Calculating excitation energies by extrapolation along adiabatic connections

Abstract

In this paper, an alternative method to range-separated linear-response time-dependent densityfunctional theory and perturbation theory is proposed to improve the estimation of the energies of a physical system from the energies of a partially interacting system. Starting from the analysis of the Taylor expansion of the energies of the partially interacting system around the physical system, we use an extrapolation scheme to improve the estimation of the energies of the physical system at an intermediate point of the range-separated or linear adiabatic connection where either the electron-electron interaction is scaled or only the long-range part of the Coulomb interaction is included. The extrapolation scheme is first applied to the range-separated energies of the helium and beryllium atoms and of the hydrogen molecule at its equilibrium and stretched geometries. It improves significantly the convergence rate of the energies toward their exact limit with respect to the range-separation parameter. The range-separated extrapolation scheme is compared with a similar approach for the linear adiabatic connection, highlighting the relative strengths and weaknesses of each approach.

Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

“…Recently, an alternative extrapolation approach has been put forward as a computational route to determine correlation energies 33 and has also been applied to the computation of excitation energies. 43 This alternative AC representation may also be useful when tailored to approach 0 for large λ, the tendency for static correlation to be concentrated towards low λ values meaning that extrapolations beginning from weakly interacting references, with small values of λ, may be accurate.…”

A road to a multiconfigurational ensemble density functional theory without ghost interactions

“…(9). However, to fully take into account the spin polarization, it is necessary to rather use the functional of the form (11). Unfortunately, there is a computational disadvantage related to such a choice.…”

“…A related but more sophisticated approach to the problem of finding excitation energies within DFT is offered by a constrained‐variational DFT . Other approaches involve combining the density functional theory with perturbation theory or with configuration interaction method …”

“…[6,7] Other approaches involve combining the density functional theory with perturbation theory [8,9] or with configuration interaction method. [10,11] The last group of methods, the ensemble DFT, originates from the ensemble variational principle (EVP), [12] which states that a weighted sum of m lowest eigenvalues of the Hamiltonian is not greater than the weighted sum of m expectation values of this Hamiltonian with respect to any set of orthogonal wavefunctions, i.e.…”

Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states

“…µ → +∞) can be used for improving the energy at a given (finite) µ value. This approach, known as extrapolation technique, has been extended to excited states by considering the (µ-dependent) individual excited-state energies of a ground-state-densityfunctional long-range-interacting Hamiltonian 50 . An extension to range-separated eDFT has been recently proposed by Senjean et al 48 One drawback of the latter approach is that it does not incorporate ghost interaction corrections.…”