Kohn-Sham Equations with Constrained Electron Density

Wesolowski, T. A. and J. Weber. 1996. Kohn-Sham equations with constrained electron density an iterative evaluation of the ground-state electron density of interacting molecules. Chem. Phys. Lett. 248,71. 

The label KSCED standing for Kohn-Sham Equations with Constrained Electron Density is used here to indicate that, despite die similarity to Kohn-Sham equations, the effective potential and die one-electron functions differ from die corresponding quantities in these two frameworks. 

To underline these differences, we refer to each of the coupled equations (Eqs. 31 or 32) as Kohn-Sham Equations with Constrained Electron Density (KSCED). For the same reason, the effective potential in these equations is referred to by KSCED effective potentialc. 

Throughout this chapter, equations are written in atomic units. For the sake of simplicity, equations are given for spin-compensated electron densities hence the factor 2 in Eq. (3). The acronym KSCED stands for the Kohn-Sham equations with constrained electron density and is used to distinguish the two effective potentials expressed as density functionals the one in the considered one-electron equations, which involves an additional constraint (see Eq. (5) below), from that in the Kohn-Sham equations. 

Casida ME, Wesolowski TA (2003) Generalization of the Kohn-Sham equations with constrained electron density formalism and its time-dependent response theory formulation. Int J Quantum Chem 96 577-588... 

The connection to HF theory has been accomplished in a rather ingenious way by Kohn and Sham (KS) by referring to a fictitious reference system of noninteracting electrons. Such a system is evidently exactly described by a single Slater determinant but, in the KS method, is constrained to share the same electron density with the real interacting system. It is then straightforward to show that the orbitals of the fictitious system fulfil equations that very much resemble the HF equations ... 

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