Unconstrained Variational Determination of the KohnSham Potential.pdfVIP

Unconstrained Variational Determination of the Kohn-Sham Potential Nikitas I. Gidopoulos ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, England, UK Density Functional Theory’s Kohn-Sham (KS) potential emerges as the minimizing effective potential in an unconstrained variational scheme that does not involve fixing the unknown single- 6 electron density. The physical content behind the virtual KS system, that of a non-interacting 0 electronic system representing optimally the interacting one, is brought to light. 0 2 r a M I. INTRODUCTION II. THEOREM 0 To proceed, denote by Ψ , E the j-th eigenstate, 2 j j eigenvalue of the system of N interacting electrons that ] we are interested in (with a non-degenerate gs): r e Density Functional Theory [1–6] (DFT) has revolu- ˆ h H Ψj = Ej Ψj , j = 1, 2, . . . (1) t tionised the study of electronic structure. Its applica- o tion, especially under the Kohn-Sham (KS) scheme [2,7], where the Hamiltonian which describes the system is . t prevails: in condensed matter physics DFT is, without ˆ ˆ