The exact exchange part in hybrid density functionals is analyzed with respect to the prediction of ground state multiplicities. It has been found [M. Reiher, O. Salomon, and B. A. Hess, Theor. Chem. Acc., 107, 48 (2001)] that pure and hybrid density functionals yield energy splittings between high-spin and low-spin states of Fe-sulfur complexes that differ by more than 100 kJ/mol and thus fail to reliably predict the correct multiplicity of the ground state. This deviation can lead to meaningless reaction energetics for metal-catalyzed reactions. The finding that the energy splitting depends linearly on the exact exchange admixture parameter led to a new parametrization of the B3LYP functional which was dubbed B3LYP(star). In the present paper we investigate the generality and transferability of this functional. We study the extent to which the exact exchange admixture affects the thermochemistry validated with respect to the reference data set of molecules from the G2 test set. Metallocenes and bis(benzene) metal complexes of the first transition metal period are chosen to test the transferability of the findings for Fe-sulfur complexes. Moreover, the slope of the linear dependence of the energy splitting of high-spin and low-spin states on the amount of admixture of exact exchange is studied in detail.