Mixed quantum-classical dynamics on the exact time-dependent potential energy surface: A fresh look at non-adiabatic processes

TL;DR

This paper explores the exact time-dependent potential energy surface in mixed quantum-classical dynamics, revealing dynamical steps that influence nuclear motion during non-adiabatic processes, and assesses classical approximations' performance.

Contribution

It provides a detailed analysis of the features of the exact potential, especially the dynamical steps, and extends the Ehrenfest theorem to the nuclear subsystem using the exact factorization.

Findings

The potential develops dynamical steps after wave-packet splitting at avoided crossings.

The steps connect regions with different slopes corresponding to adiabatic surfaces.

The extended Ehrenfest theorem applies to the nuclear subsystem with the exact potential.

Abstract

The exact nuclear time-dependent potential energy surface arises from the exact decomposition of electronic and nuclear motion, recently presented in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on nuclear dynamics. We observe that the potential, after the nuclear wave-packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorization of the electron-nuclear wave-function is at the basis of the decomposition. In particular, the nuclear part is the true nuclear wave-function, solution of a time-dependent Schroedinger euqation and leading to the exact many-body density and current density. As a consequence, the Ehrenfest theorem can be extended to the nuclear subsystem and Hamiltonian, as discussed here with an analytical derivation and numerical results.