Alternative separation of exchange and correlation energies in multi-configuration range-separated density-functional theory

TL;DR

This paper introduces a new way to separate exchange and correlation energies in multi-configuration range-separated density-functional theory, improving accuracy by using wavefunctions with the full Hamiltonian and optimized effective potentials.

Contribution

It proposes an alternative energy decomposition relying on the long-range interacting wavefunction and integrates short-range optimized effective potentials with wavefunction theory at HF and MCSCF levels.

Findings

Significant improvements in binding energies for small molecules.

Demonstrated importance of optimizing short-range OEP at MCSCF level.

Analytical gradient derived and implemented for HF, ongoing for MCSCF.

Abstract

The alternative separation of exchange and correlation energies proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] is explored in the context of multi-configuration range-separated density-functional theory. The new decomposition of the short-range exchange-correlation energy relies on the auxiliary long-range interacting wavefunction rather than the Kohn-Sham (KS) determinant. The advantage, relative to the traditional KS decomposition, is that the wavefunction part of the energy is now computed with the regular (fully-interacting) Hamiltonian. One potential drawback is that, because of double counting, the wavefunction used to compute the energy cannot be obtained by minimizing the energy expression with respect to the wavefunction parameters. The problem is overcome by using short-range optimized effective potentials (OEPs). The resulting combination of OEP techniques with wavefunction theory has been investigated in this work, at the Hartree-Fock (HF) and multi-configuration self-consistent-field (MCSCF) levels. In the HF case, an analytical expression for the energy gradient has been derived and implemented. Calculations have been performed within the short-range local density approximation on H2, N2, Li2 and H2O. Significant improvements in binding energies are obtained with the new decomposition of the short-range energy. The importance of optimizing the short-range OEP at the MCSCF level when static correlation becomes significant has also been demonstrated for H2, using a finite-difference gradient. The implementation of the analytical gradient for MCSCF wavefunctions is currently in progress.