Mixed quantum–classical dynamics

Abstract

We present a unified derivation of the mean-field (Ehrenfest) and surface-hopping approaches to mixed quantum–classical dynamics that elucidates the underlying approximations of the methods and their strengths and weaknesses. We then report a quantitative test of alternative mixed quantum–classical methods against accurate quantum mechanical calculations for a simple one-dimensional curve-crossing model. We conclude that, for this model, surface-hopping with the adiabatic representation is decidedly superior to either mean-field or surface-hopping with the diabatic representation.

References

1. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford, 1987.
2. R. Car and M. Parrinello, Phys. Rev. Lett., 1985, 55, 2471.
3. M. Born and J. R. Oppenheimer, Ann. Phys., 1927, 84, 457.
4. A. G. Redfield, Adv. Magn. Reson., 1965, 1, 1.
5. J. M. Jean, R. A. Friesner and G. R. Fleming, J. Chem. Phys., 1992, 96, 5827.
6. N. F. Mott, Proc. Cambridge Philos. Soc., 1931, 27, 553.
7. E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes in Gases, Clarendon, Oxford, 1974.
8. A. D. McLachlan, Mol. Phys., 1964, 8, 39.
9. J. C. Tully and R. K. Preston, J. Chem. Phys., 1971, 55, 562.
10. H. D. Meyer and W. H. Miller, J. Chem. Phys., 1980, 72, 2272.
11. D. A. Micha, J. Chem. Phys., 1983, 78, 7138.
12. Z. Kirson, R. B. Gerber, A. Nitzan and M. A. Ratner, Surf. Sci., 1984, 137, 527.
13. S. I. Sawada, A. Nitzan and H. Metiu, Phys. Rev. B, 1985, 32, 851.
14. H. J. C. Berendsen and J. Mavri, J. Phys. Chem., 1993, 97, 13464.
15. P. Bala, B. Lesyng and J. A. McCammon, Chem. Phys. Lett., 1994, 9, 259.
16. G. D. Billing, Int. Rev. Phys. Chem., 1994, 13, 309.
17. M. Head-Gordon and J. C. Tully, J. Chem. Phys., 1995, 103, 10137.
18. P. A. M. Dirac, Proc. Cambridge Philos. Soc., 1930, 26, 376.
19. J. Linderberg and Y. Ohrn, Propagators in Quantum Chemistry, Academic Press, New York, 1972.
20. E. J. Heller, J. Chem. Phys., 1976, 64, 63.
21. R. B. Gerber, V. Buch and M. A. Ratner, J. Chem. Phys., 1982, 77, 3022.
22. B. Jackson, Annu. Rev. Phys. Chem., 1995, 46, 251.
23. J. C. Tully, in Modern Methods for Multidimensional Dynamics Computation in Chemistry, ed. D. L. Thompson, World Scientific, Singapore, 1998, ch. 2.
24. A. Messiah, Quantum Mechanics, John Wiley, New York, 1962, vol. 1, pp. 222–228.
25. H. Goldstein, Classical Mechanics, Addison-Wesley, New York, 1950, pp. 273–317.
26. F. A. Bornemann, P. Nettesheim and C. Schutte, J. Chem. Phys., 1996, 105, 1074.
27. L. D. Landau, Phys. Zts. Sowjet., 1932, 2, 46.
28. C. Zener, Proc. Roy. Soc. Sci. A, 1932, 137, 696.
29. H. Nakamura and C. Zhu, Comments At. Mol. Phys., 1996, 32, 249.
30. U. Muller and G. Stock, J. Chem. Phys., 1997, 107, 6230.
31. D. Kohen, F. H. Stillinger and J. C. Tully, J. Chem. Phys., in press.
32. C. C. Martens and J.-Y. Fang, J. Chem. Phys., 1997, 106, 4918.
33. J. R. Stine and J. T. Muckerman, J. Chem. Phys., 1976, 65, 3975.
34. N. C. Blais and D. G. Truhlar, J. Chem. Phys., 1983, 79, 1334.
35. G. Parlant and E. A. Gislason, J. Chem. Phys., 1989, 91, 4416.
36. J. C. Tully, J. Chem. Phys., 1990, 93, 1061.
37. P. J. Kuntz, J. Chem. Phys., 1991, 95, 141.
38. F. J. Webster, P. J. Rossky and R. A. Friesner, Comput. Phys. Commun., 1991, 63, 494.
39. I. H. Gersonde and H. Gabriel, J. Chem. Phys., 1993, 98, 2094.
40. D. F. Coker and L. Xiao, J. Chem. Phys., 1995, 102, 496.
41. A. I. Krylov, R. B. Gerber and R. D. Coalson, J. Chem. Phys., 1996, 105, 4626.
42. O. V. Prezhdo and P. J. Rossky, J. Chem. Phys., 1997, 107, 6230.
43. J. C. Tully, in Modern Theoretical Chemistry: Dynamics of Molecular Collisions, ed. W. H. Miller, Plenum Press, New York, 1976, p. 217.
44. J. C. Tully, Int. J. Quantum Chem., 1991, 25, 299.
45. M. F. Herman, Annu. Rev. Phys. Chem., 1994, 45, 83.
46. S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys., 1995, 103, 8528.
47. E. Neria and A. Nitzan, J. Chem. Phys., 1993, 99, 1109.
48. S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys., 1994, 101, 4657.
49. B. J. Schwartz, E. R. Bittner, O. V. Prezhdo and P. J. Rossky, J. Chem. Phys., 1996, 104, 5942.
50. M. F. Herman, J. Chem. Phys., 1995, 103, 8081.
51. T. J. Martinez, M. Ben-Nun and R. D. Levine, J. Phys. Chem., 1996, 100, 7884.
52. X. Sun and W. H. Miller, J. Chem. Phys., 1997, 106, 6346.