  Many experimental techniques such as tagging photodissociation and helium
nanodroplet isolation spectroscopy operate at very low temperatures in order to
investigate hydrogen bonding. To elucidate the differences between such
ultra-cold and usual ambient conditions, different hydrogen bonded systems are
studied systematically from 300 K down to about 1 K using path integral
simulations that explicitly consider both, the quantum nature of the nuclei and
thermal fluctuations. For that purpose, finite sized water clusters,
specifically the water dimer and hexamer, protonated water clusters including
the Zundel and Eigen complexes, as well as hexagonal ice as a condensed phase
representative are compared directly as a function of temperature. While weaker
hydrogen bonds, as present in the neutral systems, show distinct structural
differences between ambient conditions and the ultra-cold regime, the stronger
hydrogen bonds of the protonated water clusters are less perturbed by
temperature compared to their quantum ground state. In all studied systems, the
quantum delocalization of the nuclei is found to vary drastically with
temperature. Interestingly, upon reaching temperatures of about 1 K, the
spatial quantum delocalization of the heavy oxygens approaches that of the
protons for relatively weak spatial constraints, and even significantly exceeds
the latter in case of the centered hydrogen bond in the Zundel complex. These
findings are relevant for comparisons between experiments on hydrogen bonding
carried out at ultra-cold versus ambient conditions as well as to understand
quantum delocalization phenomena of nuclei by seamlessly extending our insights
into noncovalent interactions down to ultra-low temperatures.
