Generalized Discrete Truncated Wigner Approximation for Nonadiabtic Quantum-Classical Dynamics

Abstract

Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases and it is thus desirable to have accurate yet affordable methods for their simulation.Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g. the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space, and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two Linear Vibronic Coupling models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independently of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

“…Recently, progress has been made in improving the accuracy of such methods through the use of a resolution of the identity, 28,29 optimized zero-point energy parameters, 30,31 the generalized master equation, 32 nonadiabatic ring-polymer molecular dynamics, 33 symmetric windowing (SQC), 34 spin-mapping, 35,36 and other alternative classical mapping models. [37][38][39][40] Some of these advancements have also already been used to obtain both linear and nonlinear optical spectra. 11,[41][42][43][44] A particularly successful method for computing dynamical observables within exciton systems is the standard partially linearized density matrix (PLDM) [45][46][47][48] approach, which uses coherent states within the MMST mapping space to describe the dynamics associated with the forward and backward exciton paths separately through the use of two independent sets of mapping variables.…”