Beyond Born-Oppenheimer Time-Dependent Density Functional Theory

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 $|χ({\bdu R},t)|^2$, 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.

Figures (1)

• Figure 1: Comparison between the exact reverse-engineered Kohn-Sham potential $\Delta v_s$ and PES (black solid) with the ones obtained by plugging the exact $n_R$ and $|\chi|$ into the BO (blue solid) and beyond-BO (red dashed) ground state functional in the adiabatic regime ($T=24$ ps) and an intermediate regime ($T=6$ ps). All variables are evaluated at $t=\frac{T}{2}$. The inset illustrates the transformation of two enol tautomers of acetylacetone that is the target of our model.