Factorized Electron–Nuclear Dynamics with an Effective Complex Potential

Abstract

We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.

Dynamics of mixed quantum–classical spin systems *

“…We provide here some details concerning the form of the right hand side of the momentum equation in (35), which involves the sum of two terms: the von Neumann operator term D, d H and the stress tensor term div T. We also explain the symmetry of T as emerging from the rotational invariance of the Lagrangian in terms of ∇̺, β = c∇b, ∇ H. so that the stress tensor T as defined in (52) gives the expression (36).…”

“…Even if one attempted to discard V Q , the other nonlinear terms involving second-order gradients would still lead to analogous complications. Overall, the full hydrodynamic system (1) is accompanied by computational difficulties that still challenge the chemistry community [35,42,65,74].…”

Complex Fluid Models of Mixed Quantum–Classical Dynamics

“…Overall, the full hydrodynamic system ( 1 ) is accompanied by computational difficulties that still challenge the chemistry community (Garashchuk et al. 2023 ; Gu and Franco 2017 ; Suzuki and Watanabe 2016 ; Zhao and Makri 2003 ).…”