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

Abstract

We study linear-response time-dependent density-functional theory (DFT) based on the singledeterminant 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.

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

“…A similar reduction of error has been observed by Rebolini et al after applying the range-separation in the TD-HF method. 17 …”

“…15 The range-separation concept leads to new functionals that employ both a wavefunction (usually of a multiconfigurational character) in the description of the long-range regime of the electronelectron interaction and a short-range density functional. The central assumption in the range-separation methods is to split the electron-electron interaction into the shortand long-range components, r Only very recently, the idea of range-separation has been extended to embrace time-dependent systems, which has led to methods combining short-range exchange-correlation DFT kernels with the long-range multiconfiguration 16 or single determinantal 17 wavefunction approaches or with the longrange density matrix functionals. 18 It has been argued in Refs.…”

Calculating excitation energies by extrapolation along adiabatic connections

“…Several such range-separated linear-response schemes have been developed, in which the short-range part is described by an approximate adiabatic semi-local density-functional kernel and the long-range linear-response part is treated at the Hartree-Fock [32][33][34][35], multiconfiguration self-consistent field (MCSCF) [34,35], second-order polarization-propagator approximation (SOPPA) [35], or density-matrix functional theory (DMFT) [36] level.…”

“…39, 40. This extrapolation scheme involves low-order derivatives of the energies with respect to µ and constitutes an alternative to perturbation theory and to range-separated TDDFT [32,41,42].…”

Excitation energies along a range-separated adiabatic connection

“…In this case, the excitation energies of the long-range interacting Hamiltonian act as starting approximations that are then corrected using a shortrange density-functional kernel, just as the KS excitation energies act as starting approximations in linear-response time-dependent density-functional theory (TDDFT). Several such range-separated linear-response schemes have been developed, in which the short-range part is described by an approximate adiabatic semi-local density-functional kernel and the long-range linear-response part is treated at the Hartree-Fock [52][53][54][55], MCSCF [52,55], second-order polarization-propagator approximation (SOPPA) [55], or DMFT [56] levels. These schemes aim at overcoming the limitations of standard linear-response TDDFT applied with usual adiabatic semi-local approximations for describing systems with static correlation [57], double or multiple excitations [58], and Rydberg or chargetransfer excitations [59,60].…”