OFFPRINT Different water scenarios for a primitive model with two types of hydrogen bonds

Using a primitive water model, we find that the strength of tetrahedral interactions can change the behavior of liquid water from the liquid-liquid critical point scenario to the singularity-free scenario. Specifically, we find that the strongly tetrahedral model has a liquid-liquid critical point from which the Widom line emanates with a negative slope, but that the weakly tetrahedral model lacks the second critical point and the line of the specific heat maxima analogous to the Widom line has a positive slope. The strongly tetrahedral interaction is characterized by a double-step potential that depends on hydrogen-bond bending, while the weakly tetrahedral interaction has a uniform single-step potential. Copyright c © EPLA, 2012 When water is cooled, its thermodynamic response functions, e.g., specific heat CP , isothermal compressibility KT , and thermal expansivity −αP , dramatically increase. Theorists have proposed several interpretations for these low-temperature anomalies in liquid water, including the stability limit scenario [1], the liquid-liquid critical point (LLCP) scenario [2], and the singularity-free scenario [3]. Theoretical models of the hydrogen-bond (H-bond) interactions with different cooperativity have been designed to support one or more of these scenarios [4–6]. Very recently a Hamiltonian lattice model was proposed which can reproduce all the above scenarios by tuning the parameter of H-bond cooperativity strength [7]. The increase of CP upon cooling is weak in molecular simulations of TIP3P and SPC-E water models but is more pronounced in TIP5P and ST2 models [2,8], which have stronger tetrahedrality. Moreover, the TIP5P and ST2 models clearly display a first-order liquid-liquid phase transition (LLPT) at low temperatures [9,10], while the TIP3P and SPC-E do not. The discrepancy between these water models in computational simulations is not well understood, and it is still unclear how the details of molecular bonding affect the behavior of real water in the deeply supercooled region of its phase diagram. To explore the relationship between water anomalies and H-bond interactions, we adopt a coarse-grained model for H-bond tetrahedral orientation [11,12]. We expand the complex H-bond interactions by a zeroth-order approximation of a broad angular well (weakly tetrahedral), which corresponds to the orientations of distorted and weak H-bonds, and a first-order approximation of an additional narrow angular well (strongly tetrahedral), which corresponds to the orientations of linear H-bonds caused by strong electrostatic interactions between protons and lone pairs. Eisenberg and Kauzmann used a well-defined angular region of the energy curve to describe “distorted” H-bonds [13]. The question of how the potential energy of H-bonds depends on their distortion is still unclear and under debate [13–17]. Preliminary results [12] suggest that a strongly tetrahedral model reproduces the thermodynamic properties of liquid water, including both the anomalies at ambient temperatures and the LLCP at low temperatures indicated by the divergence of CP and KT . By systematically studying both strongly and weakly tetrahedral models over a broad range of pressures and temperatures, we find that weakening tetrahedrality of H-bonds may change the behavior from the LLCP scenario to the singularity-free