Spin-component-scaling second-order Møller-Plesset theory and its variants for economical correlation energies:...

The spin-component-scaling second-order Møller-Plesset theory proposed by Grimme, the scaled opposite-spin variant of Head-Gordon and co-workers, and other variants of the theory to treat the electron correlation energy are examined. A refinement of scaled opposite-spin theory for strong chemical interactions is suggested where the scaled correlation contribution is chosen such as to mimic closely the one obtained by more sophisticated methods of the coupled cluster type. With the scaling factor chosen to vary in a simple statistical manner with the number of opposite-spin electron pairs of the system, the parameters have been calibrated from standard coupled cluster type calculations for a chosen ab initio test data set. The new approach, termed as variable-scaling opposite spin, aims to be applicable at any regions of the molecule configuration space where second-order Møller-Plesset perturbation theory converges. It thus benefits of all advantages inherent to the original theory, which makes it an attractive approach on a computational cost basis. Because the method in one of its formats fails size-extensivity, the consequences and remedies of this are analyzed. Illustrations are presented for many molecules utilizing Dunning-type basis sets, in particular, for a detailed analysis of N(3) in its lowest quartet state, which does not belong to the test set. Extrapolations of the calculated raw energies to the complete one-electron basis set limit are also reported, giving the most reliable estimates available thus far of the energetics for the N((4)S)+N(2) exchange reaction. All spin-component-scaling schemes are known to show difficulties in dealing with weak interactions of the van der Waals type, which has justified the design of specific variants of the theory according to the property and regime of interactions. Several variants of the theory are then examined using a second test set of molecules, and shown to be linked via a coordinate that evolves gradually between two known extreme regimes. It is further shown that such a coordinate can be specified via a constrained Feenberg-type scaling approach, a theory whose merits are also explored.