Electronic structure calculations and molecular dynamics simulations with linear system-size scaling

TL;DR

This paper introduces a linear-scaling computational method for total energy and molecular dynamics simulations based on localized orbitals, applicable to complex systems like disordered liquids, enabling efficient simulations with high accuracy.

Contribution

The authors develop a novel orbital formulation and energy functional that eliminate the need for orthogonalization and matrix inversion, achieving linear computational scaling for large systems.

Findings

Accurate results for diamond, graphite, and carbon liquids.

Linear scaling enables simulations of thousands of atoms.

Good agreement with standard diagonalization methods.

Abstract

We present a method for total energy minimizations and molecular dynamics simulations based either on tight-binding or on Kohn-Sham hamiltonians. The method leads to an algorithm whose computational cost scales linearly with the system size. The key features of our approach are (i) an orbital formulation with single particle wavefunctions constrained to be localized in given regions of space, and (ii) an energy functional which does not require either explicit orthogonalization of the electronic orbitals, or inversion of an overlap matrix. The foundations and accuracy of the approach and the performances of the algorithm are discussed, and illustrated with several numerical examples including Kohn-Sham hamiltonians. In particular we present calculations with tight-binding hamiltonians for diamond, graphite, a carbon linear chain and liquid carbon at low pressure. Even for a complex case such as liquid carbon -- a disordered metallic system with differently coordinated atoms -- the agreement between standard diagonalization schemes and our approach is very good. Our results establish the accuracy and reliability of the method for a wide class of systems and show that tight binding molecular dynamics simulations with a few thousand atoms are feasible on small workstations.