Beyond Born-Oppenheimer Time-Dependent Density Functional Theory

TL;DR

This paper develops a time-dependent density functional theory that accurately models coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation, including a Kohn-Sham scheme and numerical demonstrations.

Contribution

It introduces a novel TDDFT framework for electron-nuclear systems beyond BO, with a Kohn-Sham scheme and validation on a proton transfer model.

Findings

The theory uniquely determines the full electron-nuclear wave function.

The proposed Kohn-Sham scheme reproduces exact densities and currents.

Adiabatic extension captures dominant nonadiabatic effects in slow regimes.

Abstract

We formulate a time-dependent density functional theory for the coupled dynamics of electrons and nuclei that goes beyond the Born-Oppenheimer (BO) approximation. We prove that the time-dependent marginal nuclear probability density $|\chi({\bdu R},t)|^2$, the conditional electronic density $n_{\bdu R}(\br,t)$, and the current density $\bm J_{\bdu R}(\br,t)$ are sufficient to uniquely determine the full time-evolving electron-nuclear wave function, and thus the dynamics of all observables. Moreover, we propose a time-dependent Kohn-Sham scheme which reproduces the exact conditional electronic density and current density and the exact N-body nuclear density. The remaining task is to look for functional approximations for the Kohn-Sham exchange-correlation scalar and vector potentials. Using a model driven proton transfer system, we numerically demonstrate that the adiabatic extension of a beyond-BO ground state functional captures the dominant nonadiabatic effects in the regime of slow driving.