Homogeneity properties of the embedding potential in frozen-density embedding theory

ABSTRACT

In numerical simulations, based on frozen-density embedding theory, the independent variables describing the total system are the embedded wave function (Ψ_A) and the density ${\rho }_B\left(\overrightarrow{r}\right)$ representing the environment. Due to inhomogeneity of the non-electrostatic component of the total energy: $E_{xcT}^{\mathrm{nad}}[{\rho }_A,{\rho }_B]\ne \int {\rho }_A\left(\overrightarrow{r}\right)\frac{\delta E_{xcT}^{\mathrm{nad}}[{\rho }_A,{\rho }_B]}{\delta {\rho }_A\left(\overrightarrow{r}\right)}d\overrightarrow{r}$), the expectation value of the embedding potential is not equal to the corresponding component of the total energy. The differences ${\Delta }_{xcT}^{\mathrm{nad}}=E_{xcT}^{\mathrm{nad}}[{\rho }_A,{\rho }_B]-\int {\rho }_A\left(\overrightarrow{r}\right)\frac{\delta E_{xcT}^{\mathrm{nad}}[{\rho }_A,{\rho }_B]}{\delta {\rho }_A\left(\overrightarrow{r}\right)}d\overrightarrow{r}$ are evaluated using local and semi-local approximations for the functional E^nad_xcT[ρ_A, ρ_B] in two model systems representing embedded species weakly interacting with the environment. It is found that Δ^nad_xcT is typically one order of magnitude smaller than E^nad_xcT[ρ_A, ρ_B] and decreases with the overlap between ${\rho }_A\left(\overrightarrow{r}\right)$ and ${\rho }_B\left(\overrightarrow{r}\right)$. The kinetic- and exchange-correlation contributions to Δ^nad_xcT cancel partially reducing its magnitude to mHartrees. Compared to local approximation for E^nad_xcT[ρ_A, ρ_B], the inhomogeneity is more pronounced in semi-local functionals.

GRAPHICAL ABSTRACT

Keywords:

• Embedding
• multi-level simulations
• density functional theory
• homogeneity
• frozen-density embedding theory

Acknowledgements

The authors would like to dedicate this work to Professor Andreas Savin on the occasion of his 65th birthday. Francesco Aquilante gratefully acknowledges support from the FIRB “PROGRAMMA FUTURO IN RICERCA” RBFR1248UI by the Italian ‘Ministero dell’Istruzione, dell’Università e della Ricerca’ (MIUR).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by grants from Swiss National Science Foundation [200021_152779].