  Density functional theory (DFT) simulations corrected by the intramolecular
Coulomb repulsion U, are performed to evaluate the vibrational inelastic
electron tunneling spectroscopy (IETS) of O_2 molecules on Ag(110). Semilocal
DFT calculations predict a spinless adsorbed molecule, however the inclusion of
the U leads to the polarization of the molecule by shifting a spin-polarized
molecular orbital towards the Fermi level. A molecular resonance at the Fermi
level can imply a decrease in conductance while in the off-resonance case, an
increase in conductance is the expected IETS signal. We use the lowest-order
expansion on the electron-vibration coupling, in order to evaluate the
magnitude and spatial distribution of the inelastic signal. This allows us to
reproduce the experimental data in: (i) the negative conductance variation
observed in the vibrational spectra of O_2 along the [001] direction, (ii) the
spatial distribution of the conductance changes recorded over the O_2 molecule
for the O--O stretch and the antisymmetric O_2--Ag stretch vibrations, (iii)
the absence of signal for the center-of-mass and hindered rotations modes, and
(iv) the lack of IETS signal for the molecule chemisorbed along the [1-10]
direction. Moreover, our results give us insight of the electronic and
vibrational symmetries at play. The vibrational frequencies need to go beyond
the harmonic approximation in order to be compared with the experimental ones,
hence we present a Morse-potential fitting of the potential energy surface in
order to evaluate accurate vibrational frequencies. The final IET spectra are
evaluated with the help of the self-consistent Born Approximation and the
effect of temperature and modulation-voltage broadening are explored. This
ensemble of results reveals that the IETS of O_2 cannot be ascribed to the
effect of a single orbital molecular resonance.
