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
M. P. Allen and D. J. Tildesley, Computer Simulations in Liquids (Oxford Univ. Press, Great Britain, 1990 ).
W. Stier and O. V. Prezhdo, J. Phys. Chem. B, j. C. Tully special issue, in press.
O. V. Prezhdo and P. J. Rossky, J. Phys. Chem. 100, 17094 (1996).
A. A. Mosyak, O. V. Prezhdo, and P. J. Rossky, J. Mol. Struct. 485–486, 545 (1999).
U. Muller and G. Stock, J. Chem. Phys. 107, 6230 (1997).
F. A. Webster, J. Schnitker, M. S. Friedrichs, R. A. Friesner, and P. J. Rossky, Phys. Rev. Lett. 66, 3172 (1991).
X. Song and R. A. Marcus, J. Chem. Phys. 99, 7768 (1993).
S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).
D. Borgis and J. T. Hynes, J. Phys. Chem. 100, 1118 (1996).
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.
M. Head-Gordon and J. C. Tully, J. Chem. Phys. 103, 10137 (1995).
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.
D. S. Sholl and J. C. Tully, J. Chem. Phys. 109, 7702 (1998).
J. C. Tully, J. Chem. Phys. 93, 1061 (1990).
J. C. Tully and R. K. Preston, J. Chem. Phys. 55, 562 (1971).
E. E. Nikitin, Theory of Elementary Atomic and Molecular Processes in Gases ( Clarendon, Oxford, 1974 ).
O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. 107, 825 (1997).
O. V. Prezhdo and P. J. Rossky, J. Chem. Phys. 107, 5863 (1997).
O. V. Prezhdo and P. J. Rossky, Phys. Rev. Lett. 81, 5294 (1998).
O. V. Prezhdo, J. Chem. Phys. ll, 8366 (1999).
C. Brooksby and O. V. Prezhdo, Chem. Phys. Lett. 346, 463 (2001).
O. V. Prezhdo and C. Brooksby, Phys. Rev. Lett. 86, 3215 (2001).
O. V. Prezhdo and C. Brooksby, Phys. Rev. Lett. 90, 118902 (2003).
F. A. Webster, P. J. Rossky, and R. A. Friesner, Comp. Phys. Comm. 63, 494 (1991).
P. Pechukas, Phys. Rev. 181, 174 (1969).
D. F. Coker and L. Xiao, J. Chem. Phys. 102, 496 (1995).
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.
X. Sun, H. B. Wang, and W. H. Miller, J. Chem. Phys. 109, 7064 (1998).
X. Sun and W. H. Miller, J. Chem. Phys. 106, 6346 (1997).
H. D. Meyer and W. H. Miller, J. Chem. Phys. 72, 2272 (1980).
N. C. Blais and D. G. Truhlar, J. Chem. Phys. 79, 1334 (1983).
M. F. Herman, J. Chem. Phys. 103, 8081 (1995).
O. V. Prezhdo and V. V. Kisil, Phys. Rev. A 56, 162 (1997).
J. Caro and L. L. Salcedo, Phys. Rev. A 60, 842 (1999).
I. V. Aleksandrov, Z. Naturforsch. 36A, 902 (1981).
W. Boucher and J. Traschen, Phys. Rev. D 37, 3522 (1988).
A. Anderson, Phys. Rev. Lett. 74, 621 (1995).
K. R. W. Jones, Phys. Rev. Lett. 76, 4087 (1996).
L. Diösi, Phys. Rev. Lett. 76, 4088 (1996).
I. R. Senitzky, Phys. Rev. Lett. 76, 4089 (1996).
A. Anderson, Phys. Rev. Lett. 76, 4090 (1996).
J. J. Halliwell, Phys. Rev. D 57, 2337 (1998).
L. Diösi and J. J. Halliwell, Phys. Rev. Lett. 81, 2846 (1998).
V. V. Kisil, Phys. Essays 11, 69 (1998).
K. Hepp, Comm. Math. Phys. 35, 265 (1974).
A. D. McLachlan, R. D. Gregory, and M. A. Ball, Mol. Phys. 7, 119 (1963–64).
W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972).
X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997).
E. J. Heller, J. Chem. Phys. 62, 1544 (1975).
R. B. Gerber, V. Buch, and M. A. Ratner, J. Chem. Phys. 77, 3022 (1982).
M. F. Herman, Annu. Rev. Phys. Chem. 45, 83 (1994).
G. D. Billing, Int. Rev. Phys. Chem. 13, 309 (1994).
F. A. Webster, P. J. Rossky, and R. A. Friesner, Comp. Phys. Comm. 63, 494 (1991).
E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995).
O. V. Prezhdo, Phys. Rev. Lett. 85, 4413 (2000).
O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 113, 6557 (2000).
O. V. Prezhdo and Y. V. Pereverzev, J. Chem. Phys. 116, 4450 (2002).
E. Pähl and O. V. Prezhdo, J. Chem. Phys. 116, 8704 (2002).
O. V. Prezhdo, J. Chem. Phys. 117, 2995 (2002).
P. Ehrenfest, Z. Physik 45, 455 (1927).
N. Makri and W. H. Miller, J. Chem. Phys. 87, 5781 (1987).
J. B. Delos, W. R. Thorson, and S. K. Knudson, Phys. Rev. A 6, 709 (1972).
J. B. Delos and W. R. Thorson, Phys. Rev. A 6, 720 (1972).
D. Böhm, Phys. Rev. 85, 166 (1952).
D. Böhm, Phys. Rev. 85, 180 (1952).
E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000).
B. J. Schwartz, E. R. Bittner, O. V. Prezhdo, and P. J. Rossky, J. Chem. Phys. 104, 5942 (1996).
W. H. Zurek, Progress of Theor. Phys. 89, 281 (1993).
W. H. Miller, W. L. Hase, and C. L. Darling, J. Chem. Phys. 91, 2859 (1989).
M. Ben-Nun and R. D. Levine, J. Chem. Phys. 101, 8768 (1994).
Y. Guo, D. L. Thompson, and T. D. Sewell, J. Chem. Phys. 104, 576 (1996).
S. T. Epstein, in Force Concept in Chemistry ( Van Nostrand Reinhold, New York, 1981 ), pp. 1–38.
L. de Broglie, Acad. Sei. Paris 183, 447 (1926).
L. de Broglie, Acad. Sei. Paris 185, 580 (1927).
O. Maroney and B. J. Hiley, Found. Phys. 29, 1403 (1999).
B. K. Dey, A. Askar, and H. Rabitz, Chem. Phys. Lett 297, 247 (1998).
C. L. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).
R. E. Wyatt, J. Chem. Phys. Ill, 4406 (1999).
G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).
N. Gisin and I. C. Percival, J. Phys. A 25, 5677 (1992).
N. Gisin and I. C. Percival, Phys. Lett. A 167, 315 (1992).
I. C. Percival, Proc. R. Soc. Lond. A 447, 189 (1994).
L. Diosi, Phys. Rev. A 40, 1165 (1989).
L. Diösi, N. Gisin, J. Halliwell, and I. Percival, Phys. Rev. Lett. 74, 203 (1995).
G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
G. J. Milburn, Phys. Rev. A 44, 5401 (1991).
C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. ( Springer-Verlag, Berlin, 1990 ).
J. R. Klauder and W. P. Petersen, SIAM J. Numer. Anal. 22, 1153 (1985).
R. W. Pastor, B. R. Brooks, and A. Szabo, Mol. Phys. 65, 1409 (1988).
V. I. Tatarskii, Sov. Phys. Usp. 26, 311 (1983).
J. Stromquist and S. Gao, J. Chem. Phys. 106, 5751 (1996).
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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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