Quantum nature of the hydrogen bond from ambient conditions down to ultra-low temperatures.
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 this 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 the 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 the case of the centered hydrogen bond in the Zundel complex. These findings are relevant for comparisons between experiments on hydrogen bonding carried out under 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.