Off-Centered Gaussian Functions

This section is devoted to Gaussian basis functions which are not placed on the atom centers but at different points in space. We note on the use of the following types of basis set functions  

The development of the basis sets with off-centered functions aimed at avoiding use of higher spherical harmonics (i e. d, f,. .. type functions) without losing the basis set flexibility. Actually, the lobe function and floating spherical function basis sets are constructed only from s-type functions. Computationally, this restriction is very advantageous..The evaluation of integrals over s-type functions is 

The Gaussian lobe function method was introduced by Preuss and developed for routine calculations by Whitten. The contraction of Gaussian lobe function (GLF) basis sets is made along the same lines as with Cartesian GTF s. As regards the primitives, the s-type functions are expressed in the usual way. But the primitives of p, d, f,. .. types are expressed as linear combinations of s-Gaussians (lobe functions) placed at different points so as to retain the proper symmetry (see Fig. 2,4 ). Thus, a p-type function on nucleus A may be 

It should be noted that in programs based on Cartesian GTF s use 

Cartesian sp basis sets established the essential equivalence of the 128 

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