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 ExcTnad[rho A,rho B] component of the FDET energy functional and (ii) the choice of the density rho(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 rho(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. Published under an exclusive license by AIP Publishing.

Automated summary

The accuracy of observable derived from multi-scale simulations in Frozen-Density Embedding Theory (FDET) is influenced by two inseparable factors: (i) the approximation for the ExcTnad[rho A,rho B] component of the FDET energy functional and (ii) the choice of density rho(B)(r) for solving the FDET eigenvalue equation. This study proposes a method to estimate the relative significance of these two factors and provides numerical examples to illustrate. It is found that the violation of the non-negativity condition is the main source of error in FDET energy when rho(B) is the density of the isolated environment, and the error can be reduced by explicitly considering the electronic polarization of the environment.