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.