Combining linear interpolation with extrapolation methods in range-separated ensemble density-functional theory

TL;DR

This paper introduces an extrapolated linear interpolation method (ELIM) that improves excitation energy calculations in range-separated ensemble density-functional theory by combining linear interpolation with Savin's extrapolation scheme.

Contribution

It presents a novel combination of LIM with extrapolation, demonstrating enhanced accuracy in excitation energies, especially for challenging states like doubly-excited ones.

Findings

ELIM yields more accurate excitation energies at typical mu values.

Significant improvement for doubly-excited states in H2.

Extrapolation does not always improve relative excitation energies.

Abstract

The combination of a recently proposed linear interpolation method (LIM) [Senjean et al., Phys. Rev. A 92, 012518 (2015)], which enables the calculation of weight-independent excitation energies in range-separated ensemble density-functional approximations, with the extrapolation scheme of Savin [J. Chem. Phys. 140, 18A509 (2014)] is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter mu when the latter is large. As a result, the extrapolation scheme, which is usually applied to long-range interacting energies, can be adapted straightforwardly to LIM. This extrapolated LIM (ELIM) has been tested on a small test set consisting of He, Be, H2 and HeH+. Relatively accurate results have been obtained for the first singlet excitation energies with the typical mu=0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly-excited 2^1Sigma+g state in the stretched H2 molecule. Three-state ensemble calculations in H2 also show that ELIM does not necessarily improves relative excitation energies, even though individual excitation energies are more accurate after extrapolation. Finally, an alternative decomposition of the short-range ensemble exchange-correlation energy is proposed in order to correct for ghost-interaction errors in multideterminant range-separated ensemble density-functional theory calculations. The implementation and calibration of such a scheme is currently in progress.