Time-resolved spectroscopy in time dependent density functional theory: An exact condition

TL;DR

This paper derives an exact condition for the exchange-correlation potential in time-dependent density functional theory, highlighting a fundamental property of response frequencies that is often violated by current approximations, affecting time-resolved spectroscopy predictions.

Contribution

It establishes a new exact condition for the exchange-correlation potential in TDDFT based on response frequency invariance after the external field is turned off.

Findings

Current approximations violate the exact condition.

Violation leads to inaccuracies in time-resolved spectroscopy predictions.

The condition provides a benchmark for developing better functionals.

Abstract

A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time-dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time-dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.