Self-consistent range-separated density-functional theory with second-order perturbative correction via the optimized-effective-potential method

TL;DR

This paper develops a fully self-consistent range-separated double-hybrid density functional method using the optimized-effective-potential approach, and evaluates its performance on small atoms and molecules.

Contribution

It introduces the RS-OEP2 method, combining long-range HF and MP2 with a local potential, and assesses its advantages over non-self-consistent approaches.

Findings

Self-consistency does not improve total energies or ionization potentials.

RS-OEP2 provides physically meaningful LUMO energies and exchange-correlation potentials.

Correlation potentials and densities remain largely inaccurate, indicating room for improvement.

Abstract

We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter $\mu=0.5$ bohr$^{-1}$, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.