The Correlation-Consistent Hierarchy of One-Electron Basis Sets

The Correlation-Consistent Hierarchy of One-Electron Basis Sets 

The quality of quantum-chemical calculations depends not only on the chosen n-electron model but also critically on the flexibility of the one-electron basis set in terms of which the MOs are expanded. Obviously, it is possible to choose basis sets in many different ways. For highly accurate, systematic studies of molecular systems, it becomes important to have a well-defined procedure for generating a sequence of basis sets of increasing flexibility. A popular hierarchy of basis functions are the correlation-consistent basis sets of Dunning and coworkers [15-17], We shall use two varieties of these sets the cc-pVXZ (correlation-consistent polarized-valence X-tuple-zeta) and cc-pCVXZ (correlation-consistent polarized core-valence X-tuple-zeta) basis sets see Table 1.1. 

As can be seen from the table, the number of AOs increases rapidly with the cardinal number X. Thus, with each increment in the cardinal number, a new shell of valence AOs is added to the cc-pVXZ set since the number of AOs added in each step is proportional to X2, the total number (Nbas) of AOs in a correlation-consistent basis set is proportional to X3. The core-valence sets cc-pCVXZ contain additional AOs for the correlation of the core electrons. As we shall see later, the hierarchy of correlation-consistent basis sets provides a very systematic description of molecular electronic systems, enabling us to develop a useful extrapolation technique for molecular energies. 

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