Calculating excitation energies by extrapolation along adiabatic connections
Résumé
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.
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