Universal features in the lifetime distribution of clusters in hydrogen-bonding liquids

Hydrogen-bonding liquids, typically water and alcohols, are known to form labile structures (network, chains, etc.); hence, the lifetime of these structures is an important microscopic parameter, which can be calculated via computer simulations. Since these cluster entities are mostly statistical in nature, one would expect that, in the short-timescale regime, their lifetime distribution would be a broad Gaussian-like function of time, with a single maximum representing their mean lifetime, and be weakly dependent on criteria such as the bonding distance and angle, much similar to non-hydrogen-bonding simple liquids, while the long-timescale regime is known to have some power law dependence. Unexpectedly, all the hydrogen-bonding liquids studied herein, namely water and alcohols, display three highly hierarchical specific lifetimes, in the sub-picosecond range 0-0.5 ps. The dominant lifetime depends very strongly on the bonding-distance criterion and is related to hydrogen-bonded pairs. This mode is absent in non-H-bonding simple liquids. The secondary and tertiary mean lifetimes are related to clusters and are nearly independent of the bonding criterion. Of these two lifetimes, only the first one can be related to that of simple liquids, which poses the question of the nature of the third lifetime. The study of alcohols reveals that this third lifetime is related to the topology of the H-bonded clusters and that its distribution may also be affected by the alkyl tail surrounding the "bath". This study shows that hydrogen-bonding liquids have a universal hierarchy of hydrogen-bonding lifetimes with a timescale regularity across very different types, and which depend on the topology of the cluster structures.