Ab initio Green's function formalism for band structures

TL;DR

This paper introduces an ab initio Green's function method for calculating crystal band structures, capable of handling strong correlations and scalable to large systems, demonstrated on lithium fluoride.

Contribution

It develops a novel crystal Green's function formalism based on the CO-ADC scheme, enabling efficient and accurate band structure calculations including inner valence bands.

Findings

Accurately predicts band gaps and valence band widths for LiF

Method scales linearly with system size under certain conditions

Stable for strongly correlated inner valence bands

Abstract

Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is formulated for crystal orbitals (CO-ADC). In this approach, the poles of the Green's function are determined by solving a suitable Hermitian eigenvalue problem. The method is not only applicable to the outer valence and conduction bands, it is also stable for inner valence bands where strong electron correlations are effective. The key to the proposed scheme is to evaluate the self-energy in terms of Wannier orbitals before transforming it to a crystal momentum representation. Exploiting the fact that electron correlations are mainly local, one can truncate the lattice summations by an appropriate configuration selection scheme. This yields a flat configuration space; i.e., its size scales only linearly with the number of atoms per unit cell for large systems and, under certain conditions, the computational effort to determine band structures also scales linearly. As a first application of the new formalism, a lithium fluoride crystal has been chosen. A minimal basis set description is studied, and a satisfactory agreement with previous theoretical and experimental results for the fundamental band gap and the width of the F 2p valence band complex is obtained.