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Theoretical Chemistry Accounts

Local-orbital-based correlated ab initio band structure calculations in insulating solids: LiF

Martin Albrecht

Published Feb 1, 2002• 18 citations
Publisher
DOI
10.1007/s00214-001-0305-y

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An ab-initio many-body method for electronic structure calculations of solids. I. Description of the method

I. Schnell, G. Czycholl, Robert C. Albers

We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.

arXiv:cond-mat/0304643•Apr 28, 2003•0 citations
A local-orbital based ab initio approach to calculate correlation effects on quasi particle energies in insulating solids is presented. The use of localized Wannier-type Hartree Fock orbitals allows to efficiently devide correlation effects into classes of strong, medium or small weight. Subsequently the strongly contributing correlations are obtained from a Green's function calculated by exact diagonalization, while the rest is taken into account by a perturbative treatment. With this method the band structure of LiH is calculated and reasonable agreement with experiment is found.
Three different many-body wave-function-based ab initio methods for the calculation of correlated (or quasi-particle) band structures of periodic systems are presented: the local Hamiltonian approach, the incremental self-energy method, and the crystal orbital variant of the algebraic diagrammatic construction. All three methods explicitly exploit the local nature of electron correlation, and by consequently switching to representations in localized Wannier orbitals O(N) scaling could be achieved in all three cases. These methods were applied to single (HF) 2 zigzag chains as found in solid hydrogen fluoride using the same geometries and basis sets. Essentially identical quasi-particle band structures were obtained, corroborating the appropriateness of the different concepts pursued in each of the presented quantum chemical correlation methods for band structures of infinite systems.
We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.