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Non-Adiabatic Molecular Dynamics and Quantum Solvent Effects

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Advanced Topics in Theoretical Chemical Physics

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 12))

Abstract

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrodinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. 1. Branching, i.e., the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. 2. Decoherence, i.e., loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. 3. Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.

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References

  1. M. P. Allen and D. J. Tildesley, Computer Simulations in Liquids (Oxford Univ. Press, Great Britain, 1990 ).

    Google Scholar 

  2. W. Stier and O. V. Prezhdo, J. Phys. Chem. B, j. C. Tully special issue, in press.

    Google Scholar 

  3. O. V. Prezhdo and P. J. Rossky, J. Phys. Chem. 100, 17094 (1996).

    Article  CAS  Google Scholar 

  4. A. A. Mosyak, O. V. Prezhdo, and P. J. Rossky, J. Mol. Struct. 485–486, 545 (1999).

    Google Scholar 

  5. U. Muller and G. Stock, J. Chem. Phys. 107, 6230 (1997).

    Article  CAS  Google Scholar 

  6. F. A. Webster, J. Schnitker, M. S. Friedrichs, R. A. Friesner, and P. J. Rossky, Phys. Rev. Lett. 66, 3172 (1991).

    Article  CAS  Google Scholar 

  7. X. Song and R. A. Marcus, J. Chem. Phys. 99, 7768 (1993).

    Article  CAS  Google Scholar 

  8. S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).

    Article  CAS  Google Scholar 

  9. D. Borgis and J. T. Hynes, J. Phys. Chem. 100, 1118 (1996).

    Article  CAS  Google Scholar 

  10. M. S. Topaler, D. G. Truhlar, X. Y. Chang, P. Piecuch, and J. C. Polanyi, J. Chem. Phys. 108, 5349 (1998), the sign of the last term in Eq.(44) was changed, and the cfaF’2 coefficient in Eq. (64) was decreased by one order of magnitude.

    Google Scholar 

  11. M. Head-Gordon and J. C. Tully, J. Chem. Phys. 103, 10137 (1995).

    Article  CAS  Google Scholar 

  12. J. C. Tully, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. F. Coker ( World Scientific, Singapore, 1998 ), pp. 489–514.

    Google Scholar 

  13. D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998).

    Article  CAS  Google Scholar 

  14. J. C. Tully, J. Chem. Phys. 93, 1061 (1990).

    Google Scholar 

  15. J. C. Tully and R. K. Preston, J. Chem. Phys. 55, 562 (1971).

    Article  CAS  Google Scholar 

  16. E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes in Gases ( Clarendon, Oxford, 1974 ).

    Google Scholar 

  17. O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. 107, 825 (1997).

    Article  CAS  Google Scholar 

  18. O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. 107, 5863 (1997).

    Article  CAS  Google Scholar 

  19. O. V. Prezhdo and P. J. Rossky, Phys. Rev. Lett. 81, 5294 (1998).

    Article  CAS  Google Scholar 

  20. O. V. Prezhdo, J. Chem. Phys. ll, 8366 (1999).

    Google Scholar 

  21. C. Brooksby and O. V. Prezhdo, Chem. Phys. Lett. 346, 463 (2001).

    Article  CAS  Google Scholar 

  22. O. V. Prezhdo and C. Brooksby, Phys. Rev. Lett. 86, 3215 (2001).

    Article  CAS  Google Scholar 

  23. O. V. Prezhdo and C. Brooksby, Phys. Rev. Lett. 90, 118902 (2003).

    Google Scholar 

  24. F. A. Webster, P. J. Rossky, and R. A. Friesner, Comp. Phys. Comm. 63, 494 (1991).

    Article  CAS  Google Scholar 

  25. P. Pechukas, Phys. Rev. 181, 174 (1969).

    Article  CAS  Google Scholar 

  26. D. F. Coker and L. Xiao, J. Chem. Phys. 102, 496 (1995).

    Article  CAS  Google Scholar 

  27. D. F. Coker, in Computer Simulations in Chemical Physics, edited by M. P. Allen and D. J. Tildesley ( Kluwer Academic Publishers, Netherlands, 1993 ), pp. 315–377.

    Google Scholar 

  28. X. Sun, H. B. Wang, and W. H. Miller, J. Chem. Phys. 109, 7064 (1998).

    Article  CAS  Google Scholar 

  29. X. Sun and W. H. Miller, J. Chem. Phys. 106, 6346 (1997).

    Article  CAS  Google Scholar 

  30. H. D. Meyer and W. H. Miller, J. Chem. Phys. 72, 2272 (1980).

    Article  CAS  Google Scholar 

  31. N. C. Blais and D. G. Truhlar, J. Chem. Phys. 79, 1334 (1983).

    Article  CAS  Google Scholar 

  32. M. F. Herman, J. Chem. Phys. 103, 8081 (1995).

    Google Scholar 

  33. O. V. Prezhdo and V. V. Kisil, Phys. Rev. A 56, 162 (1997).

    Article  CAS  Google Scholar 

  34. J. Caro and L. L. Salcedo, Phys. Rev. A 60, 842 (1999).

    Article  CAS  Google Scholar 

  35. I. V. Aleksandrov, Z. Naturforsch. 36A, 902 (1981).

    Google Scholar 

  36. W. Boucher and J. Traschen, Phys. Rev. D 37, 3522 (1988).

    CAS  Google Scholar 

  37. A. Anderson, Phys. Rev. Lett. 74, 621 (1995).

    Article  CAS  Google Scholar 

  38. K. R. W. Jones, Phys. Rev. Lett. 76, 4087 (1996).

    Google Scholar 

  39. L. Diösi, Phys. Rev. Lett. 76, 4088 (1996).

    Article  Google Scholar 

  40. I. R. Senitzky, Phys. Rev. Lett. 76, 4089 (1996).

    Google Scholar 

  41. A. Anderson, Phys. Rev. Lett. 76, 4090 (1996).

    Article  CAS  Google Scholar 

  42. J. J. Halliwell, Phys. Rev. D 57, 2337 (1998).

    Google Scholar 

  43. L. Diösi and J. J. Halliwell, Phys. Rev. Lett. 81, 2846 (1998).

    Article  Google Scholar 

  44. V. V. Kisil, Phys. Essays 11, 69 (1998).

    Google Scholar 

  45. K. Hepp, Comm. Math. Phys. 35, 265 (1974).

    Article  Google Scholar 

  46. A. D. McLachlan, R. D. Gregory, and M. A. Ball, Mol. Phys. 7, 119 (1963–64).

    Google Scholar 

  47. W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972).

    Article  CAS  Google Scholar 

  48. X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997).

    Article  CAS  Google Scholar 

  49. E. J. Heller, J. Chem. Phys. 62, 1544 (1975).

    Google Scholar 

  50. R. B. Gerber, V. Buch, and M. A. Ratner, J. Chem. Phys. 77, 3022 (1982).

    Article  CAS  Google Scholar 

  51. M. F. Herman, Annu. Rev. Phys. Chem. 45, 83 (1994).

    Google Scholar 

  52. G. D. Billing, Int. Rev. Phys. Chem. 13, 309 (1994).

    Google Scholar 

  53. F. A. Webster, P. J. Rossky, and R. A. Friesner, Comp. Phys. Comm. 63, 494 (1991).

    Article  CAS  Google Scholar 

  54. E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995).

    Article  CAS  Google Scholar 

  55. O. V. Prezhdo, Phys. Rev. Lett. 85, 4413 (2000).

    Google Scholar 

  56. O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000).

    Article  CAS  Google Scholar 

  57. O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 116, 4450 (2002).

    Article  CAS  Google Scholar 

  58. E. Pähl and O. V. Prezhdo, J. Chem. Phys. 116, 8704 (2002).

    Article  Google Scholar 

  59. O. V. Prezhdo, J. Chem. Phys. 117, 2995 (2002).

    Google Scholar 

  60. P. Ehrenfest, Z. Physik 45, 455 (1927).

    Article  Google Scholar 

  61. N. Makri and W. H. Miller, J. Chem. Phys. 87, 5781 (1987).

    Article  CAS  Google Scholar 

  62. J. B. Delos, W. R. Thorson, and S. K. Knudson, Phys. Rev. A 6, 709 (1972).

    Article  Google Scholar 

  63. J. B. Delos and W. R. Thorson, Phys. Rev. A 6, 720 (1972).

    Article  Google Scholar 

  64. D. Böhm, Phys. Rev. 85, 166 (1952).

    Article  Google Scholar 

  65. D. Böhm, Phys. Rev. 85, 180 (1952).

    Article  Google Scholar 

  66. E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000).

    Article  CAS  Google Scholar 

  67. B. J. Schwartz, E. R. Bittner, O. V. Prezhdo, and P. J. Rossky, J. Chem. Phys. 104, 5942 (1996).

    Article  CAS  Google Scholar 

  68. W. H. Zurek, Progress of Theor. Phys. 89, 281 (1993).

    Google Scholar 

  69. W. H. Miller, W. L. Hase, and C. L. Darling, J. Chem. Phys. 91, 2859 (1989).

    Article  Google Scholar 

  70. M. Ben-Nun and R. D. Levine, J. Chem. Phys. 101, 8768 (1994).

    Article  Google Scholar 

  71. Y. Guo, D. L. Thompson, and T. D. Sewell, J. Chem. Phys. 104, 576 (1996).

    Article  CAS  Google Scholar 

  72. S. T. Epstein, in Force Concept in Chemistry ( Van Nostrand Reinhold, New York, 1981 ), pp. 1–38.

    Google Scholar 

  73. L. de Broglie, Acad. Sei. Paris 183, 447 (1926).

    Google Scholar 

  74. L. de Broglie, Acad. Sei. Paris 185, 580 (1927).

    Google Scholar 

  75. O. Maroney and B. J. Hiley, Found. Phys. 29, 1403 (1999).

    Article  Google Scholar 

  76. B. K. Dey, A. Askar, and H. Rabitz, Chem. Phys. Lett 297, 247 (1998).

    Article  CAS  Google Scholar 

  77. C. L. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).

    Article  CAS  Google Scholar 

  78. R. E. Wyatt, J. Chem. Phys. Ill, 4406 (1999).

    Google Scholar 

  79. G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).

    Article  Google Scholar 

  80. N. Gisin and I. C. Percival, J. Phys. A 25, 5677 (1992).

    Google Scholar 

  81. N. Gisin and I. C. Percival, Phys. Lett. A 167, 315 (1992).

    Article  Google Scholar 

  82. I. C. Percival, Proc. R. Soc. Lond. A 447, 189 (1994).

    Google Scholar 

  83. L. Diosi, Phys. Rev. A 40, 1165 (1989).

    Google Scholar 

  84. L. Diösi, N. Gisin, J. Halliwell, and I. Percival, Phys. Rev. Lett. 74, 203 (1995).

    Article  Google Scholar 

  85. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).

    Article  Google Scholar 

  86. G. J. Milburn, Phys. Rev. A 44, 5401 (1991).

    Google Scholar 

  87. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. ( Springer-Verlag, Berlin, 1990 ).

    Google Scholar 

  88. J. R. Klauder and W. P. Petersen, SIAM J. Numer. Anal. 22, 1153 (1985).

    Article  Google Scholar 

  89. R. W. Pastor, B. R. Brooks, and A. Szabo, Mol. Phys. 65, 1409 (1988).

    Article  Google Scholar 

  90. V. I. Tatarskii, Sov. Phys. Usp. 26, 311 (1983).

    Google Scholar 

  91. J. Stromquist and S. Gao, J. Chem. Phys. 106, 5751 (1996).

    Article  Google Scholar 

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Prezhdo, O.V., Brooksby, C. (2003). Non-Adiabatic Molecular Dynamics and Quantum Solvent Effects. In: Maruani, J., Lefebvre, R., Brändas, E.J. (eds) Advanced Topics in Theoretical Chemical Physics. Progress in Theoretical Chemistry and Physics, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0635-3_12

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  • DOI: https://doi.org/10.1007/978-94-017-0635-3_12

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