Assessing excited-state geometry optimization strategies for adiabatic photophysical energies

Abstract

Accurate prediction of adiabatic $0$-$0$ excited-state energies is crucial for modeling molecular photophysical processes. Here, we benchmark computational strategies for evaluating excited-state energies and singlet-triplet gaps obtained using different geometry-optimization strategies, including time-dependent density functional theory (TDDFT), spin-unrestricted Kohn-Sham (UKS) DFT for triplet states (${\rm T}_1$), and state-specific orbital-optimized UKS (ssUKS) DFT for singlet excited states (${\rm S}_1$). Zero-point vibrational energy corrections are evaluated consistently at the optimized geometries and combined with ADC(2) excitation energies for comparison with experimental anion photoelectron spectroscopy data for a representative set of molecules. Among the protocols considered, adiabatic $0$-$0$ energies evaluated at TDDFT-optimized ${\rm S}_1$ and ${\rm T}_1$ geometries show the best agreement with experiment, with a mean absolute error below 0.1 eV. Replacing these geometries with UKS-optimized ${\rm T}_1$ and ssUKS-optimized ${\rm S}_1$ structures yields comparable accuracy. Vertical excitation energies are substantially more sensitive to the choice of geometry than the corresponding ${\rm S}_1$-${\rm T}_1$ gaps, which are comparatively more robust because of partial error cancellation. As a larger case study, we examine rubrene and find that UKS/ssUKS-based geometries remain useful for evaluating singlet-fission energetics. Overall, UKS/ssUKS-based workflows provide an efficient and accurate route to excited-state geometry optimization and to the evaluation of adiabatic $0$-$0$ energies for states with dominant single-determinant character.