Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications

TL;DR

This paper develops a detailed formalism for a range-separated density-functional theory using Green-function methods and applies it to molecular systems, comparing different RPA-based approximations.

Contribution

It introduces a formally exact adiabatic-connection fluctuation-dissipation DFT framework based on range separation and assesses various RPA-type schemes.

Findings

Range-separated RPA schemes are effective for molecular dimers.

Comparison shows differences between RPA, second-order perturbation, and coupled-cluster methods.

The formalism provides a foundation for future developments in range-separated DFT.

Abstract

Using Green-function many-body theory, we present the details of a formally exact adiabatic-connection fluctuation-dissipation density-functional theory based on range separation, which was sketched in Toulouse, Gerber, Jansen, Savin and Angyan, Phys. Rev. Lett. 102, 096404 (2009). Range-separated density-functional theory approaches combining short-range density functional approximations with long-range random phase approximations (RPA) are then obtained as well-identified approximations on the long-range Green-function self-energy. Range-separated RPA-type schemes with or without long-range Hartree-Fock exchange response kernel are assessed on rare-gas and alkaline-earth dimers, and compared to range-separated second-order perturbation theory and range-separated coupled-cluster theory.