Dielectric matrix formulation of correlation energies in the Random Phase Approximation (RPA): inclusion of exchange effects

TL;DR

This paper extends the dielectric matrix formulation of RPA correlation energies to include exchange effects, providing new formulas and computational techniques that improve accuracy in atomic and molecular energy calculations.

Contribution

It introduces a dielectric matrix approach for RPA with exchange effects, including a logarithmic formula for correlation energy and efficient computational methods.

Findings

Exchange effects improve RPA accuracy for atomic energies.

New logarithmic formulas for correlation energy are derived.

Efficient implementation techniques enhance computational performance.

Abstract

Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.