Cluster liquid water model

Water is considered to be supercooled when it exists as a liquid at lower temperatures than its melting point, for example, at less than 0°C at atmospheric pressure. In this state, the supercooled water is metastable. The properties of supercooled water have been examined in detail in excellent reviews by Angell (1982, 1983) and Debenedetti (1996, 2003). A brief review of the properties of supercooled pure liquid water and the different liquid water models are discussed in this section. These structures comprise hydrogen-bonded water networks and/or water clusters ( cages ) that are the starting points to hydrate formation. 

The SPC/E model approximates many-body effects m liquid water and corresponds to a molecular dipole moment of 2.35 Debye (D) compared to the actual dipole moment of 1.85 D for an isolated water molecule. The model reproduces the diflfiision coefficient and themiodynamics properties at ambient temperatures to within a few per cent, and the critical parameters (see below) are predicted to within 15%. The same model potential has been extended to include the interactions between ions and water by fitting the parameters to the hydration energies of small ion-water clusters. The parameters for the ion-water and water-water interactions in the SPC/E model are given in table A2.3.2. 

The intennolecular forces between water molecules are strongly non-additive. It is not realistic to expect any pair potential to reproduce the properties of both the water dimer and the larger clusters, let alone liquid water. There has therefore been a great deal of work on developing potential models with explicit pairwise-additive and nonadditive parts [44, 50, 51]. It appears that, when this is done, the energy of the larger clusters and ice has a nonadditive contribution of about 30%. 

Yu HB, van Gunsteren WF (2004) Charge-on-spring polarizable water models revisited from water clusters to liquid water to ice. J Chem Phys 121(19) 9549—9564... 

Frank-Wen flickering cluster model, of liquid water, 26 15, 16 Frascati Manual, 21 610 Frasch sulfur extraction process, 23 564, 570-573... 

Figure 2.8. Rickering cluster model of liquid water. (From Ref. 1, with permission from J. Chem. Phys.)...

In this section we discuss model potentials for small metal clusters with parameters fitted to ab initio calculated potential surfaces. We named such potentials as ab initio model potentials This approach was first elaborated by Clementi and coworkers and used for the Monte-Carlo simulation of biological systems in liquid water... 

Cluster Theories. Historically, the most important study of water structure based on the existence of clusters was Stewart s x-ray diffraction work (142). In his theory, clusters ( cybotactic swarms ) were postulated to exist, each containing on the order of 10,000 water molecules. Although this constituted an apparently reasonable theory at the time, this view has now yielded to the concept of clusters of considerably smaller sizes. It is interesting to note that without much critical analysis, Frenkel (57) viewed Stewart s theory of water as essentially correct. In fact, Frenkel apparently expected that further work on liquid structures in general would be along the lines Stewart advocated. Luck has discussed this in some detail (100). Subsequent to Stewart s papers, Nomoto (113) discussed a water model, based on ultrasonic studies, involving clusters of several thousand water molecules. 

Because of the complexity of hydrated PEMs, a full atomistic modeling of proton transport is impractical. The generic problem is a disparity of time and space scales. While elementary molecular dynamics events occur on a femtosecond time scale, the time interval between consecutive transfer events is usually 3 orders of magnitude greater. The smallest pore may be a few tenth of nanometer while the largest may be a few tens of nanometers. The molecular dynamics events that protons transfer between the water filled pores may have a timescale of 100-1000 ns. This combination of time and spatial scales are far out of the domain for AIMD but in the domain of MD and KMC as shown in Fig. 2. Because of this difficulty, in the models the complexity of the systems is restricted. In fact in many models the dynamics of excess protons in liquid water is considered as an approximation for proton conduction in a hydrated Nation membrane. The conformations and energetics of proton dissociation in acid/water clusters were also evaluated as approximations for those in a Nation membrane.16,19 20 22 24 25... 

Ab initio methods provide elegant solutions to the problem of simulating proton diffusion and conduction with the vehicular and Grotthuss mechanism. Modeling of water and representative Nation clusters has been readily performed. Notable findings include the formation of a defect structure in the ordered liquid water cluster. The activation energy for the defect formation is similar to that for conduction of proton in Nafion membrane. Classical MD methods can only account for physical diffusion of proton but can create very realistic model... 

This model accounts only partially for the specific structure of liquid water, and to refine it, calculations within supermolecular and semicontinuum models were also performed. In these cases, the properties were computed for a cluster of five water molecules, simulating the inclusion of a first solvation shell. In the semicontinuum model, the cluster was immersed in the dielectric continuum. Because of the (prohibitive for the times) size of the cluster, it was possible to obtain only an uncorrelated result. On the other hand, a nonequilibrium solvation model was used in computing the orientational contribution of Equation (2.218). Finally, to determine mC(o>, T), an extensive property, a differential shell method was employed. 

The approaches based on explicit representations of the environment molecules include full quantum mechanical (QM) and hybrid QM/MM methods. In the former, the supramolecular system that is the object of the calculations cannot be very large for instance, it can be composed of the chromophore and a few solvent molecules ( cluster or microsolvation approach). A full QM calculation can be combined with PCM to take into account the bulk of the medium [5,13], which is also a way to test the accuracy of the PCM and of its parameterization, by comparing PCM only and PCM+microsolvation results. The full QM microsolvation approach is recommended when dealing with chromophore-environment interactions that are not easily modelled in the standard ways, such as those involving Rydberg states. An example is the simulation of the absorption spectrum of liquid water, by calculations on water clusters (all QM), clusters + PCM, and a single molecule + PCM only the cluster approach (with or without PCM) yielded results in agreement with experiment [13] (but we note that this example does not conform to the above requirement for a clear distinction between chromophore and environment). 

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