A new approach to approximate the kinetic-energy-functional dependent component (v_t[ρ_A,ρ_B](r⃗)) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in [Wesolowski and Warshel, J. Phys. Chem. 97, (1993) 8050]) is proposed. The exact limit for v_t at ρ_A⟶ 0 and ∫ρ_B dr⃗=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

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... ∫ρ_B dr⃗=2. A simple approximation to v_t[ρ_A,ρ_B](r⃗) 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[ρ_A,ρ_B](r⃗) for systems comprising charged components. For complexes comprising neutral molecules or atoms the improvement occurs as well but it is numerically insignificant.