Contracted Gaussian-type orbitals

The molecular electron density function needed for EP calculation can be obtained through ab initio as well as various semi-empirical methods. Since ab initio calculations are not economical for large molecules (several hundred atoms), the use of well-parameterized semi-empirical methods are still justified. When semi-empirical methods are used the three-center potential integrals usually disappear, and therefore the electronic contribution can be easily calculated by Slater-type orbitals. In ab initio methods (primitive or contracted) Gaussian-type orbitals are used for calculating the three-center integrals because their calculations are clumsy with Slater-type orbitals. 

All calculations employed extended basis sets constructed from contracted Gaussian type orbitals. Basis sets were, in general, taken from the work of Huzlnaga (26) and Dunning and Hay (27). 

Potential energy curves for singlet and triplet A j, B, and B j states of COF j have been computed using ab initio projected-unrestricted Hartree-Fock theory with a contracted Gaussian type orbital basis set [273]. However, symmetry was strictly maintained for these excited states, so the poor agreement between the predicted and experimental band onsets (which was readily acknowledged by Brewer et al. [273]) comes as little surprise. 

Both Slater-type (STO) and Gaussian ([ ]) basis sets are used. If more than one basis set was applied, only the largest set is given in the table. (CGTO = Contracted Gaussian type orbitals). 

H. Tatewaki and S. Huzinaga, J. Comput. Chem., 1, 205 (1980). A Systematic Preparation of New Contracted Gaussian-Type Orbital Sets. 111. Second-Row Atoms from Li Through Ne. 

In making practical SCF calculations we introduce a basic set x, which usually consists of contracted Gaussian-type orbitals centered on each atom 7,... 

Figure 11. Graph of the H Is Slater-type orbital (STO) and its approximation using a contracted gaussian-type orbital (GTO). Three gaussian functions, centered at r = 0, are allowed to vary in a fitting routine that adjusts their relative heights (leading to the contraction coefficient) and widths (exponents) until their sum best matches the STO behavior. The best fit is found with the exponents 0.11, 0.41, and 2.2 for gaussians 1-3 respectively, giving the STO-3G basis set. Although in this case the decay of the STO is well approximated by the STO-3G basis set, the cusp near r = 0 is not.

H. Tatewaki and S. Huzinaga, A systematic preparation of new contracted Gaussian-type orbital set. 1. Transition metal atoms from Sc to Zn, J. Chem. Phys. 71 4339... 

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