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

摘要

A mixed basis all-electron full-potential method, which uses two kinds ofaugmented waves, the augmented plane waves and the muffin-tin orbitalssimultaneously, in addition to the local orbitals, was proposed by Kotani andvan 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 newformalism named as the 3-component formalism, which is a mathematicallytransparent version of the additive augmentation originally due to Soler andWilliams in Phys. Rev. B47, 6784(1993). Atomic forces are easily derivedsystematically. We discuss some problems in the mixed basis method and ways tomanage them. In addition, we compare the method with the PAW method on the samefooting. This PMT method is the basis for our new development of thequasiparticle self-consistent $GW$ method in J.Phys.Soc.Jpn 83, 094711(2014).