A semiclassical generalized quantum master equation for an arbitrary system-bath coupling

Abstract

The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.

Ab initio study of exciton transfer dynamics from a core–shell semiconductor quantum dot to a porphyrin-sensitizer

“…The energy and electron transfer processes in the light-harvesting systems are driven by the ultrafast photoinduced evolution of the electronic degrees of freedom, which are strongly affected by the dynamic reorganization of the quantized vibrational modes [39][40][41]. Therefore, theoretical description of the transfer processes requires explicit modeling of the coupled electronic and vibrational dynamics together with bath-induced dephasing and renormalization of the system energies [40][41][42][43][44][45].…”

“…An intermediate description between the rate theories and molecular dynamics is provided by the reduced density matrix methods [38,[41][42][43][62][63][64], which couple several explicit electronic or vibrational modes to a thermal bath of many modes.…”

Thermal weights for semiclassical vibrational response functions

“…(4), which arises from the application of a pair of semiclassical propagators with opposite time sense. Alternative treatments of this phase were employed in forward-backward semiclassical calculations 13,14,[55][56][57][58] of canonical correlation functions and in the simplified linearized [59][60][61][62][63] semiclassical treatments. Application of a linearized semiclassical approximation 53 to R (1) (t) results in setting the phase Ψ to zero 33 so that the semiclassical quantization condition in Eq.…”

The Initial Value Representation of Semiclassical Theory: A Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations of Complex Molecular Systems

“…27 have developed a local harmonic approximation that also makes it possible to evaluate the multi-dimensional Fourier transform analytically, and have carried out some impressive applications for vibrational relaxation in liquids (where the relevant quantity is a force-force correlation function). Rossky et al 22 (using a variational harmonic approximation to obtain the Wigner function involving the Boltzmann operator) have treated a 1-dimensional chain of helium atoms, and also liquid oxygen (32 O 2 molecules in a box) at low temperature (70K), and Coker et al 28 have extended the linearized approximation to able to describe electronically non-adiabatic dynamics.…”