An approach in which the total energy of interacting subsystems is expressed as a bifunctional depending explicitly on two functions: electron densities of the two molecules forming a complex (rho(1) and rho(2)) was used to determine the equilibrium geometry and the binding energy of several weak intermolecular complexes involving carbazole and such atoms or molecules as Ne, Ar, CH4, CO, and N-2. For these complexes, the experimental dissociation energies fall within the range from 0.48 to 2.06 kcal/mol. Since the effect of the intermolecular vibrations on the dissociation energy is rather small, the experimental measurements provide an excellent reference set. The obtained interaction energies are in a good agreement with experiment and are superior to the ones derived from conventional Kohn-Sham calculations. A detailed analysis of relative contribution of the terms which are expressed using approximate functionals (i.e., exchange-correlation E-xc[rho(1)+rho(2)] and nonadditive kinetic energy T-s(nad)[rho(1),rho(2)]=T-s[rho(1)+rho(2)]-T-s[rho(1)]-T-s[rho(2)]) is made. The nonvariational version of the applied formalism is also discussed.