The extension of the frozen-density embedding theory for nonvariational methods [J. Chem. Theory Comput.2020,16, 6880] was utilized to evaluate intermolecular interaction energies for complexes in the Zhao–Truhlar basis set. In the applied method (FDET-MP2-FAT-LDA), the same auxiliary system is used to evaluate the correlation energy by means of the second-order Møller–Plesset perturbation theory (MP2), as in our previous work [J. Chem. Phys.2019,150, 121101]. Local density approximation is used for E_xcT^nad[ρ_A,ρ_B] in both cases. Additionally, the contribution to the energy due to the neglected correlation potential was evaluated and analyzed. The domain of applicability of the local density approximation for E_xcT^nad[ρ_A,ρ_B] was determined based on deviations from the interaction energies from the conventional MP2 calculations. The local density approximation for E_xcT^nad[ρ_A,ρ_B] performs well for hydrogen- or dipole-bound complexes. The relative errors in the interaction energy lie within 3–30%. While for charge-transfer complexes, this approximation fails consistently, and for other types of complexes, the performance of this approximation is not systematic. The sources of error are discussed in detail.