The bi-functional for the non-additive kinetic potential at dissociation

The eigenvalue equations defined in frozen-density embedding theory (FDET) [T. A. Wesołowski, Phys. Rev. A 77, 012504 (2008)] feature the non-additive kinetic potential given as a bi-functional, depending on a pair of electron densities (vtnad[ρNA,ρNB]). In computational methods of FDET, vtnad[ρNA,ρNB] is usually approximated by means of approximants ṽtnad[ρNA,ρNB] given by some explicit analytic dependence on ρNA and ρNB. We investigate the behavior of errors in quantities derived from the FDET eigenvalue equation applying several semi-local approximants in cases where ρNA and ρNB are associated with molecules or radicals forming complexes prone to qualitatively incorrect redistribution of charge (charge-leak) at some finite separation between the interacting molecules. The results reveal a close relationship between these errors and the eigenstates corresponding to infinite separation. This relation is rationalized by means of a simple two-state model.