Mixed quantum-classical surface hopping dynamics

Journal of Chemical Physics

Volumn 112, Issue 15, 2000, Pages 6543-6553

  Nielsen, Steve ^a   Kapral, Raymond ^a   Ciccotti, Giovanni ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001537736     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.481225     Document Type: Article

References (31)

1. J. C. Tully in Modern Methods for Multidimensional Dynamics Computations in Chemistry, edited by D. L. Thompson (World Scientific, New York, 1998), p. 34.
2. M. F. Herman, Annu. Rev. Phys. Chem. 45, 83 (1994).
3. P. Pechukas, Phys. Rev. 181, 166 (1969); 181, 174 (1969).
4. P. Pechukas, Phys. Rev. 181, 166 (1969); 181, 174 (1969).
5. J. C. Tully, J. Chem. Phys. 93, 1061 (1990); J. C. Tully, Int. J. Quantum Chem. 25, 299 (1991); D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998); S. Hammes-Schiffer and J. C. Tully, ibid. 101, 4657 (1994).
6. J. C. Tully, J. Chem. Phys. 93, 1061 (1990); J. C. Tully, Int. J. Quantum Chem. 25, 299 (1991); D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998); S. Hammes-Schiffer and J. C. Tully, ibid. 101, 4657 (1994).
7. J. C. Tully, J. Chem. Phys. 93, 1061 (1990); J. C. Tully, Int. J. Quantum Chem. 25, 299 (1991); D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998); S. Hammes-Schiffer and J. C. Tully, ibid. 101, 4657 (1994).
8. J. C. Tully, J. Chem. Phys. 93, 1061 (1990); J. C. Tully, Int. J. Quantum Chem. 25, 299 (1991); D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998); S. Hammes-Schiffer and J. C. Tully, ibid. 101, 4657 (1994).
9. L. Xiao and D. F. Coker, J. Chem. Phys. 100, 8646 (1994): D. F. Coker and L. Xiao, ibid. 102, 496 (1995); H. S. Mei and D. F. Coker, ibid. 104, 4755 (1996).
10. L. Xiao and D. F. Coker, J. Chem. Phys. 100, 8646 (1994): D. F. Coker and L. Xiao, ibid. 102, 496 (1995); H. S. Mei and D. F. Coker, ibid. 104, 4755 (1996).
11. L. Xiao and D. F. Coker, J. Chem. Phys. 100, 8646 (1994): D. F. Coker and L. Xiao, ibid. 102, 496 (1995); H. S. Mei and D. F. Coker, ibid. 104, 4755 (1996).
12. F. Webster, P. J. Rossky, and R. A. Friesner, Comput. Phys. Commun. 63, 494 (1991); F. Webster, E. T. Wang, P. J. Rossky, and R. A. Friesner, J. Chem. Phys. 100, 4835 (1994).
13. F. Webster, P. J. Rossky, and R. A. Friesner, Comput. Phys. Commun. 63, 494 (1991); F. Webster, E. T. Wang, P. J. Rossky, and R. A. Friesner, J. Chem. Phys. 100, 4835 (1994).
14. R. Kapral and G. Ciccotti, J. Chem. Phys. 110, 8919 (1999).
15. For other derivations of related equations, see W. Y. Zhang and R. Balescu, J. Plasma Phys. 40, 199 (1988); R. Balescu and W. Y. Zhang, ibid. 40, 215 (1988); C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
16. For other derivations of related equations, see W. Y. Zhang and R. Balescu, J. Plasma Phys. 40, 199 (1988); R. Balescu and W. Y. Zhang, ibid. 40, 215 (1988); C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
17. For other derivations of related equations, see W. Y. Zhang and R. Balescu, J. Plasma Phys. 40, 199 (1988); R. Balescu and W. Y. Zhang, ibid. 40, 215 (1988); C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
18. For other derivations of related equations, see W. Y. Zhang and R. Balescu, J. Plasma Phys. 40, 199 (1988); R. Balescu and W. Y. Zhang, ibid. 40, 215 (1988); C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
19. E. Wigner, Phys. Rev. 40, 749 (1932).
20. K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 5, 1097 (1967).
21. Equation (12) corrects a sign error in the definition of the phase factor W in Eq. (41) of Ref. 7.
22. V. S. Filinov, Yu. V. Medvedev, and V. L. Kamskyi, Mol. Phys. 85, 711 (1995); V. S. Filinov, S. Bonella, Y. L. Lozovik, A. V. Filinov, and I. Zacharov, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. Coker (World Scientific, Singapore, 1998), p. 667.
23. V. S. Filinov, Yu. V. Medvedev, and V. L. Kamskyi, Mol. Phys. 85, 711 (1995); V. S. Filinov, S. Bonella, Y. L. Lozovik, A. V. Filinov, and I. Zacharov, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. Coker (World Scientific, Singapore, 1998), p. 667.
24. See, for example, A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987); R. Silbey and R. A. Harris, J. Phys. Chem. 93, 7062 (1989); X. Song and R. Marcus, J. Chem. Phys. 99, 7768 (1993); M. Topaler and N. Makri, J. Phys. Chem. 100, 4430 (1996), and references therein.
25. See, for example, A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987); R. Silbey and R. A. Harris, J. Phys. Chem. 93, 7062 (1989); X. Song and R. Marcus, J. Chem. Phys. 99, 7768 (1993); M. Topaler and N. Makri, J. Phys. Chem. 100, 4430 (1996), and references therein.
26. See, for example, A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987); R. Silbey and R. A. Harris, J. Phys. Chem. 93, 7062 (1989); X. Song and R. Marcus, J. Chem. Phys. 99, 7768 (1993); M. Topaler and N. Makri, J. Phys. Chem. 100, 4430 (1996), and references therein.
27. See, for example, A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987); R. Silbey and R. A. Harris, J. Phys. Chem. 93, 7062 (1989); X. Song and R. Marcus, J. Chem. Phys. 99, 7768 (1993); M. Topaler and N. Makri, J. Phys. Chem. 100, 4430 (1996), and references therein.
28. Systems with low-dimensional classical baths have been used to test the validity of mixed quantum-classical schemes. See, for instance, D. Kohen, F. H. Stillinger, and J. C. Tully, J. Chem. Phys. 109, 4713 (1998).
29. 12 is equal to the bare bath Liouvillian.
30. E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995); O. V. Prezhdo and P. J. Rossky, Phys. Rev. Lett. 81, 5294 (1998).
31. E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995); O. V. Prezhdo and P. J. Rossky, Phys. Rev. Lett. 81, 5294 (1998).