Finite basis functions Gaussian-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. 

Extended basis set SCF and configuration interaction (CISD) calculations for CO have been carried out by Amos [359] with die aim to assess the effect of electron correlation on calculated molecular polarizability and polarizability derivatives. The basis set employed has been of the type (5s4p2d) contracted Gaussian function on each atom. The configuration interaction function consisted of single and double excitations of the valence shell orbitals. Polarizabilities have been calculated by the finite field method [179]. Polarizability derivatives are evaluated by numerical differentiation. The results are given in Table 10.5. 

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