Density fitting for the decomposition of three-electron integrals in explicitly correlated electronic structure theory

It is shown that the convergence of R12-type explicitly correlated electronic structure theories can be improved by rearranging the three-electron integrals before using a resolution of the identity to decompose them into expressions involving only two-electron integrals. The new scheme is illustrated for some test systems within the explicitly correlated second order many-body perturbation theory.