Assessment of the Performance of DFT Functionals Using Off-Diagonal Hypervirial Relationships

TL;DR

This paper evaluates the accuracy of various DFT functionals in predicting electronic excited-state properties using off-diagonal hypervirial relationships and sum rules, providing a reference-free assessment method.

Contribution

It introduces a novel approach combining hypervirial relationships and sum rules to benchmark DFT functionals without external references.

Findings

General agreement with previous benchmarks

Effective assessment of DFT functionals using hypervirial deviations

High-quality results from extended TD-DFT calculations

Abstract

Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way for testing electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relations were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen to the purpose, adopting a large basis set to ensure high quality results. A general agreement with previous benchmarks is observed.