Progress in the theory of mixed quantum-classical dynamics

Annual Review of Physical Chemistry

Volumn 57, Issue , 2006, Pages 129-157

  Kapral, Raymond ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Nonadiabatic dynamics; Quantum rate processes; Quantum classical systems

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); ELECTRON TRANSPORT PROPERTIES; EQUATIONS OF MOTION; MOLECULAR DYNAMICS;

NONADIABATIC DYNAMICS; QUANTUM RATE PROCESSES; QUANTUM-CLASSICAL SYSTEMS; SURFACE-HOPPING;

QUANTUM THEORY;

EID: 33646737290     PISSN: 0066426X     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.physchem.57.032905.104702     Document Type: Conference Paper

References (80)

1. Davis EB. 1916. Quantum Theory of Open Systems. London: Academic
2. Weiss U. 1999. Quantum Dissipative Systems. Singapore: World Sci.
3. Lindblad G. 1976. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48:119-30
4. Gorini V, Kossakowski A, Sudarshan ECG. 1976. Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17:821-25
5. Aliki R, Lendi K. 1987. Quantum dynamical semigroups and applications. In Lecture Notes in Physics, Vol. 286. Berlin: Springer-Verlag
6. Redfield A. 1965. In Advances in Magnetic Resonance, ed. J Waugh, Vol 1. New York: Academic
7. Blum K. 1981. Density Matrix Theory and Applications. New York: Plenum
8. Laria D, Ciccotti G, Ferrario M, Kapral R. 1992. Molecular-dynamics study of adiabatic proton-transfer reactions in solution. J. Chem. Phys. 97:378-88
9. Azzouz H, Borgis D. 1993. A quantum molecular-dynamics study of proton-transfer reactions along asymmetrical H bonds in solution. J. Chem. Phys. 98:7361-74
10. Hammes-Schiffer S, Tully JC. 1994. Proton transfer in solution: Molecular dynamics with quantum transitions. J. Chem. Phys. 101:4657-67
11. Consta S, Kapral R. 1995. Dynamics of proton transfer in mesoscopic clusters. J. Chem. Phys. 104:4581-90
12. Tully JC. 1990. Molecular dynamics with electronic transitions. J. Chem. Phys. 93:1061-71
13. Tully JC. 1998. Mixed quantum-classical dynamics: mean-field and surface-hopping. In Classical and Quantum Dynamics in Condensed Phase Simulations, ed. BJ Berne, G Ciccotti, DF Coker, pp. 489-514. Singapore: World Sci.
14. Thompson K, Makri N. 1998. Rigorous forward-backward semiclassical formulation of many-body dynamics. Phys. Rev. E 59:R4729-32
15. Thoss M, Wang H, Miller WH. 2001. Generalized forward-backward initial value representation for the calculation of correlation functions in complex systems. J. Chem. Phys. 114:9220-35
16. Bonella S, Coker D. 2005. LAND-map, a linearized approach to nonadiabatic dynamics using the mapping formalism. J. Chem. Phys. 122:194102-13
17. Rabani E, Reichman D. 2004. A fully self-consistent treatment of collective fluctuations in quantum liquids. J. Chem. Phys. 120:1458-65
18. Kapral R, Ciccotti G. 2002. A statistical mechanical theory of quantum dynamics in classical environments. In Bridging Time Scales: Molecular Simulations for the Next Decade, ed. P Nielaba, M Mareschal, G Ciccotti, 605:445-72. Berlin: Springer-Verlag
19. Pechukas P. 1969, Time-dependent semi-classical scattering theory. I. Potential scattering. Phys. Rev. 181:166-74
20. Pechukas P. 1969. Time-dependent semi-classical scattering theory. II. Atomic collisions. Phys. Rev. 181:174-85
21. Wigner E. 1932. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40:749-59
22. Imre K, Özizmir E, Rosenbaum M, Zwiefel PF. 1967. Wigner method in quantum statistical mechanics. J. Math. Phys. 8:1097-108
23. Hillery M, O'Connell RF, Scully MO, Wigner EP. 1984. Distribution functions in physics: Fundamentals. Phys. Rep. 106:121-67
24. Kapral R, Ciccotti G. 1999. Mixed quantum-classical dynamics. J. Chem. Phys. 110:8919-29
25. Shiokawa K, Kapral R. 2002. Emergence of quantum-classical dynamics in an open quantum environment. J, Chem. Phys. 117:7852-63
26. Aleksandrov IV. 1981. The statistical dynamics of a system consisting of a classical and a quantum subsystem. Z. Naturforsch. Teil A 36:902-8
27. Gerasimenko VI. 1982. Dynamical equations of quantum-classical systems. Theor. Math. Phys. 50:49-55
28. Boucher W, Traschen J. 1988. Semiclassical physics and quantum fluctuations. Phys. Rev. D 37: 3522-32
29. Zhang WY, Balescu R. 1988. Statistical mechanics of a spin-polarized plasma. J. Plasma Phys. 40:199-213
30. Martens CC, Fang JY. 1996. Semiclassical-limit molecular dynamics on multiple electronic surfaces. J. Chem. Phys. 106:4918-30
31. Horenko I, Salzmann C, Schmidt B, Schütte C. 2002. Quantum-classical Liouville approach to molecular dynamics: Surface hopping Gaussian phase-space packets. J. Chem. Phys. 117:11075-88
32. Shi Q, Geva E. 2004. A derivation of the mixed quantum-classical Liouville equation from the influence functional formalism. J. Chem. Phys. 121:3393-404
33. Nielsen S, Kapral R, Ciccotti G. 2001. Statistical mechanics of quantum-classical systems. J. Chem. Phys. 115:5805-15
34. Kapral R. 2001. Quantum-classical dynamics in a classical bath. J. Phys. Chem. A 105:2885-89
35. Toutounji M, Kapral R. 2001. Subsystem dynamics in mixed quantum-classical systems. Chem. Phys. 268:79-89
36. Romero-Rochin V, Oppenheim I. 1989. Relaxation properties of two-level systems in condensed phases. Physica A 155:52-72
37. Romero-Rochin V, Orsky A, Oppenheim I. 1989. Theory of spin-relaxation processes. Physica A 156:244-59
38. Nakajima S. 1958. On quantum theory of transport phenomena. Prog. Theor. Phys. 20:948-59
39. Zwanzig R. 1961. Statistical mechanics of irreversibility. In Lectures in Theoretical Physics, ed. WE Brittin, BW Downs, J Downs, 3:106-41. New York: Interscience
40. Caldeira AO, Leggett AJ. 1983. Path integral approach to quantum Brownian motion. Physica A 121:587-616
41. Hakim V, Ambegaokar V. 1985. Quantum theory of a free particle interacting with a linearly dissipative environment. Phys. Rev. A 32:423-34
42. Grabert H, Schramn P, Ingold GL. 1988. Quantum Brownian motion: The functional integral approach. Phys. Rep. 168:115-207
43. Unruh WG, Zurek WH. 1989. Reduction of a wave packet in quantum Brownian motion. Phys. Rev. D 40:1071-94
44. Anastopoulos C, Halliwell JJ. 1995. Generalized uncertainty relations and long-time limits for quantum Brownian motion models. Phys. Rev. D 51:6870-85
45. Hu BL, Paz JP, Zhang Y. 1992. Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. Phys. Rev. D 45:2843-61
46. Thompson K, Makri N. 1999. Influence functional with semiclassical propagators in combined forwardbackward time. J. Chem. Phys. 110:1343-53
47. Makri N. 1999. The linear response approximation and its lowest order corrections: An influence functional approach. J. Phys. Chem. B 103:2823-29
48. Donoso A, Martens CC. 1998. Simulation of coherent nonadiabatic dynamics using classical trajectories. J. Phys. Chem. A 102:4291-300
49. Wan CC, Schofield J. 2000. Mixed quantum-classical molecular dynamics: Aspects of the multithreads algorithm. J. Chem. Phys. 113:704754
50. Wan CC, Schofield J. 2002. Solutions of mixed quantum-classical dynamics in multiple dimensions using classical trajectories. J. Chem. Phys. 116:494-506
51. Sanier M, Manthe U, Stock G. 2001, Quantum-classical Liouville description of multidimensional nonadiabatic molecular dynamics. J. Chem. Phys. 114:2001-12
52. Horenko I, Weiser M, Schmidt B, Schütte C. 2004. Fully adaptive propagation of the quantum-classical Liouville equation. J. Chem. Phys. 120:8913-23
53. MacKernan D, Ciccotti G, Kapral R. 2002. Sequential short-time propagation of quantum-classical dynamics. J. Phys. Condens. Matter 14:9069-76
54. Tully JC. 1991. Nonadiabatic molecular dynamics. Int. J, Quantum Chem. 25:299-309
55. 2 in liquid argon. J. Chem. Phys. 100:8646-55
56. 2 transport in water. J. Chem. Phys. 104:4755-67
57. Webster F, Rossky PJ, Friesner RA. 1991. Nonadiabatic processes in condensed matter; Semi-classical theory and implementation. Comput. Phys. Commun. 63:494-522
58. Webster F, Wang ET, Rossky PJ, Friesner RA. 1994. Stationary-phase surface hopping for nonadiabatic dynamics: Two-state systems. J. Chem. Phys. 100:4835-47
59. Sergi A, MacKernan D, Ciccotti G, Kapral R. 2003. Simulating quantum dynamics in classical environments. Theor. Chem. Acc. 110:49-58
60. Hanna G, Kapral R. 2005. Quantum-classical Liouville dynamics of nonadiabatic proton transfer. J. Chem. Phys. 122:244505-11
61. Sergi A, Kapral R. 2003. Non-adiabatic reaction rates for dissipative quantum-classical systems. J. Chem. Phys. 119:12776-83
62. Tuckerman M, Berne BJ, Martyna GJ. 1992. Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97:1990-2001
63. Sergi A, Ferrario M, Costa D. 1999. Reversible integrators for basic extended system molecular dynamics. Mol. Phys. 97:825-32
64. Suzuki M. 1993. General decomposition theory of ordered exponentials. Proc. Jpn. Acad. B 69:161-66
65. Kubo R. 1957. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12:570-86
66. Mori H. 1965. Transport, collective motion, and Brownian motion. Prog. Theor. Phys. 33:423-55
67. Sergi A, Kapral R. 2004. Quantum-classical limit of quantum correlation functions. J. Chem. Phys. 121:7565-76
68. Kim H, Kapral R. 2005. Transport properties of quantum-classical systems. J. Chem. Phys. 122:214105
69. Sergi A, Kapral R. 2003. Quantum-classical dynamics of nonadiabatic chemical reactions. J. Chem. Phys. 118:8566-75
70. Bell RP. 1973. The Proton in Chemistry. London: Chapmann & Hall
71. Kornyshev AA, Tosi M, Ulstrup J, eds. 1997. Electron and Ion Transfer in Condensed Media. Singapore: World Sci.
72. McRae RP, Schenter GK, Garrett BC, Svetlicic Z, Truhlar DG. 2001. Variational transition state theory evaluation of the rate constant for proton transfer in a polar solvent. J. Chem. Phys. 115:8460-80
73. Antoniou D, Schwartz SD. 1999. A molecular dynamics quantum Kramers study of proton transfer in solution. J. Chem. Phys. 110:465-72
74. Antoniou D, Schwartz SD. 1999. Quantum proton transfer with spatially dependent friction: Phenol-amine in methyl chloride. J. Chem. Phys. 110:7359-64
75. Kim SY, Hammes-Schiffer S. 2003. Molecular dynamics with quantum transitions for proton transfer: Quantum treatment of hydrogen and donoracceptor motions. J. Chem. Phys. 119:4389-98
76. Yamamoto T, Miller WH. 2005. Path integral evaluation of the quantum instanton rate constant for proton transfer in a polar solvent. J. Chem. Phys. 122:044106
77. Marcus RA, Sutin N. 1985. Electron transfers in chemistry and biology. Biochim. Biophys. Acta 811:265-322
78. Warshel A. 1982. Dynamics of reactions in polar solvents. Semiclassical trajectory studies of electron-transfer and proton-transfer reactions. J. Phys. Chem. 86:2218-24
79. Kiefer PM, Hynes JT. 2004. Adiabatic and nonadiabatic proton transfer rate constants in solution. Solid State Ion. 168:219-24
80. Carter EA, Ciccotti G, Hynes JT, Kapral R. 1989. Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 156:472-77