Abstract
We explore the possibility of calculating electronic excited states by using perturbation theory along a range-separated adiabatic connection. Starting from the energies of a partially interacting Hamiltonian, a first-order correction is defined with two variants of perturbation theory: a straightforward perturbation theory and an extension of the Görling–Levy one that has the advantage of keeping the ground-state density constant at each order in the perturbation. Only the first, simpler, variant is tested here on the helium and beryllium atoms and on the hydrogen molecule. The first-order correction within this perturbation theory improves significantly the total ground- and excited-state energies of the different systems. However, the excitation energies mostly deteriorate with respect to the zeroth-order ones, which may be explained by the fact that the ionisation energy is no longer correct for all interaction strengths. The second (Görling–Levy) variant of the perturbation theory should improve these results but has not been tested yet along the range-separated adiabatic connection.
Highlights
In density-functional theory (DFT) of quantum electronic systems, the most widely used approach for calculating excitation energies is nowadays linear-response timedependent density-functional theory (TDDFT)
We study in detail two variants of range-separated density-functional perturbation theory based either on the Rayleigh–Schrodinger (RS) or Gorling– Levy (GL) perturbation theories and test the first, simpler variant on the He and Be atoms and the H2 molecule, performing accurate calculations along a rangeseparated adiabatic connection without introducing density-functional approximations
Excitation energies in range-separated DFT can be obtained by linear-response theory starting from the time-dependent generalization of Eq (1) [63], where the excited states and their associated energies are obtained from timeindependent many-body perturbation theory
Summary
In density-functional theory (DFT) of quantum electronic systems, the most widely used approach for calculating excitation energies is nowadays linear-response timedependent density-functional theory (TDDFT) (see, e.g., Refs. [1, 2]). A fourth possible approach, proposed by Gorling [39], is to calculate the excitation energies from Gorling–Levy (GL) perturbation theory [40, 41] along the adiabatic connection using the non-interacting Kohn–Sham (KS) Hamiltonian as the zeroth-order Hamiltonian. In this approach, the zeroth-order approximation to the exact excitation energies is provided by KS orbital energy differences (which, for accurate KS potentials, is known to be already a fairly good approximation [42,43,44]).
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