Gaussian Geminal Methods

Table 7 Selected Results from the Variational Gaussian Geminals Method ...

Explicitly correlated Gaussians (ECG) methods have already been developed earlier 10,11,12) and have been used for accurate calculations on small molecules. The main difference between these ECG methods and the use of Gaussian geminals in the framework of R12 theory is that in the latter, their purpose is to dampen the linear r term more than being a correlation factor on its own. 

A diffusion quantum Monte Carlo method based on floating spherical Gaussian orbitals and Gaussian geminals Dipole moment of lithium hydride molecule. 

A scientific research group, concentrated mainly at Gainesville, Florida, carried out a detailed study on various quantum chemical methods, incorporating explicitly correlated Gaussian geminals into the basis set [75, 76, 77, 78, 79], The research in this direction is still in progress [80, 81, 82, 83, 84]. 

As to problem (a) it is at least understood that the basic difficulty is caused by the correlation cusp and that much better convergence is obtained if one uses wave functions depending explicitly on the interelectronic coordinates. The problem of difficult integrals can be avoided in the R12-methods, or possibly by using Gaussian geminals. One may also think of improved extrapolation techniques based on the known behaviour of the wave function for r,j —> 0. 

The area of application of this method is-for practical (computational) reasons- elatively small. The method of Gaussian geminals has been applied in unusually accurate calculations... 

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]... 

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