Gaussian-type primitives

Sometimes it turns out that we need to include a number of polarization functions, not just one of each type. The notation 4-31G(3d, 2p) indicates a standard 4-31G basis set augmented with three d-type primitive Cartesian Gaussians per centre and two p-type primitives on every hydrogen atom. Again, details of the... 

On the convergence of the many-body perturbation theory second-order energy component for negative ions using systematically constructed basis sets of primitive Gaussian-type functions... 

Using the F ion as a prototype, the convergence of the many-body perturbation theory second-order energy component for negative ions is studied when a systematic procedure for the construction of even-tempered btisis sets of primitive Gaussian type functions is employed. Calculations are reported for sequences of even-tempered basis sets originally developed for neutral atoms and for basis sets containing supplementary diffuse functions. 

Figure 2.2. Radial dependence of basis functions a) correct exponential decay (STO) (b) primitive Gaussian-type function (solid line) vs. an STO (dotted line) (c) least-squares expansion of the STO in terms of three Gaussian-type orbitals (STO-3G).

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. 

For computational reasons only (particularly for ab initio calculations), the atomic orbitals are usually expressed as a linear combination of primitive functions centered on the atom (Eq. [3]). These primitives are typically Gaussian-type functions, but Slater-type functions have also been used. 

For a given molecular structure characterised by initial nuclear coordinates the basis set functions are attributed to each atom. These simulate the behaviour of atomic orbitals and are given in terms of a (fixed) linear combination of the primitive (usually Gaussian type) functions p as follows... 

Appendix 1 Fitting of 5-type Primitive Gaussian Orbitals that Best Reproduce Two-Electron Coulomb Integrals over 5-Type Slater Orbitals... 

In this appendix, we describe how we found the exponents given in Table 1, which are of x-type primitive Gaussian orbitals such that the two-electron Coulomb integrals over them best reproduce those over s-type Slater orbitals. We construct... 

II2 = s/if f)i is the L -norm, is the two-electron Coulomb integral over, r-type primitive Gaussian orbitals... 

In this equation, the original Gaussian-type functions are called primitive functions to distinguish them from the contracted ones. The primitive functions are specified only by the orbital exponent, a p, contracted coefficient, c p, and coordinate vector of the center of the function, Ra. By using these contracted Gaussian-type functions as basis functions, it was expected that highly accurate results could be obtained with far fewer basis functions. 

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