Gaussian geminals

At this point one can conjecture that the relatively rapid convergence of Gaussian geminals [22]... 

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. 

Valeev, E.F. Combining explicitly correlated R12 and Gaussian geminal electronic structure theories. J. Chem. Phys. 2006, 125, 244106. 

Korona T, Williams HL, Bukowski R, Jeziorski B, Szalewicz K (1997) Helium dimer potential from symmetry-adapted perturbation theory calculations using large Gaussian geminal and orbital basis sets. J Chem Phys 106 5109—5122... 

Figure 3. Plots of the dispersion function for the equilibrium He dimer from Ref. 36. The electron coordinates, xj and X2 are defined in fig. (a). The accurate dispersion function (calculated with Gaussian geminals) is shown in plot (b). If the dispersion term is reduced to the dipole-dipole component, one obtains plot (c). If every electron is allowed to use the complete dimer basis set as well as the bond functions one obtains plot (d).

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

Ornstein-Uhlenbeck diffusion quantum Monte Carlo calculations on BH and HF with the floating spherical Gaussian orbitals and spherical Gaussian geminals. 

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]. 

In the calculations in terms of Gaussian geminal wave functions [10, 96] an interesting observation was made. While generally the DPT results converge much faster with extension of the basis than the results from the Breit-Pauli approximation, only small differences between the two ap-... 

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

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. 

A geminal is an analog of an orbital-there is a one-electron function, and here is a two-electron one. A single geminal is very rarely used in computations, we apply hundreds or even thousands of Gaussian geminals. When we want to find out the optimal positions A, B and... 

Ludwik Adamowicz introduced an idea of the minimal basis of the Gaussian geminals [equal to the number of the electron pairs) and applied to the LiH and HF molecules, L. Adamowicz and A J. Sadlej, J. Chem. Phys., 69, 3992 (1978). 

The Gaussian geminals do not satisfy the correlation cusp condition (p. 587). because of factor exp —brfj). It is required (for simplicity, we write = r) that... 

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... 

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