Molecular model liquid water

The most important molecular interactions of all are those that take place in liquid water. For many years, chemists have worked to model liquid water, using molecular dynamics and Monte Carlo simulations. Until relatively recently, however, all such work was done using effective potentials [4T], designed to reproduce the condensed-phase properties but with no serious claim to represent the tme interactions between a pair of water molecules. 

Not unexpectedly, the widespread and continuing interest in water has prompted many molecular models for water (Perram and Levine, 1974 Ives and Lemon, 1968 Frank, 1973). We will not review all the attempts at formulating a structure for water. This brief account will reflect the opinions of the author and recognize that in chemists terms we are interested in providing a basis for a discussion of the properties of aqueous solutions. The overiding difficulty is that an account of water structure also reflects the general problems involved in describing the liquid state (Powles, 1974). 

F. H. Stillinger, Effective pair interactions in liquid water. J. Phys. Chem., 74 (1970), 3677 F. H. Stillinger, Theory and molecular models for water. Adv. Chem. Phys., 31 (1975), 1. 

F.H. Stillinger, Theory and Molecular Models for Water. In Advances in Chemical Physics Non-Simple Liquids, Volume 31, eds I. Prigogine and S. A. Riee (John Wiley Sons, Inc., Hoboken, NJ, USA, 1975). 

So far, the multipole approach has been rather limited for modeling liquid water. For rigid, nonpolarizable models, the SSDQOl discussed here uses multipoles up to the octupole that have been optimized for various properties of liquid water at STP [29]. In addition, SCME, a polarizable molecular multipole model using multipoles up to the hexadecapole, has recently been developed [49]. 

In this section, we derive some general statistical mechanical expressions for the thermodynamic quantities of solvation which are independent of any assumptions about the model. We shall later examine special cases of these relations for either a molecular model for water (in terms of a model pair potential) or for a specific mixture-model view of liquid water. 

A. Wallqvist and P.-O. Astrand, /. Chem. Phys., 102, 6559 (1995). Liquid Densities and Structural Properties of Molecular Models of Water. 

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. 

TIk experimentally determined dipole moment of a water molecule in the gas phase is 1.85 D. The dipole moment of an individual water molecule calculated with any of thv se simple models is significantly higher for example, the SPC dipole moment is 2.27 D and that for TIP4P is 2.18 D. These values are much closer to the effective dipole moment of liquid water, which is approximately 2.6 D. These models are thus all effective pairwise models. The simple water models are usually parametrised by calculating various pmperties using molecular dynamics or Monte Carlo simulations and then modifying the... 

TIte NCC water model. (After Corongiu G 1992. Molecular Dynamics Simulation fir Liquid Water Using risable and Flexible Potential. International Journal of Quantum Chemistry 42 1209-1235.)... 

One important class of integral equation theories is based on the reference interaction site model (RISM) proposed by Chandler [77]. These RISM theories have been used to smdy the confonnation of small peptides in liquid water [78-80]. However, the approach is not appropriate for large molecular solutes such as proteins and nucleic acids. Because RISM is based on a reduction to site-site, solute-solvent radially symmetrical distribution functions, there is a loss of infonnation about the tliree-dimensional spatial organization of the solvent density around a macromolecular solute of irregular shape. To circumvent this limitation, extensions of RISM-like theories for tliree-dimensional space (3d-RISM) have been proposed [81,82],... 

Halley JW, Rustad JR, Rahman A (1993) A polarizable, dissociating molecular-dynamics model for liquid water. J Chem Phys 98(5) 4110-4119... 

A recent breakthrough in molecular theory of hydrophobic effects was achieved by modeling the distribution of occupancy probabilities, the pn depicted in Figure 4, rather than applying a more difficult, direct theory of po for cavity statistics for liquid water (Pohorille and Pratt, 1990). This information theory (IT) approach (Hummer et al., 1996) focuses on the set of probabilities pn of finding n water centers inside the observation volume, with po being just one of the probabilities. Accurate estimates of the pn, and po in particular, are obtained using experimentally available information as constraints on the pn. The moments of the fluctuations in the number of water centers within the observation volume provide such constraints. 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

Diffusion constants are enhanced with the approximate inclusion of quantum effects. Changes in the ratio of diffusion constants for water and D2O with decreasing temperature are accurately reproduced with the QFF1 model. This ratio computed with the QFF1 model agrees well with the centroid molecular dynamics result at room temperature. Fully quantum path integral dynamical simulations of diffusion in liquid water are not presently possible. 

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