Explicitly correlated wave functions: summary and perspective

We summarize explicitly correlated electronic structure theory in perspective of future work in the field. Earlier stages of approaches with different Ansätze in physics and chemistry are described. We then discuss recent advances focusing on explicitly correlated wave functions using cusp conditions. Removal of Coulomb singularities in terms of the rational generator is brought out from the viewpoint of many-body perturbation theory. On the basis of decomposition schemes for many-electron integrals in R12 and F12 methods, we further discuss the possibility of increasing the accuracy of molecular numerical integration and massively parallel calculations of explicitly correlated methods.