The transcorrelated method for accurate correlation energies using gaussian-type functions: examples on He, H2, LiH and H2O

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Abstract
The first transcorrelated calculations for correlated wavefunctions CФ which use purely analytical integration methods are presented. If we write C = exp (G T(r i , r j )), where G T is a linear combination of functions like exp (-arij 2) and exp (-br iB 2), and Ф is a Slater determinant whose orbital basis set is the usual gaussians, then Boys showed that all the integrals of the transcorrelated method could be evaluated. These are the bases used here. However, the use of a limited gaussian orbital basis set makes Ф a bad approximation to the best determinant. The results in atomic units are (giving the S.C.F. energy W SCF = <Ф|H|Ф>/<Ф|Ф> and the correlation energy W c, with their exact values in parenthesis): Calculations were performed at the experimental geometry. A few three-electron integrals used in the determination of parameters, but not in the determination of energies, were ignored in LiH and H2O, but this is not thought to affect the nature of the results. The reason why the convergence of the energy in these calculations is much closer to variational-type convergence than in previous transcorrelated calculations is explained. These results give great potentiality for the method when bigger orbital basis sets are used, which is already possible with the faster computers now available.