The structures of Ga2O3 have been studied using the SCF, MP2, QCISD(T), and B3LYP methods with one-particle basis sets of at least triple-zeta plus double-polarization quality. The V-shaped (C-2v) structure was found to be the most stable isomer of Ga2O3, with the linear OGaOGaO (inversion transition state) structure lying about 3 kcal/mol above the former at the QCISD(T)/TZ2P level. The results show that inclusion of electron correlation is very important in determining the energy difference between the V-shaped C-2v isomer and the linear D-infinity h form. The calculated harmonic vibrational frequencies, especially the isotopic ratios obtained with the MP2/TZ2P+f and B3LYP/TZ2P+f models, when compared to the available experimental IR data reinforce our prediction that Ga2O3 is a V-shaped planar system with C-2v symmetry. Furthermore, calculations at the Hartree-Fock and MP2 levels using ab-initio relativistic effective core potential and a double-zeta valence basis set predict In2O3 and Tl2O3 as linear systems. Computed geometrical parameters, harmonic vibrational frequencies, and isotopic ratios are provided for the linear OMOMO (M = In, Tl) to complement future experimental studies on these systems.