Contracted Gaussian basis functions

Gaussian Basis Functions for use in Molecular Calculations III Contraction of (10s, 6p) Atomic Basis Sets for the First-Row Atoms T. FI. Dunning, Jr... 

Initially, the polyatom program was coded to limit the basis set to 50 elements . By 1966, the ibmol program could (in principle) handle a maximum of 800 Gaussian functions distributed on 50 centers. This program also used contracted Gaussian basis functions which had been introduced earlier by dementi. 

Dunning TH Jr. Gaussian basis functions for use in molecular calculations. I. Contraction of (9s5p) atomic basis sets for the first-row atoms. J Chem Phys 1970 53 2823-33. 

The ability to compute the two-electron repulsion integrals (ERIs) efficiently is of a pivotal importance to the issue of feasibility of large-scale ab initio calculations. Since the pioneering work of Boys, several computer algorithms for the evaluation of ERIs over Gaussian basis functions have been published. Most of these algorithms work with contracted basis functions 4i,(a,r). Each of these real functions is a linear combination... 

Repulsion Integrals Involving Contracted Gaussian Basis Functions. 

In order to demonstrate the efficiency of the DLU approximation, we review results of the three relativistic exact-decoupling approaches for the AgB cluster originally reported in Ref. [647]. A total of 119 primitive Gaussian basis functions were contracted to 46 functions for each Ag atom. The dimension of the matrices involved in the setup of the relativistic one-electron Hamiltonian is then roughly three times the dimension of the matrices used in the SCF iterations (e.g., the Fock matrix). For the two-component calculations, both dimensions are doubled if no s)mimetries are considered. 

In summary, nearly all ab initio calculations currently use contracted Gaussian basis functions. Uncontracted sets have been relegated to investigations seeking very high accuracy in small systems where it might be desirable to retain as much flexibility as possible. ... 

Figure 6 Diffuse basis functions are more spatially extended than their valence counterparts. The dashed curve represents the radial plot of the normalized diffuse Is Gaussian basis function for H from the aug-cc-pVDZ basis set while the solid curve is for the corresponding contracted valence Is basis function.

Since each atom has two valence basis functions, there are two coefficients for H(s) in Tables All.l and All.2. Similarly, the O valence basis contains two coefficients per MO, one for the contraction of three Caussians and one for the single Gaussian basis function. In addition, the O core basis function is a contraction of six Caussians, and we note that only a single s-symmetry core function is required. 

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