We present results of electronic structure calculations for well-relaxed Au/benzene-1,4-dithiol/Au molecular contacts, based on density functional theory and the generalized gradient approximation. Electronic states in the vicinity of the Fermi energy are mainly of Au 5d and S 3p symmetry, whereas contributions of C 2p states are very small. Hybridization between C 2p orbitals within the benzene substructure is strongly suppressed due to S-C bonding. In agreement with experimental findings, this corresponds to a significantly reduced conductance of the molecular contact.