A centroid molecular dynamics (CMD) approach [J. Chem. Phys. 1999 111, 2357; 111, 2371] is developed to study nonadiabatic dynamic in condensed phases, as represented by the spin-boson model. The CMD variables for both electronic and nuclear degrees of freedom are defined on the basis of the concept of a quasi-density operator. The initial distribution of the system investigated is not at thermal equilibrium, and the quasi-density operator is therefore constructed using a mixed centroid and Wigner representation. The CMD approximation is employed for the motion of both electronic and nuclear variables, and a set of nonadiabatic CMD equations are then derived. For the case of the spin-boson model, consisting of two electronic states bilinearly coupled to a harmonic bath, a set of nonadiabatic CMD spin-boson stochastic (generalized Langevin-like) equations can also be obtained by integrating out the bath centroid variables. From the numerical simulations, good agreement is found between the CMD calculations and the exact results.
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