Density Functional Theory for Fractional Particle Number: Derivative Discontinuity of the Energy at the Maximum Number of Bound Electrons

2011/11/08 by Daniel L. Whitenack, Daniel Whitenack, Whitenack, Daniel L. +4
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #Density functional theory #Derivative (finance) #Discontinuity (linguistics) #Electron #FOS: Physical sciences #Fractional calculus #Geology #Mathematical analysis #Mathematics #Particle (ecology) #Physics #Quantum Physics (quant-ph) #Quantum mechanics #Surface and Thin Film Phenomena #Upper and lower bounds #quant-ph

paper · pdf · doi:10.48550/arxiv.1111.1934

8 pages, 6 figures

arxiv created 2011/11/08 · openalex publication_date 2011/11/08 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The derivative discontinuity in the exact exchange-correlation potential of ensemble Density Functional Theory (DFT) is investigated at the specific integer number that corresponds to the maximum number of bound electrons, J_max. A recently developed complex-scaled analog of DFT is extended to fractional particle numbers and used to study ensembles of both bound and metastable states. It is found that the exact exchange-correlation potential experiences discontinuous jumps at integer particle numbers including J_max. For integers below J_max the jump is purely real because of the real shift in the chemical potential. At J_max, the jump has a non-zero imaginary component reflecting the finite lifetime of the (J_max+1) state.

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