Assessment of correlation energies based on the random-phase approximation

Joachim Paier,Matthias Scheffler,Andreas Grüneis,Gustavo E Scuseria,Xinguo Ren,Georg Kresse,Patrick Rinke

doi:10.1088/1367-2630/14/4/043002

Abstract

The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn–Sham (KS) density functional theory one step closer towards a universal, ‘general purpose first-principles method’. In an effort to systematically assess the influence of several correlation energy contributions beyond RPA, this paper presents dissociation energies of small molecules and solids, activation energies for hydrogen transfer and non-hydrogen transfer reactions, as well as reaction energies for a number of common test sets. We benchmark EX + RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single-excitation (SE) corrections, renormalized single-excitation (rSE) corrections and their combinations. Both the SE correction and the SOSEX contribution to the correlation energy significantly improve on the notorious tendency of EX + RPA to underbind. Surprisingly, activation energies obtained using EX + RPA based on a KS reference alone are remarkably accurate. RPA + SOSEX + rSE provides an equal level of accuracy for reaction as well as activation energies and overall gives the most balanced performance, because of which it can be applied to a wide range of systems and chemical reactions.

Highlights

The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn–Sham (KS) density functional theory one step closer towards a universal, ‘general purpose first-principles method’
We repeat that experimental binding energies are corrected for zero-point effects and are taken from the literature
We calculated atomization energies of solids and molecules using (EX + RPA)@PBE, (EX + RPA + second-order screened exchange (SOSEX))@PBE as well as HF + RPA @PBE and HF + (RPA + SOSEX)@PBE, where the latter approach gives binding energies improved by approximately 50% compared to ‘conventional’ (EX + RPA)@PBE

Summary

Introduction

The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn–Sham (KS) density functional theory one step closer towards a universal, ‘general purpose first-principles method’. We benchmark EX + RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single-excitation (SE) corrections, renormalized singleexcitation (rSE) corrections and their combinations Both the SE correction and the SOSEX contribution to the correlation energy significantly improve on the notorious tendency of EX + RPA to underbind. The underbinding problem can be alleviated, in particular for weakly interacting systems, by adding a correction deriving from single excitations (SEs) [25] to EX + RPA built on a reference state obtained from the Kohn–Sham (KS) density functional theory (DFT) This suggests that RPA(+SOSEX) yields good estimates for the correlation energy, but errors in the exchange energy are sizeable if KS orbitals are used to evaluate the EX.

Methods

Results

Conclusion