The geometry, energetic, and spectroscopic properties of molecular structures of silica-supported vanadium oxide catalysts are studied using periodic density functional calculations. Isolated vanadia units deposed on amorphous silica are modeled at low coverage, 0.44 atoms nm(-2). The models are built following the grafting process through the reaction of a vanadium precursor with surface silanols: OV(OH)(3) + (Si-OH)(n) -> OV(OH)(3-n)(O-Si)(n) + nH(2)O (with n = 1-3). The most stable grafted structures involve one vanadyl group together with n(V-O-Si) bonds. The predominance of the vanadate groups is analyzed as a function of hydration by means of atomistic thermodynamics. At dehydrated conditions, the trigrafted pyramidal OV(O-Si)(3) species are predominant, whereas partial hydration stabilizes digrafted OV(OH)(O-Si)(2) and monografted OV(OH)(2)(O-Si) species. The harmonic vibrational spectra for selected models are compared to recent experimental infrared and Raman data, for representative bands, and vibrational modes. Hydration effects are discussed in terms of thermodynamic stability and vibrational spectra. The results obtained in this study show that the pyramidal OV(O-Si)(3), digrafted OV(OH)(O-Si)(2), and monografted OV(OH)(2)(O-Si) models can exist at a support surface, a trend in agreement with recent experimental findings.