Hohenberg-Kohn-Sham

I do not recall when I first heard of the Hohenberg-Kohn-Sham papers, but I do know that the quantum chemistry community at first paid little attention to them. In June of 1966 Lu Sham spoke about DFT at a Gordon Conference. But in those days, there was more discussion about another prescription that had been on the scene since 1951, the Slater Xa method. The Xa method was a well-defined, substantial improvement over the Thomas-Fermi method, a sensible approximation to exact Kohn-Sham. Debate over Xa went on for a number of years. Slater may never have recognized DFT as the major contribution to physics that it was. [When I asked John Connolly five or six years ago how he thought Slater had viewed DFT, he replied that he felt that Slater regarded it as obvious. ]... 

The general relativistic Hohenberg-Kohn-Sham formalism, outlined above, contains the spin degrees of freedom in a complete form. Consequently, the spin and kinetic motion effects are not separable. Indeed, they are contained in the external potential term as one can see if such term is written using the orbital current... 

As in the case of the Schrodinger approach in which spin is introduced by giving a specific form to the wave function, the spin dependence in the Hohenberg-Kohn-Sham formalism in a nonrelativistic framework is introduced by imposing some form of restrictions to the functional. Namely, the total energy can be written as [3,5]... 

The local-scaling transformation version of density functional theory (LS-DFT), [1-12] is a constructive approach to DFT which, in contradistinction to the usual Hohenberg-Kohn-Sham version of this theory (HKS-DFT) [13-18], is not based on the IIohenberg-Kohn theorem [13]. Moreover, in the context of LS-DFT it is possible to generate explicit energy density functionals that satisfy the variational principle [8-12]. This is achieved through the use of local-scaling transformations. The latter are coordinate transformations that can be expressed as functions of the one-particle density [19]. 

HOHENBERG-KOHN-SHAM DENSITY FUNCTIONAL THEORY... 

Hohenberg-Kohn-Sham Density Functional Theory... 

The Hohenberg-Kohn-Sham density functional theory provides the common formal framework for various computational methods. Since each of the methods in use involves approximations, the calculated properties are not exact. Nevertheless, these methods proved to be very useful in chemistry and materials science. The huge and ever growing number of applications (see Figure 2-1) speaks for itself. Frequently,... 

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