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Functional derivative δ E /δ ρ in calculation of chemical potential for the Kohn–Sham electronic system
Author(s) -
Tkaczśsamiech Katarzyna,
Ptak W. S.,
Koleżyński A.,
Mrugalski J.
Publication year - 1994
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560510621
Subject(s) - kohn–sham equations , functional derivative , derivative (finance) , limit (mathematics) , density functional theory , electronic systems , electronic structure , ionization energy , second derivative , hybrid functional , relation (database) , chemistry , computational chemistry , statistical physics , ionization , physics , mathematics , quantum mechanics , computer science , mathematical analysis , ion , electronic engineering , financial economics , engineering , economics , database
A method for finding the chemical potential for an electronic system with density ρ = Σ ρ i represented within the Kohn–Sham approximation is proposed. To find the chemical potential of the system under consideration, we propose to refer to the definition μ = δ E /δ ρ and to apply the mathematical properties of functional derivatives. Particularly, in the case examined, the result μ = μ( r ) ≠ const has been obtained, which may be explained in the framework of the calculus of variation. Taking the limit lim r →∞ μ( r ) as the best approximation to the proper equilibrium chemical potential of a free atom, one obtains μ = − I , where I denotes first ionization energy. A possibility of further applications of the proposed method in relation to crystalline systems is also discussed. © 1994 John Wiley & Sons, Inc.