Formulation of the augmented plane-wave and muffin-tin orbital method

TL;DR

The paper reformulates the mixed basis all-electron full-potential method, called the PMT method, using a new 3-component formalism, enabling systematic atomic force calculations and comparisons with PAW, advancing quasiparticle GW computations.

Contribution

It introduces a new 3-component formalism for the PMT method, improving transparency and systematic force derivation, and compares it with PAW for enhanced electronic structure calculations.

Findings

Systematic derivation of atomic forces in the PMT method.

Comparison of PMT and PAW methods on equal footing.

Application of the PMT method to quasiparticle GW calculations.

Abstract

A mixed basis all-electron full-potential method, which uses two kinds of augmented waves, the augmented plane waves and the muffin-tin orbitals simultaneously, in addition to the local orbitals, was proposed by Kotani and van Schilfgaarde in Phys. Rev. B81, 125117(2010). We named it the PMT method. In this paper, this mixed basis method is reformulated on the basis of a new formalism named as the 3-component formalism, which is a mathematically transparent version of the additive augmentation originally due to Soler and Williams in Phys. Rev. B47, 6784(1993). Atomic forces are easily derived systematically. We discuss some problems in the mixed basis method and ways to manage them. In addition, we compare the method with the PAW method on the same footing. This PMT method is the basis for our new development of the quasiparticle self-consistent $GW$ method in J.Phys.Soc.Jpn 83, 094711(2014).