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Comparison of variational real-space representations of the kinetic energy operator

Comparison of variational real-space representations of the kinetic energy operator
Comparison of variational real-space representations of the kinetic energy operator
We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a real-space method that is not variational) and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-difference method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B 64, 193101 (2001)] satisfies one of the two properties of variational behavior at the cost of larger errors than the conventional finite-difference method. On the other hand, a technique which represents functions in a number of plane waves which is independent of system size closely follows the plane-wave method and therefore also the criteria for variational behavior. Its application is only limited by the requirement of having functions strictly localized in regions of real space, but this is a characteristic of an increasing number of modern real-space methods, as they are designed to have a computational cost that scales linearly with system size.
density-functional theory, electronic-structure calculations, solids, molecules, basis-set
1550-235X
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
Diéguez, Oswaldo
e45e10cd-778e-4c24-a1ca-c698a90b4d27
Haynes, Peter D.
7672b51a-83dc-417e-9ffc-7eb9f8c0334c
Payne, Mike C.
abb730ea-f683-4bec-a7e0-766f0a180a05
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
Diéguez, Oswaldo
e45e10cd-778e-4c24-a1ca-c698a90b4d27
Haynes, Peter D.
7672b51a-83dc-417e-9ffc-7eb9f8c0334c
Payne, Mike C.
abb730ea-f683-4bec-a7e0-766f0a180a05

Skylaris, Chris-Kriton, Diéguez, Oswaldo, Haynes, Peter D. and Payne, Mike C. (2002) Comparison of variational real-space representations of the kinetic energy operator. Physical Review B, 66 (7). (doi:10.1103/PhysRevB.66.073103).

Record type: Article

Abstract

We present a comparison of real-space methods based on regular grids for electronic structure calculations that are designed to have basis set variational properties, using as a reference the conventional method of finite differences (a real-space method that is not variational) and the reciprocal-space plane-wave method which is fully variational. We find that a definition of the finite-difference method [P. Maragakis, J. Soler, and E. Kaxiras, Phys. Rev. B 64, 193101 (2001)] satisfies one of the two properties of variational behavior at the cost of larger errors than the conventional finite-difference method. On the other hand, a technique which represents functions in a number of plane waves which is independent of system size closely follows the plane-wave method and therefore also the criteria for variational behavior. Its application is only limited by the requirement of having functions strictly localized in regions of real space, but this is a characteristic of an increasing number of modern real-space methods, as they are designed to have a computational cost that scales linearly with system size.

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More information

Published date: 2 August 2002
Keywords: density-functional theory, electronic-structure calculations, solids, molecules, basis-set

Identifiers

Local EPrints ID: 54163
URI: http://eprints.soton.ac.uk/id/eprint/54163
ISSN: 1550-235X
PURE UUID: 1586b17d-1d7b-40db-ac04-2c581ac62dcb
ORCID for Chris-Kriton Skylaris: ORCID iD orcid.org/0000-0003-0258-3433

Catalogue record

Date deposited: 29 Jul 2008
Last modified: 08 Jan 2022 03:04

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Contributors

Author: Oswaldo Diéguez
Author: Peter D. Haynes
Author: Mike C. Payne

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