EVALUATION OF QUANTUM TRANSITION RATES FROM QUANTUM-CLASSICAL MOLECULAR-DYNAMICS SIMULATIONS

The impact of quantum decoherence and zero point motion on non-adiabat ic transition rates in condensed matter systems is studied in relation to non-adiabatic (NA) molecular dynamics (MD) techniques. Both effect s, and decoherence in particular, strongly influence the transition ra te, while neither is accounted for by straightforward quantum-classica l approaches. Quantum corrections to the quantum-classical results are rigorously introduced based on Kubo's generating function formulation of Fermi's Golden rule and the frozen Gaussian approximation for the nuclear wave functions. The development provides a one-to-one correspo ndence between the decoherence function and the Franck-Condon factor. The decoherence function defined in this paper corrects an error in ou r previous work [J. Chem. Phys. 104, 5942 (1996)]. The relationship be tween the short time approach and the real time NA MD is investigated and a specific prescription for incorporating quantum decoherence into NA simulations is given. The proposed scheme is applied to the hydrat ed electron. The rate of excited state non-radiative relaxation is fou nd to be very sensitive to the decoherence time. Quantum coherence dec ays about 50% faster in H2O than in D2O, providing a theoretical ratio nalization for the lack of experimentally observed solvent isotope eff ect on the relaxation rate. Microscopic analysis of solvent mode contr ibutions to the coherence decay shows that librational degrees of free dom are primarily responsible, due to the strong coupling between the electron and molecular rotations and to the small widths of the wave p ackets describing these modes. Zero point motion of the O-H bonds decr eases the life time of the excited state of the hydrated electron by a factor of 1.3-1.5. The implications of the use of short time approxim ations for the NA transition rate and for the evolution of the nuclear wave functions are considered. (C) 1997 American Institute of Physics .