Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

Abstract

It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), secondorder screened exchange (SOSEX), and approximate exchange kernel (AXK) methods.Our analysis is facilitated by efficient and robust algorithms based on the resolutionof-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium-and large-size molecules with sizeindependent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measureᾱ of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a criticalᾱ value of approximately 0.5, the RPA errors increase rapidly, and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA, but only for systems and properties qualitatively well captured by RPA, as indicated by small α values.

Coupled Cluster Theory in Materials Science

“…Therefore, the RPA + SOSEX approximation yields more accurate cohesive energies compared to experiment than the RPA. We note that similar findings have been obtained using related corrections to the RPA, such as AXK (Chen et al, 2018).…”

Theory and practice of modeling van der Waals interactions in electronic-structure calculations

“…186 Account for the resulting leading-order term, referred to as ''approximate exchange kernel'' (AXK), considerably improves RPA energies and has been found to provide a more balanced correction to RPA than the SOSEX approach, when treating main-group compounds. 190 5.1.3 ACFD/RPA in electronic structure codes. As a general remark, it has unanimously been found that EXX/cRPA calculations are more reliable when based on KS states obtained from GGA-DFT calculations rather than Hybrid density functionals.…”

Screened Exchange Corrections to the Random Phase Approximation from Many-Body Perturbation Theory

“…It consistently overestimates the magnitude of the (negative) correlation energy and tends to slightly underestimate cohesive energies and overestimate bond lengths as well as lattice constants. 1,6,[11][12][13][14][15][16][17][18] This is supposed to originate from contributions in the ring terms of the RPA that violate the Pauli exclusion principle, as outlined in more detail in Section 3. By the merit of Wick's theorem such exclusion principle violating (EPV) contributions are exactly canceled by contributions in other terms of the exact many-body perturbation expansion where the offending states are exchanged.…”

“…To correct for this deficiency a number of post-RPA approaches have been proposed and have been assessed for a range of systems. 11,16,21 In direct ring coupled cluster doubles (drCCD) theory, the total energy can be calculated by anti-symmetrizing the final Coulomb interaction when tracing over the drCCD amplitudes. This approach offers a more balanced approximation to total correlation energies and some other properties but does not always improve energy differences.…”