Electronic energy minimisation with ultrasoft pseudopotentials

Phil Hasnip; C. J. Pickard

doi:10.1016/j.cpc.2005.07.011

Electronic energy minimisation with ultrasoft pseudopotentials

Phil Hasnip, C. J. Pickard

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

The introduction of ultrasoft pseudopotentials transforms the Schrödinger equation into a generalised eigenvalue problem with metric S, and in order to obtain the correct contravariant gradient the inverse of the S-matrix must be applied. We present an analytic derivation of the inverse S-matrix and a Hermitian preconditioning operator suitable for use in ultrasoft schemes. We show how the preconditioner may be calculated semi-analytically and applied without the need to store the matrix explicitly. The new scheme has been implemented within Castep, a plane-wave DFT program, and shown to offer considerable improvements over standard schemes for a set of representative test cases, as well as a SrTiO3 system of particular scientific interest.

Original language	English
Pages (from-to)	24-29
Number of pages	6
Journal	Computer Physics Communications
Volume	174
Issue number	1
DOIs	https://doi.org/10.1016/j.cpc.2005.07.011
Publication status	Published - 1 Jan 2006

Keywords

Eigenvalue problem
Preconditioning;
Ultrasoft pseudopotentials
Electronic structure

Access to Document

10.1016/j.cpc.2005.07.011

http://www.sciencedirect.com/science/article/pii/S0010465505004716

Cite this

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title = "Electronic energy minimisation with ultrasoft pseudopotentials",

abstract = "The introduction of ultrasoft pseudopotentials transforms the Schr{\"o}dinger equation into a generalised eigenvalue problem with metric S, and in order to obtain the correct contravariant gradient the inverse of the S-matrix must be applied. We present an analytic derivation of the inverse S-matrix and a Hermitian preconditioning operator suitable for use in ultrasoft schemes. We show how the preconditioner may be calculated semi-analytically and applied without the need to store the matrix explicitly. The new scheme has been implemented within Castep, a plane-wave DFT program, and shown to offer considerable improvements over standard schemes for a set of representative test cases, as well as a SrTiO3 system of particular scientific interest.",

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AB - The introduction of ultrasoft pseudopotentials transforms the Schrödinger equation into a generalised eigenvalue problem with metric S, and in order to obtain the correct contravariant gradient the inverse of the S-matrix must be applied. We present an analytic derivation of the inverse S-matrix and a Hermitian preconditioning operator suitable for use in ultrasoft schemes. We show how the preconditioner may be calculated semi-analytically and applied without the need to store the matrix explicitly. The new scheme has been implemented within Castep, a plane-wave DFT program, and shown to offer considerable improvements over standard schemes for a set of representative test cases, as well as a SrTiO3 system of particular scientific interest.

KW - Eigenvalue problem

KW - Preconditioning;

KW - Ultrasoft pseudopotentials

KW - Electronic structure

U2 - 10.1016/j.cpc.2005.07.011

DO - 10.1016/j.cpc.2005.07.011

M3 - Article

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EP - 29

JO - Computer Physics Communications

JF - Computer Physics Communications

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