The model system of the diamidinate CrI-CrI complex is investigated by wave function theory (WFT) and Kohn-Sham density functional theory (KS-DFT). The multireference perturbation theory (RASPT2) estimates a stabilization energy of ca. 20 kcal mol-1 for the δ bonding. The multiconfiguration pair-density functional theory (MC-PDFT) with the ftPBE functional well predicts the singlet energy curve comparable to the RASPT2 level. For the KS-DFT scheme based on a single determinant, seven functionals including BP86, BLYP, PBE, B3LYP, M06-L, M06, and ωB97X-D are assessed: two types of functionals are classified according to the nature of the restricted and broken symmetry potential energy curves. The broken symmetry scheme with the type I functionals can give good results for the energy curve in agreement with the multireference calculations. In regard to the metal-metal bonding, the restricted KS-DFT calculations performed by all of the seven functionals yield inferior description due to the lack of significant multiconfigurational character. The Mayer bond order, the electron localization function, and electron density predicted by the broken symmetry formalism with the type II functionals are consistent with those obtained with the multireference theory.