We investigate the quantum-mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real-space and momentum-space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(kθ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly. © 2012 Wiley Periodicals, Inc.