The molecular and electronic structures of the Rieske iron-sulfur [2Fe-2S] cluster with an imidazolate and imidazole were investigated by using usual unrestricted and broken symmetry B3LYP methods for the highest and lowest spin states, respectively. The electronic structures of the lowest spin states were determined by the spin contaminations and natural orbital analyses. It was shown that the spin contamination presents the number of pairs of the antiferromagnetic spin couplings. The oxidation mechanism of the ubquinol at the Q(p) site of the cytochrome bc(1) complex was also examined by the broken symmetry B3LYP methods. In the [2Fe-2S] clusters with an imidazolate, the oxidized and lowest spin state, [(Imz(-))FeS](ox)LS, was lowest in energy among four possible states, consistent with experimental observations. In the examination of the mechanism of the ubquinol oxidation, it was confirmed that the ubiquinol docks between the imidazolate of [2Fe-2S] clusters and Glu272(-) of cytochrome b by the hydrogen bonds before the oxidation proceeds, consistent with the experimental proposals. Our results support a "Glu272-first" mechanism that Glu272 serves as an acceptor of the first proton from the ubiquinol and subsequently the proton-coupled electron transfer (PCET) occurs from the ubisemiquinone anion to the Rieske iron-sulfur [2Fe-2S] cluster.