Excitation energies from Görling–Levy perturbation theory along the range-separated adiabatic connection

Abstract

A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740(2015], this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionization energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

Range‐separated multiconfigurational density functional theory methods

“…In a series of papers, Rebolini et al 171–174 considered approximate RS MC‐DFT approaches aiming at correcting excited‐state energies of the LR Hamiltonian . Corrections can be derived either by considering the exact expansion in orders of μ along a range separated adiabatic connection, 172 or from the perturbation theory 173,174 . In the latter case, the Hamiltonian is chosen as the unperturbed operator and the perturbation is defined as , cf.…”

“…Equations () and (). Both Rayleigh–Schrödinger 173 and Görling–Levy 174 perturbation theories have been applied. For the i th eigenstate of one recovers the pertinent eigenvalue in the 0th order.…”

“…In a series of papers, Rebolini et al [171][172][173][174] considered approximate RS MC-DFT approaches aiming at correcting excited-state energies of the LR Hamiltonian ĤLR . Corrections can be derived either by considering the exact expansion in orders of μ along a range separated adiabatic connection, 172 or from the perturbation theory.…”

Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density

“…Besides assessing the present method on more systems, possible future developments include adding the second-order CIPSI perturbative correction, performing self-consistent calculations with the srPBEontop approximation, combining this approximation with the recent local-µ approach of Ref. 79, and calculating excited states for example using perturbation theory along the groundstate range-separated adiabatic connection [28,32] or using ghost-interaction-corrected ensemble RS-DFT [29][30][31].…”

“…In particular, this permits to drastically reduce self-interaction errors since the exchange energy is now calculated with a wave function and not with an approximate exchange density functional. This strategy has been pursued in various RS-DFT approaches [25][26][27][28][29][30][31][32]. However, only a local-density approximation (LDA) for this short-range correlation energy functional with multideterminantal reference was available so far [20,24], which tends to substantially overcorrelate.…”