Selfconsistent order-N density-functional calculations for very large systems

TL;DR

This paper introduces a linear-scaling, selfconsistent density-functional method suitable for very large systems, utilizing localized orbitals and real-space calculations to efficiently compute energies and forces.

Contribution

It presents a novel linear-scaling DFT approach using localized pseudoatomic orbitals and real-space grids, enabling efficient calculations for systems with thousands of atoms.

Findings

Successfully applied to large silicon and carbon systems with up to 1000 atoms.

Resolved a controversy on fullerene faceting through dynamical simulations.

Achieved O(N) computational effort for total energy and forces.

Abstract

We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis functions. The sparse Hamiltonian and overlap matrices are calculated with an $O(N)$ effort. The long range selfconsistent potential and its matrix elements are computed in a real-space grid. The other matrix elements are directly calculated and tabulated as a function of the interatomic distances. The computation of the total energy and atomic forces is also done in $O(N)$ operations using truncated, Wannier-like localized functions to describe the occupied states, and a band-energy functional which is iteratively minimized with no orthogonality constraints. We illustrate the method with several examples, including carbon and silicon supercells with up to 1000 Si atoms and supercells of $\beta$-C$_3$N$_4$. We apply the method to solve the existing controversy about the faceting of large icosahedral fullerenes by performing dynamical simulations on C$_{60}$, C$_{240}$, and C$_{540}$.