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

• Published in: Molecular physics Vol. 114; no. 7-8; pp. 968 - 981
• Main Authors: Senjean, Bruno, Hedegård, Erik D., Alam, Md. Mehboob, Knecht, Stefan, Fromager, Emmanuel
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 17.04.2016; Taylor & Francis Ltd
• Subjects: Approximation; Chemical Physics; Chemical Sciences; Density functional theory; Ensemble density functional theory; Excitation; Extrapolation; ghost interaction; Interpolation; Inverse; linear interpolation method; Mathematical analysis; Molecular physics; or physical chemistry; Physics; range separation; Theoretical and
• ISSN: 0026-8976; 1362-3028
• DOI: 10.1080/00268976.2015.1119902

The combination of a recently proposed linear interpolation method (LIM), which enables the calculation of weight-independent excitation energies in range-separated ensemble density functional approximations, with the extrapolation scheme of Savin is presented in this work. It is shown that LIM excitation energies vary quadratically with the inverse of the range-separation parameter μ 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, H 2 and HeH + . Relatively accurate results have been obtained for the first singlet excitation energies with the typical μ = 0.4 value. The improvement of LIM after extrapolation is remarkable, in particular for the doubly excited 2 1 Σ + g state in the stretched H 2 molecule. Three-state ensemble calculations in H 2 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 multi-determinant range-separated ensemble density functional theory calculations. The implementation and calibration of such a scheme are currently in progress.