Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation

Abstract

Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

“…This overdamping is consistent with that observed in previous FBTS and PLDM results in similar regimes [9,40]. The MF-GQME results are in quantitative agreement at low nonadiabaticity, and even at the highest nonadiabaticity exhibit only a very subtle phase shift relative to the exact results.…”

Perspective: Nonadiabatic dynamics theory

“…42 Density matrix, quantum Liouville, and quantum trajectory approaches also appear quite promising. [43][44][45][46][47][48][49][50][51] Finally, the class of methods referred to as mixed quantum-classical (MQC) dynamics treat the slow coordinate (nuclear) motion by classical mechanics, but the forces that govern the classical motion incorporate the influence of nonadiabatic transitions. The two most widely used methods for simulating nonadiabatic dynamics, Ehrenfest [52][53][54][55] and surface hopping 56,57 are examples of MQC dynamics.…”

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

“…These inaccuracies are emphasized when the subsystem and the bath are strongly coupled. Higher accuracy can be achieved by foregoing linearization of the quantum subsystem degrees of free- * Electronic address: tmarkland@stanford.edu dom, thus obtaining a partially linearized approach [37][38][39][40]. However, simulations based on these techniques are limited to short time-scales due to undesirable scaling of their computation cost with evolution time.…”