The geometric and electronic structures of titanium fulleride complexes have been studied at the gradient corrected density-functional theory level by using various ${\mathrm{C}}_{60}{\mathrm{Ti}}_{x}$ $(x=1,2)$ clusters. The cluster with the Ti atom binding on the six-ring site $({\ensuremath{\eta}}^{6})$ of the fullerene is shown to be lower in energy than those with Ti atom adsorbed on either five-ring $({\ensuremath{\eta}}^{5})$ or bridge $({\ensuremath{\eta}}^{2})$ sites. The bond formation for titanium fulleride has further been examined by calculated nonresonant, resonant, and off-resonant x-ray emission spectra of the clusters, and a comparison to the experimental counterpart. The examination shows that only the theoretical spectra of clusters with a six-ring adsorption site are in close agreement with the experimental x-ray emission spectra of titanium fulleride films. Our results indicate that off-resonant x-ray emission spectra provide an excellent basis for the probing of the bonding between metals and organic molecules.