Semiquantal time-dependent Hartree approach to condensed phase chemical dynamics: Application to the system-bath model

Journal of Chemical Physics

Volumn 121, Issue 15, 2004, Pages 7136-7143

  Ando, Koji ^a  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHEMICAL RELAXATION; COMPUTER SIMULATION; CONDENSATION; CONFORMATIONS; CORRELATION METHODS; ENERGY TRANSFER; FUNCTIONS; HYDRIDES; PROTONS; QUANTUM THEORY; RATE CONSTANTS;

CORRELATION FUNCTIONS (CF); SEMIQUANTAL TIME-DEPENDENT HARTREE (SQTDH) METHOD; VIBRATIONAL RELAXATION; WAVE PACKETS (WP);

MOLECULAR DYNAMICS;

EID: 8344227720     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1793152     Document Type: Article

References (48)

1. M. P. Allen and D. J. Tidesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
2. W. F. van Gunsteren and H. J. C. Berendsen, Angew. Chem., Int. Ed. Engl. 29, 992 (1990).
3. Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. Coker (World Scientific, Singapore, 1998).
4. D. Marx and J. Hutter, in Modern Methods and Algorithms of Quantum Chemistry, edited by J. Grotendorst (John von Neumann Institute, Jülich, 2000).
5. H. B. Schlegel, J. M. Millam, S. S. Iyengar, G. A. Voth, A. D. Daniels, G. E. Scuseria, and M. J. Frisch, J. Chem. Phys. 114, 9758 (2001).
6. W. H. Zurek, Phys. Today 44, 36 (1991).
7. K. Ando and J. T. Hynes, Adv. Chem. Phys. 110, 381 (1999), and references therein.
8. J. Borysow, M. Moraldi, and L. Frommhold, Mol. Phys. 56, 913 (1985).
9. K. Ando, J. Chem. Phys. 107, 4585 (1997).
10. S. A. Egorov, K. F. Everitt, and J. L. Skinner, J. Phys. Chem. A 103, 9494 (1999).
11. E. J. Heller, J. Chem. Phys. 62, 1544 (1975).
12. E. J. Heller, J. Chem. Phys. 64, 63 (1976).
13. M. H. Beck, A. Jäckle, G. A. Worth, and H. D. Meyer, Phys. Rep. 324, 1 (2000).
14. I. Burghardt, M. Nest, and G. A. Worth, J. Chem. Phys. 119, 5364 (2003).
15. M. Ben-Nun and T. J. Martinez, J. Chem. Phys. 108, 7244 (1998).
16. M. Ben-Nun and T. J. Martinez, J. Chem. Phys. 112, 6113 (2000).
17. N. Corbin and K. Singer, Mol. Phys. 46, 671 (1982).
18. K. Singer and W. Smith, Mol. Phys. 57, 761 (1986).
19. We follow Ref. 25 to call the present theory "semiquantal," whereas the specific functional form for the one-dimensional basis was proposed earlier in Ref. 22. It is also intriguing to note that an essentially equivalent extended Hamiltonian was rederived in Ref. 26 via a quite different route starting from a mixed quantum-classical theory of the Heisenberg EOMs. This QHD-2 approach was also presented as one-dimensional, and truncated the expansion of 〈V〉 at the fourth order, although the extension to many-dimension and to the higher order expansion seems similarly straightforward by assuming an appropriate decoupling of the coordinates.
20. R. Jackiw and A. Kerman, Phys. Lett. 71, 158 (1979).
21. M. Andrews, J. Phys. A 14, 1123 (1981).
22. F. Arickx, J. Broeckhove, E. Kesteloot, L. Lathouwers, and P. van Leuven, Chem. Phys. Lett. 128, 310 (1986).
23. F. Cooper, S. Y. Pi, and P. N. Standoff, Phys. Rev. D 34, 3831 (1986).
24. Y. Tsue, Prog. Theor. Phys. 88, 911 (1992).
25. A. K. Pattanayak and W. C. Schieve, Phys. Rev. E 50, 3601 (1994).
26. O. V. Prezhdo, J. Chem. Phys. 117, 2995 (2002).
27. J. Frenkel, Wave Mechanics: Advanced General Theory (Clarendon, Oxford, 1934).
28. P. Kramer and M Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics (Springer, Berlin, 1981).
29. J. Broeckhove, L. Lathouwers, E. Kesteloot, and P. van Leuven, Chem. Phys. Lett. 149, 547 (1988).
30. K. Ando, Chem. Phys. Lett. 376, 532 (2003).
31. α] which is also related to the canonicity condition Eq. (2.7).
32. T. Marumori, T. Maskawa, F. Sakata, and A. Kuriyama, Prog. Theor. Phys. 64, 1294 (1980).
33. M. Yamamura and A. Kuriyama, Prog. Theor. Phys. Suppl. 93, 1 (1987).
34. R. Kubo, M. Toda, and N. Hashitsume. Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer, New York, 1985).
35. i(t).
36. R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 (1980).
37. B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989).
38. We used the renormalized Numerov method for the quantum calculations. B. R. Johnson, J. Chem. Phys. 67, 4086 (1077); J. Roemelt, Chem. Phys. Lett. 74, 263 (1980).
39. We used the renormalized Numerov method for the quantum calculations. B. R. Johnson, J. Chem. Phys. 67, 4086 (1077); J. Roemelt, Chem. Phys. Lett. 74, 263 (1980).
40. M. S. Child, Semiclassical Mechanics with Molecular Applications (Clarendon, Oxford, 1991).
41. S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).
42. S. Y. Kim and S. Hammes-Schiffer, J. Chem. Phys. 119, 4389 (2003).
43. K. Takatsuka and H. Ushiyama, Phys. Rev. A 51, 4353 (1995).
44. S. Sawada and H. Metiu, J. Chem. Phys. 84, 6293 (1986).
45. R. D. Coalson, J. Phys. Chem. 100, 7896 (1996).
46. J. S. Bader and B. J. Berne, J. Chem. Phys. 100, 8359 (1994).
47. R. D. Coalson and M. Karplus, J. Chem. Phys. 79, 6150 (1983).
48. K. Ando and M. Santer, J. Chem. Phys. 118, 10399 (2003), and references therein.