Variational projector augmented-wave method: theoretical analysis and preliminary numerical results

TL;DR

The paper introduces and analyzes the VPAW method, an improved approach for electronic structure calculations that enhances convergence by smoothing eigenfunctions, with preliminary numerical results supporting its effectiveness.

Contribution

It proposes the VPAW method, a novel variation of PAW, providing theoretical analysis and demonstrating improved convergence in plane-wave expansions.

Findings

VPAW improves convergence rates in plane-wave expansions.

Numerical tests show VPAW's efficiency on idealized cases.

Theoretical analysis confirms the smoothing benefits of VPAW.

Abstract

In Kohn-Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane-wave expansions give a poor approximation of the eigenfunctions. In conjunction with the use of pseudo-potentials, the PAW (projector augmented-wave) method circumvents this issue by replacing the original eigenvalue problem by a new one with the same eigenvalues but smoother eigenvectors. Here a slightly different method, called VPAW (variational PAW), is proposed and analyzed. This new method allows for a better convergence with respect to the number of plane-waves. Some numerical tests on an idealized case corroborate this efficiency.