# RPACorrEn

This page gives hints on how to calculate the RPA correlation energy with the ABINIT package.

## Introduction¶

In the adiabatic-connection fluctuation-dissipation framework, the correlation energy of an electronic system can be related to the density-density correlation function, also known as the reducible polarizability. When further neglecting the exchange-correlation contribution to the polarizability, one obtains the celebrated random-phase approximation (RPA) correlation energy. This expression for the correlation energy can alternatively be derived from many-body perturbation theory. In this context, the RPA correlation energy corresponds to the GW total energy.

The RPA correlation energy can be expressed as an integral function of the dielectric matrix (see [Gonze2016]). The integral over the frequencies is performed along the imaginary axis, where the integrand function is very smooth. Only a few sampling frequencies are then necessary. In ABINIT, the RPA correlation energy is triggered by setting the keyword gwrpacorr to 1.

The RPA correlation energy is a post-processed quantity from the GW module of ABINIT, which takes care of evaluating the dielectric matrix for several imaginary frequencies.

The RPA correlation has been shown to capture the weak van der Waals interactions [Lebegue2010] and to drastically improve defect formation energies [Bruneval2012].

The convergence versus empty states and energy cutoff is generally very slow.

It requires a careful convergence study. The situation can be improved with the use of an extrapolation scheme ([Bruneval2008], [Harl2010]).

compulsory:

basic:

v67mbpt: