Orbital-free effective embedding potential at nuclear cusp
  A new approach to approximate the kinetic-energy-functional dependent component ($v_t[\rho_A,\rho_B](\vec{r})$) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in [Wesolowski and Warshel, {\it J. Phys. Chem.} {\bf 97}, (1993) 8050]) is proposed. The exact limit for $v_t$ at $\rho_A\longrightarrow 0$ and $\int \rho_B d\vec{r}=2$ is enforced. The significance of this limit is analysed formally and numerically for model systems including a numerically solvable model and real cases where $\int \rho_B d\vec{r}=2$. A simple approximation to $v_t[\rho_A,\rho_B](\vec{r})$ is constructed which enforces the considered limit near nuclei in the environment. Numerical examples are provided to illustrate the numerical significance of the considered limit for real systems - intermolecular complexes comprising, non-polar, polar, charged constituents. Imposing the limit improves significantly the quality of the approximation to $v_t[\rho_A,\rho_B](\vec{r})$ for systems comprising charged components. For complexes comprising neutral molecules or atoms the improvement occurs as well but it is numerically insignificant. 
Juan Maria Garcia Lastra, Jakub W. Kaminski, and Tomasz A. Wesolowski