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

ABSTRACT

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, H₂ 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 2¹Σ⁺_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 multi-determinant range-separated ensemble density functional theory calculations. The implementation and calibration of such a scheme are currently in progress.

GRAPHICAL ABSTRACT

Keywords:

• Ensemble density functional theory
• range separation
• linear interpolation method
• ghost interaction

Acknowledgments

The authors are pleased to dedicate this work to Andreas Savin on the occasion of his 65th birthday (congratulations Andreas and thanks for everything !). E. Fromager would like to thank Julien Toulouse for stimulating discussions on extrapolation schemes. E.D. Hedegård acknowledges the Villum Kann Rasmussen foundation for a post-doc fellowship.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

E. Fromager acknowledges financial support from the LABEX ‘Chemistry of complex systems’ and the ANR (MCFUNEX project).