Basis Set Choice and Design

Up to now the basis sets have appeared mostly as formal entities. However, the success of any computational scheme is crucially dependent on the size and suitability of the basis sets used. In this section, we discuss the various considerations that influence the choice of a good basis set for relativistic four-component calculations. It is obvious that we want basis sets that are generally applicable, give a good approximation of the exact functions with a minimum number of terms in the expansion, and provide for fast and easy calculation of matrix elements. 

the overwhelming majority of quantum chemical calculations are done using basis sets of Gaussian functions, that is, functions of the type 

While this is by no means the only possible choice for relativistic four-component calculations, it is definitely the most efficient and convenient. It permits programmers to exploit an extensive technology that has been refined and tested through years of development of nonrelativistic methods. The usual complaint about the poor behavior of Gaussian functions close to nuclei is less severe for relativistic calculations, where nuclei of finite size are normally used and not point nuclei. As we discussed in chapter 7, Gaussians actually are particularly suitable for describing the wave function close to a nucleus of finite size. 

It is tempting to assume that the basis for the large component should be quite close to the nonrelativistic basis. While this holds for lighter elements, it is normally not accurate enough for heavy elements. Some of the reasons for this are  

High exponents are required for an accurate description of the relativistically contracted inner shells. 

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