A kinetic-energy-based fitting metric for application in the context of resolution of the identity second-order Moller-Plesset perturbation theory is presented, which is derived from the Poisson equation. Preliminary tests of the applicability include the evaluation, of the error in the correlation energy, compared to standard Moller-Plesset perturbation theory, with respect to the auxiliary basis set employed. We comment on the potential merits of this fitting metric, compared to standard resolution of the identity second-order Moller-Plesset perturbation theory, and discuss its scaling behavior in the limit of large molecules.