How do hydrogen bonds break in supercooled water?: Detecting pathways not going through the saddle point of two-dimensional potential of mean force

Supercooled water exhibits remarkably slow dynamics similar to the behavior observed for various glass-forming liquids. The local order of tetrahedral structures due to hydrogen-bonds (H-bonds) increases with decreasing temperature. Thus, it is important to clarify the temperature dependence of the H-bond breakage process. This was investigated here using molecular dynamics simulations of TIP4P supercooled water. The two-dimensional (2D) potential of mean force (PMF) is presented using combinations of intermolecular distance and angle between two water molecules. The saddle point of the 2D PMF suggests the presence of the transition state that distinguishes between H-bond and non H-bond states. However, we observed pathways not going through this saddle point particularly at supercooled states, which are due to translational, rather than rotational motions of the molecules. We quantified the characteristic time scales of rotational and translational H-bond breakages. The time scale of translational H-bond breakage shows a non-Arrhenius temperature dependence comparable to that of the H-bond lifetime. This time scale is relevant for the temperature dependence of the transmission coefficient based on the transition state theory. The translational H-bond breakage is also related to cage-jumps observed in glass-forming liquids, which mostly involve spatially correlated molecules. Our findings warrant further exploration of an appropriate free-energy surface or reaction coordinates beyond the geometrical variables of the water dimer to describe a possible saddle point related to collective jump motions.