General-Order Many-Body Green’s Function Method

Abstract

Electron binding energies are evaluated as differences in total energy between the N- and (N ± 1)-electron systems calculated by the nth-order Møller-Plesset perturbation (MPn) theory using the same set of orbitals. The MPn energies up to n = 30 are, in turn, obtained by the determinant-based method of Knowles et al. (Chem. Phys. Lett. 1985, 113, 8-12). The zeroth- through third-order electron binding energies thus determined agree with those obtained by solving the Dyson equation in the diagonal and frequency-independent approximations of the self-energy. However, as n → ∞, they converge at the exact basis-set solutions from the Dyson equation with the exact self-energy, which is nondiagonal and frequency-dependent. This suggests that the MPn energy differences define an alternative diagrammatic expansion of Koopmans-like electron binding energies, which takes into account the perturbation corrections from the off-diagonal elements and frequency dependence of the irreducible self-energy. Our analysis shows that these corrections are included as semireducible and linked-disconnected diagrams, respectively, which are also found in a perturbation expansion of the electron binding energies of the equation-of-motion coupled-cluster methods. The rate of convergence of the electron binding energies with respect to n and its acceleration by Padé approximants are also discussed.

One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

“…We numerically confirmed 97 that ∆MPn reduces to MBGF(n) with the self-energy in the diagonal, frequencyindependent approximation at 1 ≤ n ≤ 3 but converges at the nonapproximated MBGF(n) at n = ∞, whose self-energy is nondiagonal and frequency dependent. This method, therefore, switches from the most approximate form of the self-energy at low orders to the nonapproximated one at an infinite order.…”

“…To this end, two of the present authors with two coauthors previously implemented 97 what we call the ∆MPn method, originated by Pickup and Goscinski 7 and extended by Chong et al, [98][99][100] in a determinant-based, general-order algorithm. In this method, the nth-order perturbation correction to the electron binding energy of a Koopmans state is defined as the difference in the MBPT(n) correlation correction between the Nand (N ± 1)-electron systems using the same N-electron Hartree-Fock (HF) reference.…”

“…This intriguing behavior occurs because it contains two unexpected and bizarre classes of diagrams, which we call the semi-reducible and linked-disconnected diagrams. 97 They act to recuperate the effects of off-diagonal elements and frequency dependence of self-energy, respectively, in a perturbative manner. This finding exacerbated our concern that we may be missing an unknown number of important diagrams in higher-order MBGF.…”

Green’s function coupled cluster formulations utilizing extended inner excitations

“…A hierarchical approximations have been recently proposed to describe self-energies using perturbative techniques for one-particle many-body Green's function (MBGF) [39,40] that have been used to re-derive linked cluster and irreducible-diagram theorems as well as to provide algorithms for general order component of the self-energy. A lot of attention has also been attracted by the Green's function formulation proposed by Nooijen and Snijders, [41][42][43] who successfully employed coupled cluster (CC) bi-orthogonal formalism to express Green's function matrix in terms of the cluster operator (T ) and the so-called Λ operator, which is frequently used in linear response CC theory.…”

Unphysical Discontinuities in GW Methods

“…Although we mainly focus on G 0 W 0 and evGW, similar observations can be made in the case of qsGW and second-order Green function (GF2) methods. 47,[54][55][56][57][58][59][60][61][62][63][64]…”