Introducing <scp>ONETEP</scp>: Linear-scaling density functional simulations on parallel computers

TLDR

We present ONETEP, a density‑functional program for parallel computers whose cost scales linearly with the number of atoms and processors. ONETEP reformulates the plane‑wave pseudopotential method to exploit electronic localization, directly optimizes strictly localized quantities expressed in a delocalized basis, and distributes the computational effort across processors for efficient parallel execution. Examples demonstrate that ONETEP achieves excellent speedups with more processors, scales linearly with system size, delivers the same accuracy as conventional cubic‑scaling approaches, and offers fast, stable convergence, enabling quantitative predictions for systems of thousands of atoms in nanoscience and biophysics.

Abstract

We present ONETEP (order-N electronic total energy package), a density functional program for parallel computers whose computational cost scales linearly with the number of atoms and the number of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theoretical developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a physical way of dividing the computational effort among many processors to allow calculations to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing numbers of processors and confirm that the time taken by ONETEP as a function of increasing number of atoms for a given number of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and mathematically consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calculations with ONETEP have the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.