The arrangement of atoms and bonds in a molecule influences its physical and chemical properties. The scanning tunneling microscope can provide electronic and vibrational signatures of single molecules. However, these signatures do not relate simply to the molecular structure and bonding. We constructed an inelastic tunneling probe based on the scanning tunneling microscope to sense the local potential energy landscape of an adsorbed molecule with a carbon monoxide (CO)-terminated tip. The skeletal structure and bonding of the molecule are revealed from imaging the spatial variations of a CO vibration as the CO-terminated tip probes the core of the interactions between adjacent atoms. An application of the inelastic tunneling probe reveals the sharing of hydrogen atoms among multiple centers in intramolecular and extramolecular bonding.