Adaptive coordinate, real-space electronic structure calculations on parallel computers

TL;DR

This paper introduces a parallelizable real-space electronic structure calculation method using curvilinear grids optimized by error analysis, enabling efficient and accurate all-electron calculations for molecules.

Contribution

It presents a novel approach combining curvilinear grids and error analysis to improve efficiency and accuracy in parallel electronic structure computations.

Findings

Accurate all-electron calculations for H2, O, and O2.

Efficient parallel computation through natural grid decomposition.

Optimized curvilinear grids for inhomogeneous electronic distributions.

Abstract

We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on a {\em regular} mesh in {\em curvilinear space}, which allows natural and efficient decomposition on parallel computers, and effective use of iterative numerical methods. A novel feature is the use of error analysis to optimize the curvilinear grid for highly inhomogeneous electronic distributions. We report accurate all-electron calculations for H$_2$, O, and O$_{2}$.