Comparison between projector augmented-wave and ultrasoft pseudopotential formalisms at the density-functional perturbation theory level

Audouze, Christophe;Jollet, Francois;Torrent, Marc;Gonze, Xavier

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We compare the recently derived density-functional perturbation expressions within the projector augmented-wave (PAW) formalism [C. Audouze , Phys. Rev. B 73, 235101 (2006)] to those found in the ultrasoft pseudopotential (USPP) framework, for the perturbations of the atomic-displacement type. As a preliminary step, we re-examine the correspondence of the two models in the unperturbed case, showing precisely the different kinds of dependencies of each physical quantity on a perturbation parameter. Then, we identify the different contributions for the first- and the second-order responses of the energy in both formalisms, pointing out the additional contributions in the PAW case. We complete also the formalism by providing nonvariational and variational second-order derivative expressions for PAW, and a variational second-order derivative expression for USPP.
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Audouze, C., Jollet, F., Torrent, M., & Gonze, X. (2008). Comparison between projector augmented-wave and ultrasoft pseudopotential formalisms at the density-functional perturbation theory level. Physical review. B, Condensed matter and materials physics, 78(3), 035105 : 1-14. https://doi.org/10.1103/PhysRevB.78.035105 (Original work published 2008)