Density functional theory simulations of the vibrational inelastic electron tunneling spectroscopy (IETS) of O2 on Ag(110) permits us to solve its unexplained IETS data [Hahn, Phys. Rev. Lett. 85, 1914 (2000)]. When semilocal density functional theory is corrected by including static intra-atomic correlations, the IETS simulations are in excellent agreement with the experiment. The unforeseen consequence of our calculations is that when adsorbed along the [001] direction, molecular O2 on Ag(110) is a mixed-valent system. This analysis of IETS unambiguously reveals the paramagnetic nature of O2 on Ag(110).