Local density functional computations that use extended Gaussian basis sets and take into account electron exchange and correlation are used to study the bonding characteristics and electronic structure of the VCr, (eta(6)-C6H6)VCr, and (eta 6-C6H6)CrV molecules. The lengths of the vanadium-chromium, benzene-vanadium, and benzene-chromium bonds, along with the angle of the hydrogen atoms with respect to the carbon ring plane, are optimized for the ground and some low-lying excited states. The naked VCr diatomic is found to have a (2) Delta ground state with the 12 sigma(2)5 pi(x)(2)5 pi(y)(2)1 delta(xy)(2)1 delta(x2-y2)up arrow electronic configuration. The VCr spectroscopic parameters omega(e), omega(e)x(e), B-e, alpha(e), and mu are also computed. The ground electronic configurations for both (eta(6)-C6H6)VCr and (eta(6)-C6H6)CrV arene-metal complexes, which have C-6 nu symmetry, are found to be 2b(1)(2)1b(2)(2)-16a(1) up arrow 9e(1)(4)4e(2)(4) which correspond to a (2)A(1) state. The structure-bonding relationships in the three molecules are also studied. The binding energies are computed along with the metal-ligand bond dissociation energies of the two half-sandwich complexes. All computed binding and dissociation energies are found to be positive, indicating the stable nature of the molecules. The (eta(6)-C6H6)CrV is predicted to be more stable than the (eta(6)-C6H6)VCr by 11 +/- 2 kcal/mol.