Semiquantal valence-bond wave packet description of chemical bonding

Bulletin of the Chemical Society of Japan

Volumn 82, Issue 8, 2009, Pages 975-983

  Ando, Koji ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING COORDINATES; CHEMICAL BONDINGS; ELECTRON-PAIR APPROXIMATIONS; ENERGY SURFACE; GAUSSIAN ORBITALS; GROUND STATE POTENTIAL; HAMILTONIAN FORMALISM; MANY ELECTRON; NUMERICAL CALCULATION; PHASE SPACES; POTENTIAL ENERGY CURVES; PSEUDOPOTENTIALS; VALENCE BOND THEORY; VALENCE BONDS;

BINDING ENERGY; CHEMICAL BONDS; ELECTRONS; PHASE SPACE METHODS; POTENTIAL ENERGY SURFACES; PUMPING PLANTS; QUANTUM CHEMISTRY; REACTION KINETICS; SURFACE PHENOMENA; WAVE PACKETS; WAVES;

POTENTIAL ENERGY;

EID: 68949187641     PISSN: 00092673     EISSN: 13480634     Source Type: Journal    
DOI: 10.1246/bcsj.82.975     Document Type: Article

References (61)

1. Recent Advances inMultireference Methods, ed. by K. Hirao, WorldScientific, Singapore, 1999.
2. 2T. Helgaker, P. Jorgensen, J. Olsen, Molecular Electronic- Structure Theory, Wiley, Chichester, 2000.
3. 3M. P. Allen, D. J. Tidesley, Computer Simulation of Liquids, Clarendon, Oxford, 1987.
4. Molecular Theory of Solvation, ed. by F. Hirata, Kluwer Academic, Dordrecht, 2003.
5. K. Yasuda, D. Yamaki, J. Chem. Phys. 2004, 121, 3964.
6. H. Lin, D. G. Truhlar, Theor. Chem. Acc. 2007, 117, 185.
7. H. B. Schlegel, S.M.Smith, X. Li, J. Chem. Phys. 2007, 126, 244110.
8. K. Burke, J. Werschnik, E. K. U. Gross, J. Chem. Phys. 2005, 123, 062206.
9. T. Kato, H. Kono, J. Chem. Phys. 2008, 128, 184102.
10. T. Yonehara, K. Takatsuka, J. Chem. Phys. 2008, 128, 154104.
11. We apologize that the reference list in the above is far from complete.
12. K. Ando, J. Chem. Phys. 2004, 121, 7136.
13. K. Ando, J. Chem. Phys. 2006, 125, 014104.
14. N. Sakumichi, K. Ando, J. Chem. Phys. 2008, 128, 164516.
15. A. A. Frost, in Modern Theoretical Chemistry, Vol. 3, ed. by H. F. Shaefer, Plenum, New York, 1977.
16. L. Wilets, E. M. Henley, M. Kraft, A. D. Mackellar, Nucl. Phys. 1977, A282, 341.
17. C. Dorso, S. Duarte, J. Randrup, Phys. Lett. B 1987, 188, 287.
18. D. Klakow, C. Toepffer, P.-G. Reinhard, J. Chem. Phys. 1994, 101, 10766.
19. A. Ono, H. Horiuchi, T. Maruyama, A. Ohnishi, Prog. Theor. Phys. 1992, 87, 1185.
20. H. Feldmeier, J. Schnack, Rev. Mod. Phys. 2000, 72, 655.
21. J. T. Su, W. A. Goddard, Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 1001.
22. This form of the trialfunction in one-dimension has been studied inRefs. 23 and 24, and called a "semiquantal" ansatz in the latter. The semiquantal and semiclassical theories were distinguished as the classical nature emerges by restricting the Hilbert space in the former, while the classical trajectories are approximately quantized in the latter.
23. F. Arickx, J. Broeckhove, E. Kesteloot, L. Lathouwers, P. van Leuven, Chem. Phys. Lett. 1986, 128, 310.
24. A. K. Pattanayak, W. C. Schieve, Phys. Rev. E 1994, 50, 3601.
25. P. Kramer, M. Saraceno, Geometry ofthe Time-Dependent Variational Principle in Quantum Mechanics, Springer, Berlin, 1981.
26. T. Marumori, T. Maskawa, F. Sakata, A. Kuriyama, Prog. Theor. Phys. 1980, 64, 1294.
27. O. V. Prezhdo, Theor. Chem. Acc. 2006, 116, 206.
28. Y. Shigeta, H. Miyachi, T. Matsui, K.Hirao, Bull. Chem. Soc. Jpn. 2008, 81, 1230.
29. S. F. Boys, Proc. Roy. Soc. Lond. A 1950, 200, 542.
30. C. M. Reeves, J. Chem. Phys. 1963, 39, 1.
31. L. Pauling, E. B. Wilson, Introduction to Quantum Mechanics with Applications to Chemistry, Dover, New York, 1985.
32. The Slater-type exponentialfunctions are, however, not adequate for the floating basis as they introduce unnecessary cusps in the free space between the nuclei.
33. W. Heitler, F. London, Z. Phys. 1927, 44, 455.
34. R. S. Mulliken, J. Chim. Phys. 1949, 46, 500;
35. R. S. Mulliken, J. Chim. Phys. 1949, 46, 521.
36. Here we deal with a single VB configuration consisting of the perfect-pairing spin-couplings such as αβ-αβ and three others, and not with the resonance between the alternative spin-coupling configuration such as ααββ. Cases where the resonance is essential will be discussed elsewhere.
37. J. C. Slater, Phys. Rev. 1931, 38, 1109.
38. M. H. Cohen, V. Heine, Phys. Rev. 1961, 122, 1821.
39. N. W. Ashcroft, Phys. Lett. 1966, 23, 48.
40. W. C. Topp, J. J. Hopfield, Phys. Rev. B 1973, 7, 1295.
41. R. Brent, Algorithms for Minimization without Derivatives, Dover, New York, 2002.
42. S. C. Wang, Phys. Rev. 1928, 31, 579.
43. H. Shull, D.D.Ebbing, J. Chem. Phys. 1958, 28, 866.
44. A. C. Hurley, Proc. Roy. Soc. Lond. A 1954, 226, 179.
45. H. Nakatsuji, S. Kanayama, S. Harada, T. Yonezawa, J. Am. Chem. Soc. 1978, 100, 7528.
46. H. Huber, THEOCHEM 1981, 76, 277.
47. T. Helgaker, J. Almlof, J. Chem. Phys. 1988, 89, 4889.
48. K. Hirao, K. Mogi, J. Comput. Chem. 1992, 13, 457.
49. M. Tachikawa, K. Taneda, K. Mori, Int. J. Quantum Chem. 1999, 75, 497.
50. W. Kolos, L. Wolniewicz, J. Chem. Phys. 1968, 49, 404.
51. F. H. Crawford, T. Jorgensen, Jr., Phys. Rev. 1935, 47, 932.
52. W. Meyer, P. Rosmus, J. Chem. Phys. 1975, 63, 2356.
53. K. Hirao, Chem. Phys. Lett. 1992, 190, 374.
54. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. J. Su, T. L. Windus, M. Dupuis, J. A. Montgomery, Jr., J. Comput. Chem. 1993, 14, 1347.
55. B. Ford, G. G. Hall, J. C. Packer, Int. J. Quantum Chem. 1970, 4, 533.
56. To quote from Ref. 54, ".a single Gaussian is such a poor representation of the cusp, (⋯), that an outer function will try to move on to the nucleus to improve the representation there rather than to routside and represent the more weakly bound electrons.
57. R. J. Gillespie, E. A. Robinson, Angew. Chem., Int. Ed. Engl. 1996, 35, 495.
58. H. Nakai, Int. J. Quantum Chem. 2007, 107, 2849.
59. T. Ishimoto, M. Tachikawa, U. Nagashima, J. Chem. Phys. 2008, 128, 164118.
60. A. Chakraborty, S. Hammes-Schiffer, J. Chem. Phys. 2008, 129, 204101.
61. A. Szabo, N. S. Ostlund, Modern Quantum Chemistry, Dover, New York, 1996.