Primitive Gaussian type orbitals

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... 

Martin et al. [355] have applied multireference Cl calculations to evaluate polarizability derivatives for H2S. The basis set for the sulfur atom consisted of 1 ls7p primitive Gaussian orbitals augmented with an additional diffuse functions on die s and p spaces and with three d type polarization functions. The primitive functions have been contracted to (7s/6p). Three s functions and two sets of p polarization functions have formed the contracted basis for the hydrogen. It is important to note that die multireference Cl calculations produce values for the molecular polarizability components approximately 25% higher than the CISD estimates. 

The remainder of the input file gives the basis set. The line, 1 0, specifies the atom center 1 (the only atom in this case) and is terminated by 0. The next line contains a shell type, S for the Is orbital, tells the system that there is 1 primitive Gaussian, and gives the scale factor as 1.0 (unsealed). The next line gives Y = 0.282942 for the Gaussian function and a contiaction coefficient. This is the value of Y, the Gaussian exponential parameter that we found in Computer Project 6-1, Part B. [The precise value for y comes from the closed solution for this problem S/Oir (McWeeny, 1979).] There is only one function, so the contiaction coefficient is 1.0. The line of asterisks tells the system that the input is complete. 

The next step was to represent each Slater atomic orbital as a fixed linear combination of Gaussian orbitals so a Slater-type orbital with exponent f is written as a sum of GTOs with exponents a, q 2, and so on. For example, in the case of three primitive GTOs we might write... 

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 correct limiting radial behavior of the hydrogen-like atom orbital is as a simple exponential, as in (A.62). Orbitals based on this radial dependence are called Slater-type orbitals (STOs). Gaussian functions are rounded at the nucleus and decrease faster than desirable (Figure 2.2b). Therefore, the actual basis functions are constructed by taking fixed linear combinations of the primitive Gaussian functions in such a way as to mimic exponential behavior, that is, resemble atomic orbitals. Thus... 

Slater Type Orbital using 3 primitive Gaussians Two Configuration Self-Consistent Field Thermal Desorption Study... 

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