The ground-state energy and external potential as functionals of the electron density and their derivatives

2011/08/18 by Tamás Gál, Tamas Gal, Gal, Tamas
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Various Chemistry Research Topics #physics.atom-ph

paper · pdf · doi:10.48550/arxiv.1108.3865

11 pages

openalex publication_date 2011/08/18 · arxiv created 2011/08/22 · arxiv updated 2011/08/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is shown that the ground-state energy as a functional solely of the electron density is determined by the asymptotic value of the derivative of the degree-one homogeneous extension of the universal density functional F[n] at the given electron number. This has the consequence that its derivative cannot be properly determined. Carrying out the derivative of E[n[N,v]] with respect to v(r) leads to a paradox, which is resolved by the non-differentiability of E[n] if one follows traditional wisdom regarding the non-invertibility of the linear response function. However, considering the derivative of v[n[v]] through the one-electron case shows that this paradox has a more elementary origin, namely, an unaccounted restriction of the v(r) domain.

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