A Fast, Parallel Algorithm for Distant-dependent Calculation of Crystal Properties

TL;DR

This paper introduces a fast, parallel algorithm for calculating crystal properties with high precision, significantly improving accuracy and efficiency over previous methods, and applicable to various lattice types and potentials.

Contribution

The paper presents a novel parallel algorithm that accelerates distant-dependent calculations of crystal properties, achieving higher precision and broader applicability than prior approaches.

Findings

Achieved up to 32 significant figures in Lennard-Jones lattice constants.

Doubled the known precision of several crystal property constants.

Corrected previously published figures for some lattice constants.

Abstract

A fast, parallel algorithm for distant-dependent calculation and simulation of crystal properties is presented along with speedup results and methods of application. An illustrative example is used to compute the Lennard-Jones lattice constants up to 32 significant figures for $4\leq p\leq30$ in the simple cubic, face-centered cubic, body-centered cubic, hexagonal-close-pack, and diamond lattices. In most cases, the known precision of these constants is more than doubled, and in some cases, corrected from previously published figures. The tools and strategies to make this computation possible are detailed along with application to other potentials, including those that model defects.