Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential

TL;DR

This paper demonstrates that the exact time-dependent exchange-correlation potential in density-functional theory exhibits non-local dynamical steps crucial for accurate modeling of non-equilibrium quantum processes, which are missing in common approximations.

Contribution

It reveals the universal presence of dynamical steps in the exact exchange-correlation potential and illustrates their importance using one-dimensional two-electron systems.

Findings

Dynamical steps are essential for accurate non-equilibrium dynamics.

Common approximations lack these steps, leading to inaccuracies.

Inclusion of these steps improves modeling of charge transfer and excitation processes.

Abstract

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer.