Gaussian-type Geminals

Unfortunately, extending Hylleraas s approach to systems containing three or more electrons leads to very cumbersome mathematics. More practical approaches, known as explicitly correlated methods, are classified into two categories. The first group of approaches uses Boys Gaussian-type geminal (GTG) functions with the explicit dependence on the interelectronic coordinate built into the exponent [95]... 

Dahle, P., Helgaker, T., Jonsson, D., Taylor, RR. Accurate quantum-chemical calculations using Gaussian-type geminal and Gaussian-type orbital basis sets applications to atoms and diatomics. Phys. Chem. Chem. Phys. 2007, 9, 3112-26. 

B. J. Persson and P. R. Tayloii /. Chem. Phys., 105, 5915 (1996). Accurate Quantum-Chemical Calculations The Use of Gaussian-Type Geminal Functions in the Treatment of Electron Correlation. 

The special case of ECG functions, referring to two-electron systems, is called Gaussian-type geminal (GTG). The mathematical form of the GTG basis function can be written... 

Furthermore, it was realized that the even-tempered basis of Gaussian-type geminals could also be applied in an uncontracted form. Some initial calculations were performed on He, and it was observed that the variationally determined linear parameters for the primitive Gaussian geminals were quite similar to the coefficients obtained from the fitting procedure. Results for Ne and H2O obtained from this (uncontracted) ansatz are presented in Table 9. The results show that augmentation of standard basis sets with a few explicitly correlated... 

Table 9 Valence Shell MP2 Correlation Energy (in m h) for Ne and H2O Obtained by Persson and Taylor from Augmentation of Standard Gaussian Orbital Expansions with Six Gaussian-type Geminals...

Recently Rychlewski and coworkers [36] have been able to achieve a similar accuracy as Pekeris even with a wave function of Gaussian geminal type... 

We note that the correlation factor is often given as/(r ) = —In fact, this form is equivalent with Eq.(12) when the strong orthogonality projector Qu (to be discussed in the following) is applied. In most present work, the Slater type correlation factor is approximated by a contracted set of Gaussian geminals (typically n = 6), " ... 

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