In computational chemistry, a water model is used to simulate and thermodynamically calculate water clusters, liquid water, and aqueous solutions with explicit solvent, often using molecular dynamics or Monte Carlo methods. The models describe intermolecular forces between water molecules and are determined from quantum mechanics, molecular mechanics, experimental results, and these combinations. To imitate the specific nature of the intermolecular forces, many types of models have been developed. In general, these can be classified by the following three characteristics; (i) the number of interaction points or sites, (ii) whether the model is rigid or flexible, and (iii) whether the model includes polarization effects. An alternative to the explicit water models is to use an implicit solvation model, also termed a continuum model. Examples of this type of model include the COSMO solvation model, the polarizable continuum model (PCM) and hybrid solvation models.
Simple water models The rigid models are considered the simplest water models and rely on non-bonded interactions. In these models, bonding interactions are implicitly treated by holonomic constraints. The electrostatic interaction is modeled using Coulomb's law, and the dispersion and repulsion forces using the Lennard-Jones potential. The potential for models such as TIP3P (transferable intermolecular potential with 3 points) and TIP4P is represented by
E a b = ∑ i on a ∑ j on b k C q i q j r i j + A r OO 12 − B r OO 6 , {\displaystyle E_{ab}=\sum _{i}^{{\text{on }}a}\sum _{j}^{{\text{on }}b}{\frac {k_{C}q_{i}q_{j}}{r_{ij}}}+{\frac {A}{r_{\text{OO}}^{12}}}-{\frac {B}{r_{\text{OO}}^{6}}},}
where kC, the electrostatic constant, has a value of 332.1 Å·kcal/(mol·e²) in the units commonly used in molecular modeling; qi and qj are the partial charges relative to the charge of the electron; rij is the distance between two atoms or charged sites; and A and B are the Lennard-Jones parameters. The charged sites may be on the atoms or on dummy sites (such as lone pairs). In most water models, the Lennard-Jones term applies only to the interaction between the oxygen atoms. The figure below shows the general shape of the 3- to 6-site water models. The exact geometric parameters (the OH distance and the HOH angle) vary depending on the model.
2-site A 2-site model of water based on the familiar three-site SPC model (see below) has been shown to predict the dielectric properties of water using site-renormalized molecular fluid theory.
3-site Three-site models have three interaction points corresponding to the three atoms of the water molecule. Each site has a point charge, and the site corresponding to the oxygen atom also has the Lennard-Jones parameters. Since 3-site models achieve a high computational efficiency, these are widely used for many applications of molecular dynamics simulations. Most of the models use a rigid geometry matching that of actual water molecules. An exception is the SPC model, which assumes an ideal tetrahedral shape (HOH angle of 109.47°) instead of the observed angle of 104.5°. The table below lists the parameters for some 3-site models.
The SPC/E model adds an average polarization correction to the potential energy function:
E pol = 1 2 ∑ i ( μ − μ 0 ) 2 α i , {\displaystyle E_{\text{pol}}={\frac {1}{2}}\sum _{i}{\frac {(\mu -\mu ^{0})^{2}}{\alpha _{i}}},}
where μ is the electric dipole moment of the effectively polarized water molecule (2.35 D for the SPC/E model), μ0 is the dipole moment of an isolated water molecule (1.85 D from experiment), and αi is an isotropic polarizability constant, with a value of 1.608×10−40 F·m2. Since the charges in the model are constant, this correction just results in adding 1.25 kcal/mol (5.22 kJ/mol) to the total energy. The SPC/E model results in a better density and diffusion constant than the SPC model. The TIP3P model implemented in the CHARMM force field is a slightly modified version of the original. The difference lies in the Lennard-Jones parameters: unlike TIP3P, the CHARMM version of the model places Lennard-Jones parameters on the hydrogen atoms too, in addition to the one on oxygen. The charges are not modified. Three-site model (TIP3P) has better performance in calculating specific heats.
Flexible SPC water model
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