Thermodynamics water models

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

We assume for simplicity that the solvent is pure water, and that only the water-oxygen atoms have explicit Lennard-Jones interactions with the solute (this is typical of several common water models). We have seen that AWnp can be viewed as the free energy to change A from zero to one. Therefore, a well-known thermodynamic integration formula gives... 

However, from our point of view, there remains a lack of sufficiently precise and reliable methods to compute thermodynamic water solubility. The majority of methods work only for congeneric series of compounds, and many have not been developed to function in areas of pharmaceutical research using drug-like molecules. Most of the methods do not use the three-dimensional structure of the compounds, while some depend on previous knowledge of certain experimental properties of the compounds of interest. Moreover, all of the methods are dependent upon the quality of solubility values in the training set used to develop the model indeed, this latter point is a critical limitation that has a major influence on solubility estimations. 

Results in Table I illustrate some of the strengths and weaknesses of the ST2, MCY and CF models. All models, except the MCY model, accurately predict the internal energy, -U. Constant volume heat capacity, Cv, is accurately predicted by each model for which data is available. The ST2 and MCY models overpredict the dipole moment, u, while the CF model prediction is identical with the value for bulk water. The ratio PV/NkT at a liquid density of unity is tremendously in error for the MCY model, while both the ST2 and CF models predictions are reasonable. This large error using the MCY model suggests that it will not, in general, simulate thermodynamic properties of water accurately (29). Values of the self-diffusion coefficient, D, for each of the water models except the CF model agree fairly well with the value for bulk water. 

Mauritz et al., motivated by these experimental results, developed a statistical mechanical, water content and cation-dependent model for the counterion dissociation equilibrium as pictured in Figure 12. This model was then utilized in a molecular based theory of thermodynamic water activity, aw, for the hydrated clusters, which were treated as microsolutions. determines osmotic pressure, which, in turn, controls membrane swelling subject to the counteractive forces posed by the deformed polymer chains. The reader is directed to the original paper for the concepts and theoretical ingredients. 

Bruno, J Duro, L. Grive, M. 2002. The applicability of thermodynamic geochemical models to simulate trace element behaviour in natural waters. Lessons learned from natural analogue studies. Chemical Geology, 190, 371-393. 

DDI DISSOL DLM DLVO DOC DOE DTA DU Distilled, deionized water Thermodynamic simulation model Diffuse layer model named after Derjaguin, Landau, Vervey, Overbeek Dissolved organic carbon Department of Energy Differential thermal analysis Depleted uranium... 

In particular, the extension of the van der Waals and Platteeuw method addresses the first assumption listed at the beginning of Section 5.1.1—namely that encaged molecules do not distort the cavity. In the development of the statistical thermodynamic hydrate model (Equation 5.23), the free energy of water in the standard hydrate (empty hydrate lattice), gt, is assumed to be known at a given temperature (T) and volume (v). Since the model was developed at constant volume, the assumption requires that the volume of the empty hydrate lattice, 7, be equal to the volume of the equilibrium hydrate, v11, so that the only energy change is due to occupation of the hydrate cavities, as shown in Figure 5.3. 

Chin, Y.P., Weber, Jr., W.J., Chiou, C.T. (1991) Chapter 14, A thermodynamic partition model for binding of nonpolar organic compounds by organic colloids and implications for their sorption to soils and sediments. In Organic Substances and Sediments in Water. Vol. 1. Baker, R.A., Editor, pp. 251-273, Lewis Publishers, Inc., Chelsea, Michigan. 

It should be noted that either the insertion or annihilation of the particle can be used to calculate the Gibbs energy of solvation, and both are related by a change of sign. With an appropriate method for solving the solubility calculations in aqueous solution, such as the one presented here, one can parameterize a model of C02 for a particular water model to reproduce these values over an extended thermodynamic window, such as over a desired temperature range that would encompass any type of brine aquifer. 

Table 16-1 shows results for the dielectric constant e(0), Kirkwood -factor gK, and the static dipole cross-correlation parameter g° = ( M(0) 2) /(Np ) — 1 where M(f) = IFit) is the system s collective dipole at time t, for a selected set of thermodynamic states. The experimental values for e(0) are shown within parentheses. The overall trend of these quantities with density and temperature is consistent with the expectation of a higher degree of dipolar correlation at higher densities and/or lower temperatures. At liquid-like densities (states 10-12), where polarizability effects are known to be important, the simulated model underestimates e(0), a feature common to most non-polarizable water models. Given the error bars and differences in thermodynamic states, our estimates for e(0) for states 10-12 are... 

Other important applications include the generation of a model to predict thermodynamic water solubility (Cruciani et al. 2003). This model is based on consistent solubility data from literature plus additional measurements for 970 compounds. Its quality allows to differentiate between very poorly/poorly/medium/ highly and very highly soluble molecules while exact rankings within individual classes are not possible. However, given the different factors influencing experimental thermodynamic solubility data, it is not likely that significantly improved models for this key property in pharmaceutical sciences can be derived. 

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

Physico-chemical speciation refers to the various physical and chemical forms in which an element may exist in the system. In oceanic waters, it is difficult to determine chemical species directly. Whereas some individual species can be analysed, others can only be inferred from thermodynamic equilibrium models as exemplified by the speciation of carbonic acid in Figure 9. Often an element is fractionated into various forms that behave similarly under a given physical (e.g., filtration) or chemical (e.g., ion exchange) operation. The resulting partition of the element is highly dependent upon the procedure utilised, and so known as operationally defined. In the following discussion, speciation will be exemplified with respect to size distribution, complexation characteristics, redox behaviour and methylation reactions. 

Realistic three-dimensional computer models for water were proposed already more than 30 years ago (16). However, even relatively simple effective water model potentials based on point charges and Leimard-Jones interactions are still very expensive computationally. Significant progress with respect to the models ability to describe water s thermodynamic, structural, and dynamic features accurately has been achieved recently (101-103). However, early studies have shown that water models essentially capture the effects of hydrophobic hydration and interaction on a near quantitative level (81, 82, 104). Recent simulations suggest that the exact size of the solvation entropy of hydrophobic particles is related to the ability of the water models to account for water s thermodynamic anomalous behavior (105-108). Because the hydrophobic interaction is inherently a multibody interaction (105), it has been suggested to compute pair- and higher-order contributions from realistic computer simulations. However, currently it is inconclusive whether three-body effects are cooperative or anticooperative (109). 

These classical interaction potentials must be parameterized, e.g. the magnitude of the partial charges on each atom in the molecule must be assigned, and the equilibrium bond length and size of the harmonic force constant must be attached to each bond. In the early biomolecular MM forcefields, these parameters were developed to produce molecular models that could reproduce known experimental properties of the bulk system. For example, several MM water models have been developed. ° One of the earliest successful models, TIP3P, was parameterized such that simulations of boxes of TIP3P molecules reproduced known thermodynamic properties of water, such as liquid density and heats of vaporisation. Such a parameterisation scheme is to be applauded, as it ties the molecular model closely to experiment. Indeed many of the common MM models of amino acids were developed by comparison to experiment, e.g. OPLS. Indeed it is such a good... 

The most expensive part of a simulation of a system with explicit solvent is the computation of the long-range interactions because this scales as Consequently, a model that represents the solvent properties implicitly will considerably reduce the number of degrees of freedom of the system and thus also the computational cost. A variety of implicit water models has been developed for molecular simulations [56-60]. Explicit solvent can be replaced by a dipole-lattice model representation [60] or a continuum Poisson-Boltzmann approach [61], or less accurately, by a generalised Bom (GB) method [62] or semi-empirical model based on solvent accessible surface area [59]. Thermodynamic properties can often be well represented by such models, but dynamic properties suffer from the implicit representation. The molecular nature of the first hydration shell is important for some systems, and consequently, mixed models have been proposed, in which the solute is immersed in an explicit solvent sphere or shell surrounded by an implicit solvent continuum. A boundary potential is added that takes into account the influence of the van der Waals and the electrostatic interactions [63-67]. 

Below we would like to state results [359,360] obtained on samples of bidistillated water (and exceptionally pure water obtained by means of ionic gum), which were partly degassed. These results correlate very well with the recent study on the two-component water model, the existence of a singularity temperature point, and the existence of thermodynamic anomalies of water. 

Simulations essentially extend possibility to study supercooled liquid water, as crystallization may be suppressed. However, there is no water model, which adequately reproduces phase diagram of water and its properties even in the thermodynamic region, where experimental data are available. In such situation, only comparative analysis of the results, obtained for various water models, can give information, relevant for the behaviour of real water in supercooled region. Additional complication appears due to the necessity to use sophisticated simulation methods, appropriate for the studies of the phase transitions, such as Monte Carlo simulations in the grand canonical or in the Gibbs ensemble (see Refs.7,16 for more details). Note, that simulations in the simple constant-volume or constant-pressure ensembles, widely used in the studies of supercooled water (see, for example Refs. 17,18), are not appropriate for the location of the phase transitions. 

Quantitative analysis of different reaction pathways for the transformation of aquated sulfur dioxide in atmospheric droplet systems has been a major objective of the research conducted in the principal investigator s laboratory for the last four years. Available thermodynamic and kinetic data for the aqueous-phase reactions of SO2 have been incorporated into a dynamic model of the chemistry of urban fog that has been developed by Jacob and Hoffmann (23) and Hoffmann and Calvert (39). The fog and cloud water models developed by them are hybrid kinetic and equilibrium models that consider the major chemical reactions likely to take place in atmospheric water droplets. Model results have verified that... 

Hess, B., van der Vegt, N.F.A. Hydration thermodynamic properties of amino acid analogues A comparison of biomolecular force fields and water models, J. Phys. Chem. B 2006,110,17616-26. 

Liquid water is an important medium in which most biomolecules perform their function. Pure liquid water may seem like a very simple system, where one may be able to identify the determining factors of its properties easily, but this is not always found to be the case. Table 2 gives examples of studying several thermodynamic properties of liquid water using a flexible SPC water model in a molecular dynamics simulation. This flexible water model was characterized by the following interaction potential ... 

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