Formal Development of Density Functional Theory

In 1964 the perception of DFT was forever changed. That year, Hohen-berg and Kohn i provided the long sought-after proof that DFT is in fact an exact theory for describing the electronic behavior of matter. This was accomplished by proving the following remarkable theorem  

There exists a variational principle in terms of the electron density which determines the ground state energy and electron density. Further, the ground state electron density determines the external potential, within an additive constant. 

This theorem means that the ground state electron density, as obtained from the Hohenberg-Kohn variational principle, uniquely determines the ground state properties of the system of interest. The electron density is obtained from the variational principle 

Here E[p,v] is the ground state energy, as a functional of both the electron density p and the external potential v (the nuclear-electron attraction potential in many cases) p, (the chemical potential) is a Lagrange multiplier intro- 

The finite difference approximation for the electronegativity is given in terms of the ionization potential (J) and electron affinity (A), namely. 

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This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

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