Resonance Raman spectra of dicopper complexes [L2Cu2(mu-O)(2)](2+) contain a number of resonance-enhanced features between 500 and 900 cm(-1), with L = R(3)TACN and various bidentate ligands (TACN = 1,4,7-triazacyclononane). Most importantly, there is a vibration near 600 cm(-1) in all [L2Cu2(mu-O)(2)](2+) compounds that is polarized, shifts by 19-27 cm(-1) upon O-18(2) substitution, and gives a new peak with (OO)-O-16-O-18 substitution, identifying it as a totally symmetric A, vibration of the bis(mu-oxo)dicopper(III) core. Changing the pendant groups on R(3)TACN causes shifts in the frequency of the Cu-2(mu-O)(2) vibration, but the direction of these shifts depends on the details of the organic fragment. A substantial shift to higher frequency is evident when bidentate ligands are used in place of TACN. Importantly, bidentate ligands with two different types of nitrogen donors show two independent core vibrations; these are assigned as "breathing" and "pairwise" modes through simple group theory considerations as well as by calculations using density functional theory. These calculations are extended to examine systematic trends with ligand variation as well as potential excited-state distortions of the core. Finally, the symmetry and energy of the Cu-2(mu-O)(2) vibrations are compared with resonance Raman data for other biologically relevant high-valent M-2(mu-O)(2) cores (M = Fe, Mn) to derive lessons for examining biological and model systems.