Electronic excitations from a linear-response range-separated hybrid scheme

Abstract

We study linear-response time-dependent density-functional theory (DFT) based on the single-determinant range-separated hybrid (RSH) scheme, i.e. combining a long-range Hartree–Fock exchange kernel with a short-range DFT exchange-correlation kernel, for calculating electronic excitation energies of molecular systems. It is an alternative to the more common long-range correction (LC) scheme which combines a long-range Hartree–Fock exchange kernel with a short-range DFT exchange kernel and a standard full-range DFT correlation kernel. We discuss the local-density approximation (LDA) to the short-range exchange and correlation kernels, and assess the performance of the linear-response RSH scheme for singlet → singlet and singlet → triplet valence and Rydberg excitations in the N₂, CO, H₂CO, C₂H₄ and C₆H₆ molecules, and for the first charge-transfer excitation in the C₂H₄–C₂F₄ dimer. For these systems, the presence of long-range LDA correlation in the ground-state calculation and in the linear-response kernel has only a small impact on the excitation energies and oscillator strengths, so that the RSH method gives results very similar to the ones given by the LC scheme. Like in the LC scheme, the introduction of long-range HF exchange in the present method corrects the underestimation of charge-transfer and high-lying Rydberg excitation energies obtained with standard (semi)local density-functional approximations, but also leads to underestimated excitation energies to low-lying spin-triplet valence states. This latter problem is largely cured by the Tamm–Dancoff approximation which leads to a relatively uniform accuracy for all excitation energies. This work thus suggests that the present linear-response RSH scheme is a reasonable starting approximation for describing electronic excitation energies, even before adding an explicit treatment of long-range correlation.

Keywords:

• time-dependent density-functional theory
• linear response; range separation
• local-density approximation
• excitation energies

Acknowledgements

It is a pleasure to dedicate this paper to Trygve Helgaker who has made outstanding contributions to many areas of quantum chemistry, including density-functional theory. We thank E. Fromager (Strasbourg, France) and K. Pernal (Łódź, Poland) for discussions.