Exact Electronic Potentials in Coupled Electron-Ion Dynamics

TL;DR

This paper introduces an exact quantum approach to electron-ion dynamics, deriving a Schr"odinger equation for electrons that incorporates a novel time-dependent potential energy surface, revealing significant differences from classical potentials.

Contribution

It presents a new exact quantum framework for electron-ion dynamics using a time-dependent potential energy surface for electrons, advancing beyond traditional classical or electrostatic models.

Findings

The exact e-TDPES differs markedly from classical electrostatic potentials.

The approach maintains a full quantum treatment of nuclei.

Demonstrates the importance of quantum effects in electronic potentials.

Abstract

We develop a novel approach to the coupled motion of electrons and ions that focuses on the dynamics of the electronic subsystem. Usually the description of electron dynamics involves an electronic Schr\"odinger equation where the nuclear degrees of freedom appear as parameters or as classical trajectories. Here we derive the exact Schr\"odinger equation for the subsystem of electrons, staying within a full quantum treatment of the nuclei. This exact Schr\"odinger equation features a time-dependent potential energy surface for electrons (e-TDPES). We demonstrate that this exact e-TDPES differs significantly from the electrostatic potential produced by classical or quantum nuclei.