Atomic orbitals higher angular momentum

In addition to the fundamental eore and valenee basis deseribed above, one usually adds a set of so-ealled polarization functions to the basis. Polarization funetions are funetions of one higher angular momentum than appears in the atom s valenee orbital spaee (e.g, d-funetions for C, N, and O and p-funetions for H). These polarization funetions have exponents ( or a) whieh eause their radial sizes to be similar to the sizes of the primary valenee orbitals... 

The number and type of basis functions strongly influence the quality of the results. The use of a single basis function for each atomic orbital leads to file minimal basis set. In order to improve the results, extended basis sets should be used. These basis sets are named double-f, triple-f, etc. depending on whether each atomic orbital is described by two, three, etc. basis functions. Higher angular momentum functions, called polarization functions, are also necessary to describe the distortion of the electronic distribution due... 

In theory, an infinite number of calculations for highly excited states is required to complete the expansion of the EP given by Eq. (24), since there are only a few occupied valence orbitals in neutral atoms. This difficulty also exists in the nonrelativistic case and is resolved by using the closure property of the projection operator with the assumption that radial parts of EPs are the same for all orbitals having higher angular momentum quantum numbers than are present in the core. The same approximation is applicable in the present... 

While SCF basis sets are the starting point for molecular calculations, it is necessary to augment the basis sets that describe the atomic orbitals in order to describe polarization of the atomic orbitals in the molecule and to describe electron correlation. These two requirements have some overlap, and the functions used for electron correlation are often adequate for molecule formation. Both of these effects usually involve basis functions with higher angular momentum than in the atomic valence orbitals. This presents a challenge in relativistic calculations because the requirements of kinetic balance for the small component adds one further unit of angular momentum to the basis for any function added to the large component for polarization or correlation. 

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