On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions

Abstract

The correlation energy in the direct random phase approximation (dRPA) can be written, among other possibilities, either in terms of the interaction strength averaged correlation density matrix, or in terms of the coupled cluster doubles amplitudes obtained in the direct ring approximation (drCCD). Although the corresponding dRPA correlation density matrix on the one hand, and the drCCD amplitude matrix on the other hand, differ significantly, they yield identical energies. Similarly, the analogous RPA and rCCD correlation energies calculated from antisymmetrized two-electron integrals are identical to each other despite very different underlying working equations. In the present communication, a direct correspondence between amplitudes and densities is established and investigated with perturbation theory arguments. Our analysis also sheds some light on the properties of recently proposed RPA/rCCD variants which use antisymmetrized integrals in part of the equations and nonantisymmetrized integrals in others.

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

“…Although the above ACFDT-based expression is not strictly equal to the drCCD-based SOSEX, their difference appears only at the third order of perturbation, as was demonstrated in Ref. 38. The difference of those two variants has been found numerically small for all of the systems studied up to now [34].…”

“…In fact, it has been shown that a very similar perturbative screened exchange formula, which has been designated by the acronym dRPA-IIa, can be obtained within the density matrix formulation of RPA [34]. Although this expression gives correlation energies numerically very close to the rCCD-based SOSEX, it has been proven that they are not strictly identical [38]. Recently, in a similar but different fashion, the AXK introduced by Bates et al reduces the self-interaction error and improves the description of static correlation over dRPA.…”

Third-order corrections to random-phase approximation correlation energies

“…II, namely, NRPA1 (rCCD), NRPA2, NRPA3, NRPA4, AC-RPA, and SOSEX are exact to second-order of perturbation theory, they differ in third order. A corresponding third order analysis of RPA correlation energies has already been made by Szabo and Ostlund, 46 Oddershede, 47 and very recently by Jansen et al 102 (see also Ref. 105).…”

“…85,100,101 In the adiabatic connection method the electron-electron interactions (here all interactions that are not described on the Hartree-Fock level) are switched on by multiplication with a coupling-strength parameter α which varies between 0 (interaction turned off) and 1 (interaction fully turned on). The electron correlation energy is then obtained by an integral over the coupling strength and is given by 47,74,102 …”

Communication: Explicitly-correlated second-order correction to the correlation energy in the random-phase approximation

“…Concerning the use of RPA in molecular electronic-structure theory, we refer the reader to a few recent articles and reviews on the subject. [8][9][10][11][12] Following the notation used in our previous work 13 on RPA, we start by solving the symplectic eigenvalue problem of time-dependent density-functional theory (TDDFT),…”