The significance of negativity of the target density in Frozen-Density Embedding Theory based simulations

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 nad approximation for the E xcT [ρ A , ρ B ] term in the FDET expression for the total energy and ii) the choice of the density ρ B (r) for which the FDET eigenvalue equation for the embedded wave-function is solved. If ρ B is locally larger than the exact density of the total system ρ AB , the difference ρ AB (r) − ρ B (r) (target density) cannot be obtained from FDET. For an arbitrary choice for ρ B , FDET provides only the upper bound of the exact energy. The relative significance of these two factors is investigated for four representative weakly bound intermolecular clusters and various choices for ρ B . 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., 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 polarisation of the environment.