Curing the Divergence in Time-Dependent Density Functional Quadratic Response Theory

TL;DR

This paper identifies the divergence issue in TDDFT quadratic response theory caused by the adiabatic approximation and proposes a new kernel approximation to correct it, demonstrated on model systems.

Contribution

The authors derive the exact quadratic response kernel and introduce a practical approximation that eliminates unphysical divergences in TDDFT quadratic response calculations.

Findings

The new kernel removes divergence in transition probabilities.

Demonstrated improved accuracy on LiH molecule.

Validated on a model system with consistent results.

Abstract

The adiabatic approximation in time-dependent density functional theory (TDDFT) is known to give an incorrect pole structure in the quadratic response function, leading to unphysical divergences in excited state-to-state transition probabilities and hyperpolarizabilties. We find the form of the exact quadratic response kernel and derive a practical and accurate approximation that cures the divergence. We demonstrate our results on excited state-to-state transition probabilities of a model system and of the LiH molecule.