Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications

Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integrals over Gaussian type geminals in the atomic orbital basis. The number of variables is reduced by orders of magnitude applying an efficient contraction scheme, leading to a naturally local representation of correlation effects. This scheme is extended by orbital optimization to describe multi-reference problems and explicit correlation to improve the basis set convergence.