Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies

Diata Traore (1) , Emmanuel Giner (1) , Julien Toulouse (1, 2)

1 LCT - Laboratoire de chimie théorique
2 IUF - Institut universitaire de France

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations, as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

Domaines: Chimie théorique et/ou physique; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]

Diata Traore, Emmanuel Giner, Julien Toulouse. Basis-set correction based on density-functional theory: Linear-response formalism for excited-state energies. Journal of Chemical Physics, 2023, 158, pp.234107. ⟨10.1063/5.0156317⟩. ⟨hal-04107625⟩