The expressions which were derived in the present work can be accelerated, perhaps automatically, using density fitting techniques (see e.g. first-order exchange in Ref. 47). Although the formalism is rigorous for dimer-centered basis set, one could try monomer-centered plus (MCBS+) approach , which does include polarization basis functions of interacting partner: such basis should be complete enough to describe properly the exchange in second-quantized approach.