Comment on "Breakdown of the Hellmann-Feynman theorem: Degeneracy is the key"
Comment on "Breakdown of the Hellmann-Feynman theorem: Degeneracy is the key"
Faculty of Sciences. Physics

article

2004
Lancaster, Pa
, 2004

Physics

Physical review : B : condensed matter and materials physics. - Lancaster, Pa, 1998 - 2015

69(2004)
:3
, p. 1-5

1098-0121

1550-235X

1098-0121

037103

E-only publicatie

English (eng)

University of Antwerp

In a recent paper, Zhang and George [Phys. Rev. B 66, 033110 (2002)] have made an application of the Hellmann-Feynman theorem (HFT) to calculate forces acting on an atom of the buckyball C-60 when subjected to small displacement. They noticed inconsistent results (as compared with that by other method) for forces connected with states belonging to a degenerate-energy level. However a sum of all such HFT forces for a given level was found consistent. Therefore they proposed the average force to be the representative of all forces connected with a degenerate level. Our analysis of these difficulties, based on degenerate perturbation theory, leads to modification of the HFT in application to degenerate-level states. By solving a matrix eigenequation of the extended HFT, as many forces are obtained as degeneracy of the level amounts. The diagonalized matrix involves unperturbed states only. Our considerations are illustrated by a simple system-a particle moving in a harmonic confinement, where forces are connected with anisotropic deformation of an isotropic confinement.

https://repository.uantwerpen.be/docman/irua/c5d678/3925.pdf

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