We report an experimental and theoretical study of single-molecule inner-shell photoemission measured over an extended range of photon energies. The vibrational intensity ratios I({ν=1)/I(ν=0)} from the C 1s photoelectron spectra of carbon monoxide, although mostly determined by the bond length change upon ionization, are shown to be affected also by photoelectron recoil and by scattering from the neighboring oxygen atom. Static-exchange density functional theory ({DFT)} is used to encompass all these effects in a unified theoretical treatment. The ab initio calculations show that the vibrational ratio as a function of the photoelectron momentum is sensitive to both the ground-state internuclear distance and its contraction upon photoionization. We present a proof-of-principle application of {DFT} calculations as a quantitative structural analysis tool for extracting the dynamic and static molecular geometry parameters simultaneously.