N-representability of the target density in Frozen-Density Embedding Theory based methods: Numerical significance and its relation to electronic polarization.

The accuracy of any observable derived from multi-scale simulations based on Frozen-Density Embedding Theory (FDET) is affected by two inseparable factors: (i) the approximation for the E xcT nad [ρ A ,ρ B ] component of the FDET energy functional and (ii) the choice of the density ρ B (r) for which the FDET eigenvalue equation for the embedded wavefunction is solved. A procedure is proposed to estimate the relative significance of these two factors. Numerical examples are given for four weakly bound intermolecular complexes. It is shown that the violation of the non-negativity condition is the principal source of error in the FDET energy if ρ B is the density of the isolated environment, i.e., it is generated without taking into account the interactions with the embedded species. Reduction of both the magnitude of the violation of the non-negativity condition and the error in the FDET energy can be pragmatically achieved by means of the explicit treatment of the electronic polarization of the environment.