Basis Sets for Relativistic Calculations of Molecules

The fully relativistic (four-component) LCAO calculations of molecular systems use contracted Gaussian-type spinors as the basis two scalar wavefunctions within a two-component basis spinor are multiplied by a common expansion coefficient, for dimensions n of both the large and small components the total number of variational parameters (the scalar expansion coefficients) is equal to 2n [496]. In the relativistic correlated calculations the atomic basis sets should be optimized in the atomic correlated calculations. As Almlof and Taylor showed [538], atomic basis sets optimized to describe correlations in atoms also describe correlation effects in molecules very well. The two main types of basis sets are used in correlation calculations of molecules basis of atomic natural orbitals (ANO) suggested by Ahnlof and Taylor [538] correlation-consistent (CC) basis set suggested by Dunning [462]. 

Atomic natural orbitals V p are obtained by rmitary transformation of some set of orthonormal basis functions pp. Natural orbitals diagonaUze density matrix Dy for some state (or group of the states) of the atom or its ions  

Unlike the ANO scheme, the different number of primitive Gaussian functions are used in each basis set in the CC approach. Ekponents of the polarization-correlation functions are optimized in correlation calculations of the atomic terms to provide the lowest possible total energy. It turns out that basis functions can be separated in groups and every function in each group lowers the total energy approximately by the same amount. Correlation-consistency means that whole group of functions are added to the basis set, not just separate functions. 

Both ANO and CC schemes have a number of advantages, i.e. the ANO basis set is relatively easy to construct and the smaller ANO basis is just a subset of the larger one. Advantages of the CC basis are the smaller number of the primitive functions and a natural criterion for estimation of the completeness of the basis set. The following disadvantages can be emphasized for CC and ANO basis sets  

1 Generation of the trial spin-orbitals, two-component spinors or four-component spinors in the atomic SCF calculation with numerical functions. Functions are obtained in SCF calculations of the atom and its ions, thus trial functions are localized in valence or outer-core regions. 

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