Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. I. Second-order perturbation treatment for He, Be, H2, and LiH

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Abstract
Second‐order correlation energies for He, Be, H2 and LiH were calculated variationally using a novel functional and a basis set of explicitly correlated Gaussian geminals. Each geminal was a product of two spherical Gaussian orbitals and a correlation factor of the form exp(−γr212). Since the time‐consuming terms resulting from the strong orthogonality do not appear in our functional, basis sets much larger than previous ones could be handled. The second‐order energies obtained after carefully optimizing all nonlinear parameters are better than the best values published hitherto in the literature, although the improvement is marginal for He and Be. This shows that the present approach is able to match the ‘‘basis set independent’’ results available for atoms, providing at the same time a similar accuracy for small molecules. The proposed approach offers a sensible alternative to the virtual orbital expansion method customarily used in MBPT calculations, since, for obtaining a comparable accuracy, orbitals much higher than f would have to be used in expanding the pair functions.