Electron correlation, extended geminal models, and intermolecular interactions: Theory

Abstract

Within this framework of extended geminal models, new and improved approximations are introduced for the calculation of electron triple pair correlation terms. There are three levels of increasing accuracy for these terms based on the coupled-cluster models: a model of single and double excitations, a model correct up to fourth order, and a model correct up to fifth order CCSD(TQ). A test calculation on the neon atom demonstrates that by adopting the CCSD(TQ) model for the triple pair correlation terms, the extended geminal model recovers 99.88% of the full CI valence shell correlation energy. To reduce the computational work involved in calculating double pair correlation terms and triple pair correlation terms, a modified set of natural orbital (NOs) is introduced. On the basis of these NOs a truncated virtual orbital space is defined. Test calculations on the neon atom, the helium dimer, and the helium trimer demonstrate that the dimension of this truncated space can be chosen to be considerably smaller than the dimension of the full virtual space at a small sacrifice in accuracy. The additive structure of the correlation terms implies that the models are appropriate for implementation on parallel processor computers. The extended geminal models have properties which make them ideally suited for describing intermolecular interactions: the models have a conceptual structure which facilitates interpretation, they can be applied for any intersystem distances, the models are size-extensive, they generate no basis set artifacts (basis set superposition errors), and the models are reliable and accurate.