Ab initio Green's function formalism for band structures

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.

20 pages, 3 figures, 1 table, RevTeX4, new section on lithium fluoride

References in corpus (4)

• Multireference configuration interaction treatment of excited-state electron correlation in periodic systems: the band structure of trans-polyacetylene
• Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
• Basis set convergence in extended systems: infinite hydrogen fluoride and hydrogen chloride chains
• Ionization of the Xenon Fluorides

Cited by in corpus (8)

• Maximally localized Wannier functions: Theory and applications
• Ab initio wavefunction based methods for excited states in solids: correlation corrections to the band structure of ionic oxides
• Algebraic Diagrammatic Construction Theory for Simulating Charged Excited States and Photoelectron Spectra
• Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids
• Correlation-induced corrections to the band structure of boron nitride: a wave-function-based approach
• Frozen local hole approximation
• Quasiparticle band structure of infinite hydrogen fluoride and hydrogen chloride chains
• A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations