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An extensive study of gradient approximations to the exchange-correlation and kinetic energy functionals

Chan, Garnet Kin-Lic and Handy, Nicholas C. (2000) An extensive study of gradient approximations to the exchange-correlation and kinetic energy functionals. Journal of Chemical Physics, 112 (13). pp. 5639-5653. ISSN 0021-9606. https://resolver.caltech.edu/CaltechAUTHORS:20160729-151752866

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Abstract

We formalize the procedure of functional development, in a general theoretical framework. Expansion in a functional basis set, and fitting via an error functional to a data set, casts functional development as a variational problem to obtain the functional basis-set and data-set limits. Overfitting is avoided by defining the optimum number of parameters. We implement our theory for an investigation of first- and second-order generalized gradient approximations (GGA) to the exchange-correlation and kinetic energy functionals, within an ab initio model. A variety of functional basis sets, including a general finite-element representation, is constructed to represent both one-dimensional and multidimensional GGA enhancement factors. An extensible data set consisting of 429 atomic and diatomic, neutral and cationic species, at stretched and equilibrium geometries, is constructed from Moller–Plesset level exchange-correlation energies, and Hartree–Fock kinetic energies. The range of chemically relevant density and gradient variables is examined. Exhaustive fitting investigations are carried out, to determine the accuracy of the GGA representation of the ab initio models. In the exchange-correlation case we demonstrate that we can reach the functional basis-set and data-set limit, which correspond to a root-mean-square (rms) error of ∼10∼10 mH (6.3 kcal/mol). Changing the functional basis set, higher-order density variables such as the kinetic energy density, multidimensional enhancement factors, and exact exchange yield no significant improvement, and our fits represent an effective solution of the GGA problem for exchange-correlation, at the Møller–Plesset level. In the kinetic energy case, accurate functionals with rms errors of ∼80∼80 mH (50 kcal/mol) are developed. These exhibit a beautifully simple kinetic energy enhancement factor, and are a step towards orbital-free calculations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.481139DOIArticle
http://scitation.aip.org/content/aip/journal/jcp/112/13/10.1063/1.481139PublisherArticle
ORCID:
AuthorORCID
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2000 American Institute of Physics. Received 7 October 1999; accepted 14 December 1999. P. H. Cake, J. H. Y. Wei, F. A. Pahl, A. J. Cohen, and R. D. Daniel are acknowledged for interesting discussions. G.K.-L.C. Chan acknowledges Christ’s College and EPSRC for financial support.
Funders:
Funding AgencyGrant Number
Christ’s CollegeUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Issue or Number:13
Record Number:CaltechAUTHORS:20160729-151752866
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160729-151752866
Official Citation:An extensive study of gradient approximations to the exchange-correlation and kinetic energy functionals Garnet Kin-Lic Chan and Nicholas C. Handy J. Chem. Phys. 112, 5639 (2000); http://dx.doi.org/10.1063/1.481139
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69331
Collection:CaltechAUTHORS
Deposited By: Donna Wrublewski
Deposited On:29 Jul 2016 22:53
Last Modified:03 Oct 2019 10:21

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