Cohesive properties of solids calculated with the simplified total-energy functional of Harris

Polatoglou, Hariton Μ.; Methfessel, Michael

doi:10.1103/physrevb.37.10403

Cited by 79 publications

(16 citation statements)

References 12 publications

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“…This approximation also avoids four-center Coulomb integrals in our calculations, which is a great simplification. The Harris functional has been used in many studies and has always given surprisingly good agreement with fully selfconsistent calculations, except for highly ionic systems [15,22]. A third approximation is made to reduce the range of the tight-binding-like Hamiltonian matrix elements.…”

Section: Modelmentioning

confidence: 99%

Physical properties of aGeS2glass using approximateab initiomolecular dynamics

2003

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Section: Modelmentioning

confidence: 99%

Physical properties of aGeS2glass using approximateab initiomolecular dynamics

2003

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“…The properties and possible applications of the Harris energy functional 1 continue to arouse interest. [2][3][4][5] For those structures for which an adequate approximation to the self-consistent charge density is known, it allows a quick yet accurate evaluation of the total energy. 3 For those situations in which a reasonable approximation to the charge density is not known, iterative methods are required.…”

Section: Does the Harris Energy Functional Possess A Local Maximum Atmentioning

confidence: 99%

Does the Harris energy functional possess a local maximum at the ground-state density?

Robertson¹,

Farid²

1991

Phys. Rev. Lett.

110

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We prove that for any system, and within the framework of any reasonable local approximation to the Hohenberg-Kohn-Sham exchange-correlation energy functional, the Harris energy functional possesses either a saddle point or a local minimum at the self-consistent ground-state charge density. This invalidates the common suggestion that this functional has a local maximum at this charge density. Some numerical results in support of our arguments are presented. PACS numbers: 71.10.+x, 31.15.+q The properties and possible applications of the Harris energy functional 1 continue to arouse interest. 2-5 For those structures for which an adequate approximation to the self-consistent charge density is known, it allows a quick yet accurate evaluation of the total energy. 3 For those situations in which a reasonable approximation to the charge density is not known, iterative methods are required. There is evidence that the Harris functional may be less sensitive to errors in the charge density and hence require fewer iterations than the alternative Kohn-Sham functional. 4 Given the importance of the Harris functional, it is crucial that its properties are understood; in particular, the proposition that it displays a local maximum at the true ground-state density n sc . If it were true, this would allow establishment of a lower bound to the total energy to complement the upper bound given by the KohnSham functional. Recently, Finnis 3 stated that the Harris functional is "in practice. . .a lower bound to the exact energy." He provided both numerical evidence and a plausibility argument to support his case. For certain extended systems, Read and Needs 4 have produced numerical evidence to show that the functional is maximal and they too have a plausibility argument for this particular case. The work of Read and Needs is limited to a subset of all possible structures, and although Finnis's arguments are more general, they are some way short of constituting a proof. Zaremba 5 has attempted to provide this proof. Whereas Read and Needs and Finnis concentrated on the situation pertaining to a local-density approximation (LDA) to the exchangecorrelation energy functional, Zaremba concentrated (not exclusively) on the situation in which the Harris functional is evaluated with an exact expression for the exchange-correlation energy functional.In this Letter we concentrate on the former (LDA) case. We regard this as the more important, since for most total-energy calculations the LDA is an approximation which must be utilized. We show rigorously that for any electronic system and for any reasonable LDA, any small neighborhood of n sc in the density space contains a section for which the errors in the Harris energy with respect to the self-consistent energy are positive. Since the Harris functional is stationary at A2 SC , then it displays either a minimum or a saddle point. We define our use of the word reasonable below.We start with an expression for the error in the Harris functional given by Zaremba: 5(0Here n m is an input elec...

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“…The Harris-Foulkes approximation is shown to work quite well for a variety of systems, especially those that are strongly covalent [9]. Tests on this functional have shown that it yields total energies which are remarkably similar to the LDA approximation but lie below them rather than above them as in a variational Kohn-Sham calculation [26][27][28][29][30][31], However, because it is not self-consistent, it can only be applied to systems without a significant difference in the electronegativity of their constituents.…”

Section: Dogs: a Self-consistent Functionalmentioning

confidence: 89%