On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation

Journal of Chemical Physics

Volumn 120, Issue 7, 2004, Pages 3086-3099

  Yamamoto, Takeshi ^a   Miller, William H ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM INSTANTON (QI) APPROXIMATION; THERMAL RATE CONSTANT;

COMPUTER SIMULATION; CORRELATION METHODS; FREE ENERGY; FUNCTIONS; HEAT FLUX; MATHEMATICAL OPERATORS; MONTE CARLO METHODS; QUANTUM THEORY; THERMAL EFFECTS;

RATE CONSTANTS;

EID: 1642269882     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1641005     Document Type: Article

References (63)

1. W. H. Miller, Y. Zhao, M. Ceotto, and S. Yang, J. Chem. Phys. 119, 1329 (2003).
2. W. H. Miller, J. Chem. Phys. 62, 1899 (1975).
3. S. Coleman, Phys. Rev. D 15, 2929 (1977).
4. A. J. Leggett, S. Chakravarty, A. T. Dosey, M. P. A. Fisger, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
5. V. A. Benderskii, V. I. Goldanskii, and D. E. Makarov, Phys. Rep. 233, 195 (1993).
6. Z. Smedarchina, M. Z. Zgierski, W. Siebrand, and P. M. Kozlowski, J. Chem. Phys. 102, 7024 (1995); 109, 1014 (1998).
7. Z. Smedarchina, M. Z. Zgierski, W. Siebrand, and P. M. Kozlowski, J. Chem. Phys. 102, 7024 (1995); 109, 1014 (1998).
8. Z. Smedarchina, W. Siebrand, A. Fernandez-Ramos, L. Gorg, and J. Leszczynski, J. Chem. Phys. 112, 566 (2000).
9. S. Chapman, B. C. Garrett, and W. H. Miller, J. Chem. Phys. 63, 2710 (1975).
10. A. Gonzalezlafont, S. N. Rai, G. C. Hancock, T. Joseph, and D. G. Truhlar, Chem. Phys. Lett. 75, 143 (1993).
11. G. A. Voth, D. Chandler, and W. H. Miller, J. Phys. Chem. 93, 7009 (1989); J. Chem. Phys. 91, 7749 (1989).
12. G. A. Voth, D. Chandler, and W. H. Miller, J. Phys. Chem. 93, 7009 (1989); J. Chem. Phys. 91, 7749 (1989).
13. S. Jang and G. A. Voth, J. Chem. Phys. 112, 8747 (2000).
14. W. H. Miller, J. Phys. Chem. 103, 9384 (1999).
15. E. Pollak and J. L. Liao, J. Chem. Phys. 108, 2733 (1998).
16. J. Shao, J. L. Liao, and E. Pollak, J. Chem. Phys. 108, 9711 (1998); J. L. Liao and E. Pollak, J. Phys. Chem. A 104, 1799 (2000).
17. J. Shao, J. L. Liao, and E. Pollak, J. Chem. Phys. 108, 9711 (1998); J. L. Liao and E. Pollak, J. Phys. Chem. A 104, 1799 (2000).
18. K. Yamashita and W. H. Miller, J. Chem. Phys. 82, 5475 (1985).
19. J. W. Tromp and W. H. Miller, J. Phys. Chem. 90, 3482 (1986).
20. N. F. Hansen and H. C. Andersen, J. Chem. Phys. 101, 6032 (1994); J. Phys. Chem. 100, 1137 (1996).
21. N. F. Hansen and H. C. Andersen, J. Chem. Phys. 101, 6032 (1994); J. Phys. Chem. 100, 1137 (1996).
22. G. Krilov, E. Sim, and B. J. Berne, J. Chem. Phys. 114, 1075 (2001).
23. E. Sim, G. Krilov, and B. J. Berne, J. Phys. Chem. A 105, 2824 (2001).
24. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
25. R. P. Feynman, Statistical Mechanics (Benjamin, New York, 1972).
26. L. S. Schulman, Techniques and Applications of Path Integrals (Wiley, New York, 1986).
27. B. J. Berne and D. Thirumalai, Annu. Rev. Phys. Chem. 37, 401 (1986).
28. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995).
29. C. Chakravarty, Int. Rev. Phys. Chem. 16, 421 (1997).
30. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).
31. γ(q) and (ii) an orthogonal transformation among mass-weighted coordinate systems (e.g., that between Cartesian and Jacobi coordinates).
32. D. Chandler, J. Chem. Phys. 68, 2959 (1978).
33. Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. F. Coker (World Scientific, Singapore, 1998).
34. D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, San Diego, 1996).
35. G. M. Torrie and J. P. Valleau, Chem. Phys. Lett. 28, 578 (1974); J. Comput. Phys. 23, 187 (1977).
36. G. M. Torrie and J. P. Valleau, Chem. Phys. Lett. 28, 578 (1974); J. Comput. Phys. 23, 187 (1977).
37. D. Chandler, An Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987).
38. M. E. Tuckerman and A. Hughes, Chap. 14 in Ref. 29.
39. E. Rabani and D. R. Reichman, J. Phys. Chem. B 105, 6550 (2001).
40. E. Rabani, D. R. Reichman, G. Krilov, and B. J. Berne, Proc. Natl. Acad. Sci. U.S.A. 99, 1129 (2002).
41. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23, 327 (1977).
42. b) becomes finite; see Sec. III for the treatment of scattering systems.
43. M. Mezei, J. Comput. Phys. 68, 237 (1987).
44. R. W. W. Hooft, B. P. van Eijck, and J. Kroon, J. Chem. Phys. 97, 6690 (1992).
45. C. Bartels and M. Karplus, J. Comput. Chem. 18, 1450 (1997).
46. Adaptive umbrella sampling is an example of the so-called extended-ensemble Monte Carlo methods. For an extensive review of the latter, see Y. Iba, Int. J. Mod. Phys. C 12, 623 (2001).
47. B. A. Berg and T. Neuhaus, Phys. Lett. B 267, 249 (1991); Phys. Rev. Lett. 68, 9 (1992).
48. B. A. Berg and T. Neuhaus, Phys. Lett. B 267, 249 (1991); Phys. Rev. Lett. 68, 9 (1992).
49. J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics (World Scientific, Singapore, 1999).
50. J. M. Bowman, D. Wang, X. Huang, F. Huarte-Larranaga, and U. Manthe, J. Chem. Phys. 114, 9683 (2001).
51. T. Yamamoto and W. H. Miller, J. Chem. Phys. 118, 2135 (2003).
52. E. L. Pollock and D. M. Ceperley, Phys. Rev. B 30, 2555 (1984).
53. M. Sprik, M. L. Klein, and D. Chandler, Phys. Rev. B 31, 4234 (1985); 32, 545 (1985).
54. M. Sprik, M. L. Klein, and D. Chandler, Phys. Rev. B 31, 4234 (1985); 32, 545 (1985).
55. M. E. Tuckerman, B. J. Berne, G. J. Martyna, and M. L. Klein, J. Chem. Phys. 99, 2796 (1993).
56. S. L. Mielke, G. C. Lynch, D. G. Truhlar, and D. W. Schwenke, J. Phys. Chem. 98, 8000 (1994).
57. P. Siegbahn and B. Liu, J. Chem. Phys. 68, 2457 (1978); D. G. Truhlar and C. J. Horowitz, ibid. 68, 2466 (1978).
58. P. Siegbahn and B. Liu, J. Chem. Phys. 68, 2457 (1978); D. G. Truhlar and C. J. Horowitz, ibid. 68, 2466 (1978).
59. J. V. Michael and J. R. Fisher, J. Phys. Chem. 94, 3318 (1990).
60. See, for example, Y. Zhao, T. Yamamoto, and W. H. Miller, J. Chem. Phys. 120, 3100 (2004).
61. J. A. Barker, J. Chem. Phys. 70, 2914 (1979).
62. K. R. Glaesemann and L. E. Fried, J. Chem. Phys. 117, 3020 (2002).
63. R. Ramirez, J. Chem. Phys. 107, 5748 (1997).