Analytical Excited-State Gradients and Derivative Couplings in TDDFT with Minimal Auxiliary Basis Set Approximation and GPU Acceleration

TL;DR

This paper introduces an efficient implementation of analytical excited-state gradients and derivative couplings within the TDDFT-ris framework, significantly accelerating calculations while maintaining accuracy for most applications.

Contribution

The authors develop and implement analytical derivatives for TDDFT with minimal auxiliary basis sets, enabling faster excited-state calculations with validated accuracy.

Findings

Two- to three-fold speedup in gradient and coupling calculations.

Reliable results for geometry optimizations and emission energies.

Noticeable errors mainly in nearly degenerate state couplings.

Abstract

Calculating excited-state gradients and derivative couplings using time-dependent density functional theory (TDDFT) remains a computationally demanding task. An efficient variant, TDDFT with resolution of the identity and a minimal auxiliary basis (TDDFT-ris), has been developed to accelerate excitation energy calculations. However, the formulation and implementation of analytical derivatives for this method have not yet been reported. In this work, we present an implementation of analytical excited-state gradients and derivative couplings within the TDDFT-ris framework. Benchmark calculations on medium-sized organic molecules demonstrate a two- to three-fold speedup for both gradients and derivative couplings compared to standard TDDFT. The accuracy of the TDDFT-ris approach is assessed for gradient-dependent applications, including geometry optimizations, emission energy calculations, and the localization of minimum-energy crossing points. Overall, the TDDFT-ris method provides reliable approximations for most cases, with noticeable errors mainly occurring in derivative couplings between nearly degenerate states.