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

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.

25 pages, 7 figures

References in corpus (4)

• Multi-configuration time-dependent density-functional theory based on range separation
• Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states
• Excitation energies along a range-separated adiabatic connection
• Calculating excitation energies by extrapolation along adiabatic connections

Cited by in corpus (10)

• New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation
• Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• A weight-dependent local correlation density-functional approximation for ensembles
• Fractional-charge and fractional-spin errors in range-separated density-functional theory
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer
• Models and corrections: range separation for electronic interaction -- lessons from density functional theory
• Ghost interaction correction in ensemble density-functional theory for excited states with and without range separation
• Excitation energies from G{ö}rling-Levy perturbation theory along the range-separated adiabatic connection