Calculating excitation energies by extrapolation along adiabatic connections

TL;DR

This paper introduces an extrapolation method along adiabatic connections to more accurately estimate excitation energies in quantum systems, outperforming traditional density-functional approaches.

Contribution

It proposes a novel extrapolation scheme based on Taylor expansion analysis to improve energy estimations from partially interacting systems in range-separated and linear adiabatic connections.

Findings

Significantly improves convergence of energies toward exact limits.

Effective for atoms and molecules at various geometries.

Compared methods highlight strengths and weaknesses.

Abstract

In this paper, an alternative method to range-separated linear-response time-dependent density-functional 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.