Practical Methods for Ab Initio Calculations on Thousands of Atoms

TL;DR

This paper discusses recent advancements in linear-scaling ab initio methods within density functional theory, enabling efficient calculations on thousands of atoms by exploiting the locality of the density matrix.

Contribution

It introduces a practical framework for linear-scaling ab initio calculations based on the locality of the density matrix within density functional theory.

Findings

Demonstrates methods achieving computational effort proportional to the number of atoms

Summarizes efficient algorithms for finding the electronic ground state

Provides a scheme for localizing orbitals in large-scale calculations

Abstract

We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then describe our scheme, which operates within density functional theory. Efficient methods for reaching the electronic ground state are summarised, both for finding the density matrix, and in varying the localised orbitals.