A new approach to decoherence and momentum rescaling in the surface hopping algorithm

Journal of Chemical Physics

Volumn 134, Issue 2, 2011, Pages

  Subotnik, Joseph E ^a   Shenvi, Neil ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BRANCHING RATIO; DECOHERENCE; ELECTRONIC SURFACE; HIGHER-DIMENSIONAL PROBLEMS; KEY FEATURE; NEW APPROACHES; NON-ADIABATIC COUPLING; NUCLEAR WAVE PACKET; QUANTUM PARTICLES; RESCALING; SURFACE HOPPING; TWO-POINT;

ALGORITHMS; IMAGE QUALITY;

QUANTUM THEORY;

ALGORITHM; ARTICLE; QUANTUM THEORY; SURFACE PROPERTY;

ALGORITHMS; QUANTUM THEORY; SURFACE PROPERTIES;

EID: 78751506139     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3506779     Document Type: Article

References (68)

1. A. M. Wodtke, J. C. Tully, and D. J. Auerbach, Int. Rev. Phys. Chem. 23, 513 (2004).
2. M. D. Newton, in Electron Transfer in Chemistry, edited by V. Balzani (Wiley-VCH Verlag, New York, 2001), p. 3.
3. M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999).
4. R. A. Marcus, J. Phys. Chem. 67, 853 (1963).
5. R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265 (1985).
6. P. F. Barbara, T. J. Meyer, and M. A. Ratner, J. Phys. Chem. 100, 13148 (1996).
7. S. Jang, Y. Jung, and R. J. Silbey, Chem. Phys. 275, 319 (2002).
8. D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, J. Phys. Chem. B 113, 6583 (2009).
9. A. Nitzan, Chemical Dyanmics in Condensed Phases (Oxford University Press, New York, 2006).
10. G. Schatz and M. A. Ratner, Quantum Mechanics in Chemistry (Dover Publications, New York, 2002).
11. A. D. McLachlan, Mol. Phys. 8, 39 (1964).
12. H. D. Meyer and W. H. Miller, J. Chem. Phys. 72, 2272 (1980).
13. J. C. Tully, J. Chem. Phys. 93, 1061 (1990).
14. J. C. Tully, Faraday Discuss. 110, 407 (1998).
15. J. Y. Fang and S. Hammes-Schiffer, J. Phys. Chem. A 103, 9399 (1999).
16. R. Kapral and G. Ciccotti, J. Chem. Phys. 110, 8919 (1999).
17. S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys. 112, 6543 (2000).
18. R. Grunwald, A. Kelly, and R. Kapral, in Energy Transfer Dynamics in Biomaterial Systems, edited by I. Burghardt (Springer-Verlag, Berlin, 2009), p. 383.
19. I. V. Z. Aleksandrov, Naturforscher. 36a, 902 (1981).
20. W. Boucher and J. Traschen, Phys. Rev. D 37, 3522 (1988).
21. W. Y. Zhang and R. Balescu, J. Plasma Phys. 40, 199 (1988).
22. R. Balescu and W. Y. Zhang, J. Plasma Phys. 40, 215 (1988).
23. A. Anderson, Phys. Rev. Lett. 74, 621 (1995).
24. O. V. Prezhdo and V. V. Kisil, Phys. Rev. A 56, 162 (1997).
25. C. C. Martens and J. Y. Fang, J. Chem. Phys. 106, 4918 (1997).
26. A. Donoso and C. C. Martens, J. Phys. Chem. A 102, 4291 (1998).
27. D. A. Micha and B. Thorndyke, Int. J. Quant. Chem. 90, 759 (2002).
28. H. D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979).
29. G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997).
30. F. Webster, P. J. Rossy, and R. A. Friesner, Comput. Phys. Comm. 63, 494 (1991).
31. F.Webster, E. T.Wang, P. J. Rossy, and R. A. Friesner, J. Chem. Phys. 100, 4835 (1994).
32. B. J. Schwartz, E. R. Bittner, O. V. Prezhdo, and P. J. Rossky, J. Chem. Phys. 104, 5942 (1996).
33. K. F. Wong and P. J. Rossky, J. Chem. Phys. 116, 8418 (2002).
34. K. F. Wong and P. J. Rossky, J. Chem. Phys. 116, 8429 (2002).
35. O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. 107, 825 (1997).
36. O. V. Prezhdo, J. Chem. Phys. 111, 8366 (1999).
37. M. J. Bedard-Hearn, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 123, 234106 (2005).
38. R. E. Larsen, M. J. Bedard-Hearn, and B. J. Schwartz, J. Phys. Chem. B 110, 20055 (2006).
39. Y. L. Volobuev, M. D. Hack, M. S. Topaler, and D. G. Truhlar, J. Chem. Phys. 112, 9716 (2000).
40. M. D. Hack and D. G. Truhlar, J. Chem. Phys. 114, 2894 (2001).
41. A. W. Jasper, M. D. Hack, and D. G. Truhlar, J. Chem. Phys. 115, 1804 (2001).
42. C. Zhu, A. W. Jasper, and D. G. Truhlar, J. Chem. Phys. 120, 5543 (2004).
43. C. Zhu, S. Nangia, A. W. Jasper, and D. G. Truhlar, J. Chem. Phys. 121, 7658 (2004).
44. A. W. Jasper and D. G. Truhlar, J. Chem. Phys. 123, 064103 (2005).
45. J. Y. Fang and S. Hammes-Schiffer, J. Chem. Phys. 110, 11166 (1999).
46. E. Neria and A. Nitzan, J. Chem. Phys. 99, 1109 (1993).
47. J. R. Schmidt, P. V. Parandekar, and J. C. Tully, J. Chem. Phys. 129, 044104 (2008).
48. A. P. Horsfield, D. R. Bowler, A. J. Fisher, T. N. Todorov, and C. G. Sanchez, J. Phys.: Condens. Matter 16, 8251 (2004).
49. E. J. Heller, J. Chem. Phys. 75, 2923 (1981).
50. A. L. Thompson, C. Punwong, and T. J. Martinez, Chem. Phys. 370, 70 (2010).
51. X /h.where the rate now depends on the surface we are collapsing to (here, labeled k). To derive this equation, one must extend the expansion in Eqs. (9) and (10) to second order (Ref. 32).
52. J. E. Subotnik, J. Chem. Phys. 132, 134112 (2010).
53. A. P. Horsfield, D. R. Bowler, A. J. Fisher, T. N. Todorov, and C. G. Sanchez, J. Phys.: Condens. Matter 17, 4793 (2005).
54. L. Stella, M. Meister, A. J. Fisher, and A. P. Horsfield, J. Phys.: Condens. Matter 127, 214104 (2007).
55. E. J. McEniry, D. R. Bowler, D. Dundas, A. P. Horsfield, C. G. Sanchez, and T. N. Todorov, J. Phys.: Condens. Matter 19, 196201 (2007).
56. T. J. Martinez, M. Ben-Nun, and R. D. Levine, J. Phys. Chem. 100, 7884 (1996).
57. M. Ben-Nun and T. J. Martinez, J. Chem. Phys. 112, 6113 (2000).
58. S. D. Yang, J. D. Coe, B. Kaduk, and T. J. Martinez, J. Chem. Phys. 130, 134113 (2009).
59. Note that, as an alternative to FSSH dynamics, the MMST formalism solves this problem correctly without applying collapsing events to force decoher ence. In this case, coherent trajectories interfere by phase cancellation, and one finds the correct branching ratios (Refs. 66-68).
60. J. E. Subotnik and A. Nitzan, J. Chem. Phys. 129, 144107 (2008).
61. Note, however, that the expressions for decoherence in this paper and in Ref. 52 are not completely analogous. In particular, the equations of motion in Ref. 52 are only approximate, for they were based on Ehrenfest dynamics rather than the quantum Liouville equation. In this paper, we have the correct equations of motion, and we have shown the approximations necessary to rigorously derive Eq. (55).
62. E. J. Heller and D. Beck, Chem. Phys. Lett. 202, 350 (1993).
63. E. J. Heller, B. Segev, and A. V. Sergeev, J. Phys. Chem. B 106, 8471 (2002).
64. Both the FSSH and A-FSSH algorithms predict there should be nearly 100% transmission near k = 29 a.u. for an incoming wave packet with infinite spatial width (i.e., a plane wave).
65. D. Kosloff and R. Kosloff, J. Comp. Phys. 52, 35 (1983).
66. X. Sun and W. H. Miller, J. Chem. Phys. 106, 6346 (1997).
67. W. H. Miller, J. Chem. Phys. 127, 084114 (2007).
68. W. H. Miller, J. Phys. Chem. A 113, 1405 (2009).