Contraction of Gaussian functions

Forming the basis of the AOs from contractions of Gaussian functions (linear combinations of a set of functions with constant coefficients) times angular functions followed by evaluating the overlap matrix S in this basis set. 

STO- G is a fixed set ( contraction ) of Gaussian functions that have been least-squares fit to give an approximate representation of a minimal basis set of STOs. The smallest and cheapest basis set used has = 3. STO-3G has been frequently used in the past and is a good starting point before doing more serious computations. 

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... 

The collections of orbitals that are applied to calculations are referred to as basis sets and typically fall into one of several categories. The smallest employs one orbital to represent each of the orbitals of each shell that is full or partially filled. A minimal basis set for a first-row atom like Li or F would thus contain 1 s, 2s, 2p, 2p, and 2p orbitals, whereas H or He would be described by a single 1 s orbital, as indicated in the first row of Table 1.1. Perhaps the most commonly used basis set of minimal type is STO-3G . The name refers to the fact that each Slater-type orbital of the minimal basis set is replaced by a triad of Gaussian functions. (This triad is called a contraction, and the three functions are referred to as primitives. ) Other minimal basis sets of this type, albeit less widely used, are STO-4G and STO-6G. 

System of Computer Programs for the Evaluation of One- and Two-Electron Integrals Involving s-, p- and d-type Contracted Cartesian Gaussian Functions," The Johns Hopkins University, 1975. 

Basis sets assign a group of basis functions to each atom within a molecule to approximate its orbitals. These functions themselves are composed of a linear combination of gaussian functions such basis functions are referred to as contracted functions, and the component Gaussian functions are referred as primitives. 

Forming the basis of Bloch functions as linear combinations of the local basis of the AOs (Eq. [29]), in turn expressed as contractions of Gaussian... 

The rnethod used constructs the one-electron Bloch orbitals as a linear combination of a double-C (split-shell) type atomic basis set, i.e., 10 and 18 contracted atomic orbitals are applied on atoms N and S, respectively. These atomic orbitals themselves are taken as contractions of Gaussian lobe functions using 25 and 46 primitive functions for atoms N and S, respectively. The exponents of the Gaussians as well as the contraction coefficients were taken from the paper of Roos et Based... 

The contracted Cartesian Gaussian function, 0(a, i, r,A), is a linear combination of primitive Gaussians centered at A, each belonging to the same shell. 

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