Consistent Basis Sets A Review

The above correlation consistent prescription has since been used essentially unchanged for all the 2nd-row main group elements Al-Ar and 3rd-row elements Ga-Kr [10-14]. While the sizes of these basis sets generally range from n = D to n = 5 or 6, selected elements have been covered up to as large as cc-pVlOZ [7]. In the case of the post-3d elements, the HF set also included d-type functions, however these cc-pVnZ basis sets defined the 3d electrons to lie within the frozen core approximation. Hence the pattern of valence correlating functions is identical in these cases to the 1st and 2nd row p-block atoms. 

There are two families of correlation consistent basis sets designed to recover core correlation effects, denoted cc-pCVnZ and cc-pwCVnZ [24,25]. Both add shells of functions to the standard cc-pVnZ sets in the usual correlation consistent prescription and both systematically lead to identical CBS limits. The number and type of added functions is dependent on the core definition. First-row atoms have a [He] core, so the DZ core correlation set adds a (Islp) set to the cc-pVDZ, while the TZ basis adds a (2s2pld) set, etc. In the case of the 2nd-row atoms, only 2s2p correlation is treated, i.e., the Is electrons are not correlated and the [Ne] core results in additional (Islpld), (2s2p2dlf), etc. added to the cc-pVDZ, cc-pVTZ, etc. sets to construct the core correlation basis sets. 

The cc-pCVnZ and cc-pwCVnZ basis sets differ only in how the additional exponents are optimized. The new functions that are added to obtain the cc-pCVnZ 

These elements are similar to the transition metals in that the valence p orbitals are unoccupied in the ground state HF wavefunction. In the correlation consistent sets, the valence p HF functions are then taken from the (Li, Na) or (Be, Mg) excited states. In the cases of Na and Mg the HF 2p functions were taken from ground state calculations while exponents describing the 3p electrons were obtained from the excited states. 

Recently correlation consistent basis sets for the Ca atom have been reported by Koput and Peterson [28]. Analogous to adding p-type functions to the Mg sets at the HP level of theory, additional HP d-type functions were included and optimized for the 4s 3d excited state of Ca. Affer confracfion, these functions played a very similar role in molecular calculations as the tight d functions in the cc-pV(n + d)Z basis sets described above for fhe 3p main group atoms. 

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