Enhanced connectivity and mobility in liquid water: Implications for the high density liquid structure and its onset

In this work, we investigate simulated liquid water at ambient pressure in both stable and metastable supercooled conditions by means of a new order parameter we recently proposed, namely the node total communicability (NTC), based on graph theory concepts. We show that this order parameter is able to identify the two liquid states differing in density, the LDL- and HDL-like states, in simulation conditions at which both states coexist. We also show that NTC is able to capture both the structural and dynamic differences between the two states, being correlated with both the local density and the mobility of water molecules within the network. In addition, we further investigate the high connectivity patches we previously identified as characteristic of the HDL-like state. We show that these extended patches are composed of molecules with an increased local density and mobility, packed in a highly connected network. The formation of these highly connected networks is characterized by a fast dynamics, with mobile molecules entering and exiting the patches. Interestingly, we observe small highly connected patches also at low temperatures, where the prevailing state is LDL-like. We show that the small-to-large patches transition is related to the Widom line crossing and we suggest that the small highly connected patches at low temperatures might function as initial sites for the formation of extended HDL-like regions characteristic of the highest temperatures