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

Abstract

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence.We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spinparallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as O(N 5 ) or O(N 4 ) in orbital space or real space, respectively. Its memory requirement scales as O(N 2 ). arXiv:1605.08643v4 [cond-mat.mtrl-sci]

A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory

“…108 As dRPA suffers from self-interaction error (it violates Pauli's exclusion principle), a lot of effort have been put to propose approximations that eliminate parts of it (one-electron self-interaction error) and reduce the many-body self-interaction error as well. 109 The acronyms SOX, SOSEX 110 , RPA+, IOSEX 111 and more recently gRPA+ 112 all refer to such approximations. Another way to overcome Pauli principle violation was reported by Kosov 113 who proposed an a posteriori correction to single particle density matrix obtained after HF based dRPA calculation.…”

Dual‐hybrid direct random phase approximation and second‐order screened exchange with nonlocal van der Waals correlations for noncovalent interactions

“…Random phase approximation (RPA) originates from the seminal works of Bohm and Pines . The RPA and related methods have become accurate and useful tools for investigating electronic structures of molecules, solids, and surfaces of solids . Moreover, most of these methods are also successfully applied to various noncovalent interactions .…”

Beyond the RPA and GW methods with adiabatic xc-kernels for accurate ground state and quasiparticle energies

“…It can also be expressed in terms of different approximations to the exchange kernel, such as the AXK kernel of Bates and Furche, 14 the NEO kernel of Bates et al, 15 or the version of Hellgren et al 16 In addition, SOSEX can be treated within the range-separation scheme using a fixed admixture of local correlation. 17 Ángyán et al 18 constructed adiabatic-connection SOSEX or ACSOSEX, which brings in higher-order exchange terms and Hümmel et al have proposed an adjacent pairs exchange correction, which goes beyond ACSOSEX 19 by introducing more than one antisymmetrized line in terms of Goldstone diagrams. In general, the SOSEX correlation energy vanishes for one-electron systems and improves the accuracy of covalent bonds slightly compared to RPA.…”

“…Briefly describing the other kernels, "CDOP" refers to the frequencyindependent kernel proposed by Corradini, Del Sole, Onida, and Palummo, 69 which has the same limiting behavior as the exact static kernel (Eqs. (19) and (21)). "CDOPs" refers to the kernel introduced in ref., 70 which modifies CDOP so that it vanishes at large q.…”

“…"CPd" refers to the dynamical kernel proposed by Constantin and Pitarke, 71 which satisfies the long wavelength static and high frequency limits (Eqs. (19) and (22)). The frequencyindependent "CP" kernel corresponds to the CPd kernel at ω ¼ 0.…”