Phys. Rev. A 2002, 66, 022104-1- 022104-10.
50. Cerf, N. J.; Adami; C. Phys. Rev. Lett. 1997, 79, 5194-5197.
51. Gaussian 03, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery Jr., J. A.; 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. 2004, Gaussian, Inc., Wallingford CT,
52. NBO 5.0. Glendening; E. D.; Badenhoop; J K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; and Weinhold, F. Theoretical Chemistry Institute 2001, University of Wisconsin, Madison.
53. MOLDEN: a pre- and post-processing program for molecular and electronic structures. J. Comput.-Aided Mol. Design 2000, 14,123-134.
54. It has been recently shown (Subin Liu, J.Chem. Phys. 2007, 126, 191107-1 - 191107-3) that the integrand of the Fisher measure of information may be expressed as the Laplacian of the density times log density, hence depletion/accumulation is multiplied by a relative entropy, i.e. log [rho(r)/1.0] in this new definition of Fisher measure. This explains the relevance of information measures in deciphering the local bonding charateristics.
55. Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553-566.
56. Liu B.; McLean, A. D. J. Chem. Phys. 1973, 59, 4557-4558.
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