Hartree-Fock method from Gaussian basis sets

Almost all contemporary ab initio molecular electronic structure calculations employ basis sets of Gaussian-type functions in a pragmatic approach in which no error bounds are determined but the accuracy of a calculation is assessed by comparison with quantities derived from experiment[l] [2]. In this quasi-empirical[3] approach each basis set is calibrated [4] for the treatment of a particular range of atoms, for a particular range of properties, and for a particular range of methods. Molecular basis sets are almost invariably constructed from atomic basis sets. In 1960, Nesbet[5] pointed out that molecular basis sets containing only basis sets necessary to reach to atomic Hartree-Fock limit, the isotropic basis set, cannot possibly account for polarization in molecular interactions. Two approaches to the problem of constructing molecular basis sets can be identified ... 

Blume and Watson,97- 98 using spherical tensor methods, were able to reduce the second part of this expression to a form suitable for calculation. They derived expectation values of this operator from non-relativistic atomic Hartree-Fock wavefunctions and hence the spin-orbit coupling constant, , for many atoms and ions. Consistent results for atoms were also obtained by Hinkley" using wavefunctions both from exponential basis sets100 and from gaussian basis sets.101 Agreement with experiment is good. 

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