Explicit correlation factors

We analyze the performance of 17 different correlation factors in explicitly correlated second-order many-body perturbation calculations for correlation energies. Highly performing correlation factors are found to have near-universal shape and size in the short range of electron-electron distance (01.5a.u.) is insignificant insofar as the factor becomes near constant, leaving an orbital expansion to describe decoupled electrons. An analysis based on a low-rank Taylor expansion of the correlation factor seems limited, except that a negative second derivative with the value of around −1.3a.u. correlates with high performance.