Forerunners to Current DFT Methods

The idea of calculating atomic and molecular properties from electron density appears to have arisen from calculations made independently by Enrico Fermi and P.A.M. Dirac in the 1920s on an ideal electron gas, work now well-known as the Fermi-Dirac statistics [19]. In independent work by Fermi [20] and Thomas [21], atoms were modelled as systems with a positive potential (the nucleus) located in a uniform (homogeneous) electron gas. This obviously unrealistic idealization, the Thomas-Fermi model [22], or with embellishments by Dirac the Thomas-Fermi-Dirac model [22], gave surprisingly good results for atoms, but failed completely for molecules it predicted all molecules to be unstable toward dissociation into their atoms (indeed, this is a theorem in Thomas-Fermi theory). 

The Xa (X = exchange, a is a parameter in the Xa equation) method gives much better results [23, 24]. It can be regarded as a more accurate version of the Thomas-Fermi model, and is probably the first chemically useful DFT method. It was introduced in 1951 [25] by Slater, who regarded it [26] as a simplification of the Hartree-Fock (Section 5.2.3) approach. The Xa method, which was developed mainly for atoms and solids, has also been used for molecules, but has been replaced by the more accurate Kohn-Sham type (Section 7.2.3) DFT methods. 

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