Spin-Adapted TDDFT

TL;DR

This paper introduces a spin-adapted TDDFT method that reduces spin contamination in excited state calculations by using tensor equations and hybrid exchange-correlation functionals, improving accuracy in benchmark tests.

Contribution

The authors develop a novel spin-adapted RPA approach for TDDFT using tensor equations and the Wigner-Eckart theorem, enhancing spin symmetry restoration.

Findings

Improved accuracy in excited state calculations for benchmark molecules.

Effective handling of Cr₂ dissociation and phenol O-H conical intersections.

Demonstrated reduction of spin contamination in spin-flip and spin-conserving channels.

Abstract

Linear-response TDDFT is widely used for excited states but suffers from spin contamination in spin-conserving and spin-flip channels. We develop a spin-adapted RPA by using tensor equation-of-motion and applying the Wigner-Eckart theorem with tensor decoupling. Casting the RPA Fock matrix and kernels as energy derivatives gives a TDDFT extension. To restore spin-component degeneracy, we use hybrids combining HF exchange with spin-unpolarized pure XC parts. Benchmarks, Cr$_2$ dissociation, and phenol O-H conical intersections demonstrate the method.