Thomas-Fermi type models

The divide-and-conquer method can be constructed such that the Thomas-Fermi type models are the consequences of the method. This will be the third construction of the method. Define a projected Hamiltonian for subsystem a using an operator 0 ... 

A practical way to handle the calculations by a unified approach comprising all ions was proposed by Brandt and Kitagawa [15]. In this approach the structure of the ion is represented by a statistical model (of Thomas-Fermi type), and/( ) is analytically expressed as... 

In one of the earliest DFT models, the Thomas-Fermi theory, the kinetic energy of an atom or a molecule is approximated using the above type of treatment on a local level. That is, for each volume element in r space, one... 

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 The Xa method, which was developed mainly for atoms and solids, has also been used for molecules, but has been replaced by the more accurate Kohn-Sham type (Section 7.2.3) DFT methods. 

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