A polynomial Ansatz for Norm-conserving Pseudopotentials

TL;DR

This paper introduces a polynomial-based approach for creating efficient norm-conserving pseudopotentials that match the performance of traditional methods while offering faster convergence of energy derivatives in electronic structure calculations.

Contribution

A new polynomial Ansatz for pseudopotentials of degree ten that simplifies construction and improves derivative convergence compared to the Troullier-Martins method.

Findings

Comparable total energy accuracy to Troullier-Martins pseudopotentials

Faster convergence of energy derivatives with plane wave cutoff

Simpler polynomial form for pseudopotential generation

Abstract

We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills the same smoothness conditions imposed by the Troullier-Martins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials are represented by a polynomial of degree twenty-two. We compare our method to the Troullier-Martins approach in electronic structure calculations for diamond and iron in the bcc structure and find that the two methods perform equally well in calculations of the total energy. However, first and second derivatives of the total energy with respect to atomic coordinates converge significantly faster with the plane wave cutoff if the standard Troullier-Martins potentials are replaced by the pseudopotentials introduced here.