Valence multiple zeta

Other hybridization procedures for double-zeta basis sets may be imagined, for instance by using projection techniques [63] Starting with a set of hybrids obtained from a parent minimal basis (e.g., STO 3G versus 6-31 G) we can project the latter hybrids into the space spanned either by the inner subset or the outer subset of the original split-valence basis. The extension of the Del Re algorithm for hybridization to multiple-zeta sets does not raise any major difficulty, which illustrates both the flexibility of the method and the perenniality of the concept. 

Even larger basis sets are now practical for many systems. Such basis sets add multiple polarization functions per atom to the triple zeta basis set. For example, the 6-31G(2d) basis set adds two d functions per heavy atom instead of just one, while the 6-311++G(3df,3pd) basis set contains three sets of valence region functions, diffuse functions on both heavy atoms and hydrogens, and multiple polarization functions 3 d functions and 1 f function on heavy atoms and 3 p functions and 1 d function on hydrogen atoms. Such basis sets are useful for describing the interactions between... 

High-accuracy calculations clearly require very flexible basis sets extended in a number of ways such as with multiple polarization sets, with diffuse basis function augmentation, and with other than atom-centered functions. Use of smaller bases goes along with less reliability however, with bases smaller than double-zeta in the valence plus one well-chosen set of polarization functions on all centers, including hydrogens, the reliability is so limited that results are not likely to be meaningful for most contemporary problems of weak interaction. 

We now examine the results when a set of larger Pople-type basis sets is used. These are based on a triple-zeta valence description. The effects of adding diffuse functions and using multiple sets of polarization effects are considered. The 6-311G basis set is a triple-zeta valence basis set, augmented with a set of polarization functions for all atoms. 6-311++G includes in addition a set of diffuse functions on aU atoms. In the 6-311++G(2df,2pd) and 6-3U++G(3df,3pd), multiple sets of polarizations are used on all atoms. 

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