Functional derivative δ E /δ ρ in calculation of chemical potential for the Kohn–Sham electronic system

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.