Finite basis functions Slater-type orbitals

It is convenient to start from the analytical expression of (r), as done by quantum calculations over a finite basis set of simple analytical functions. The basis set functions are in general of Gaussian type, and they have special mathematical properties which may be exploited here [73, 74]. The extension of this analysis to other basis functions, such as the Slater type orbitals, is however possible. 

Two types of ETO are considered here Slater type orbitals (STOs) [58, 59] and Coulomb Sturmlans and their generalisation, which may be written as a finite combination thereof [69]. Otherwise, STOs may be treated as multiple zeta basis functions in a similar way to the approach used with gaussian functions. 

Thus, one can think of the R12 wave function as representing many-body correlation effects through two types of terms /(r12)O0 responsible for the short-range two-body Coulomb correlation and y describing conventional many-body correlation. The second term is expanded in terms of Slater determinants composed of orbitals from a finite orbital basis set (OBS) ... 

J. C. Slater together with G. F. Koster developed a method called the Slater-Koster tight-binding method, which builds directly on Figure 16.1. This tight-binding model is a simplified MO model where the crystal orbitals are expressed in terms of atomic functions, as in the Hiickel model. Later, basis sets of the same type as in quantum chemical calculations on finite systems have also come to be used in infinite systems. 

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