Electronic Structure Methods Exhibiting Linear Scaling of the Computational Effort with Respect to the Size of the System

1998/06/05 by Stefan Goedecker, Goedecker, Stefan
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Atomic and Molecular Physics #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/9806073

Enlarged and corrected version, 73 pages

openalex publication_date 1998/06/05 · arxiv created 1998/10/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms which take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will therefore first be studied for both metals and insulators. Several approaches to construct O(N) algorithms will then be presented and critically examined under various aspects. Finally some issues which are relevant only for self-consistent O(N) methods such as the calculation of the Hartree potential and mixing issues will be discussed.

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