This year signs a landmark in the history of the molecular dynamics (MD) simulation method. Half a century ago 1971, Aneesur Rhaman and Frank H. Stillinger [1] published a pioneering work on the MD simulation of liquid water in the Journal of Chemical Physics. The journal received the article on May the 6th, 1971, and accepted it in October. Just seven years before (1964), the physicist A. Rahman (24 August 1927 – 6 June 1987) pioneered the computational method of MD when he published the first MD simulation study of liquid Argon [2]. The 1971 article is also the first MD study of a molecule in a condensed phase. It signed an important milestones water models are the most studied and used molecular models in MD simulations.

However, despite its structural simplicity, after 50 years of intense study, a perfect model for MD simulation is not yet available. By a perfect model, I mean one capable of computationally conveniently reproducing all the properties of water molecules in the range of possible applications. A water model needs to balance its computational simplicity required to keep computational costs for the simulations of large macromolecules in solution limited, and the accuracy to reproduce the physical chemistry properties accurately. For the most used but still 40-year-old models, this compromise was the equivalent of the inconveniently short blanket: pulling on one side would fit some properties but leave others loose. However, the continuous availability of inexpensive computer power and the advancements in simulation algorithms have allowed for significant progress in developing more accurate and efficient water models. In fact, several excellent models have been proposed since the R&S publication that can reproduce very well properties at 298 K or in a limited range of temperatures. In an updated but comprehensive article written 30 years later in the R&S paper, Guillot reported more than 100 proposed classic models for MD or Monte Carlo simulations published up to then [3]. Nineteen years after the publication of Guillot’s review, new and more sophisticated models have been proposed; nevertheless, the most used ones continue to bring the legacy of the R&S model.

In the late 1970s and early 1980s, the first molecular dynamics simulations of water were conducted using simplified models. These models represented water molecules as spheres interacting via pairwise Lennard-Jones potentials, capturing the intermolecular forces between the molecules. These developments in modeling water from molecular dynamics simulations have contributed significantly to our understanding of water’s structure, thermodynamics, and dynamics at the molecular level. They have provided insights into a wide range of phenomena, including solvation, hydrophobic interactions, phase transitions, and biomolecular interactions involving water molecules. In the following list, there is a summary of commonly used models for simulating water in molecular dynamics simulations.

1. The SPC (Simple Point Charge) and SPC/E (Extended) developed by Prof. HJC Berendsen and collaborators a the University of Groningen (The Netherlands) [4] are widely used water models in molecular dynamics simulations. These models consider three atoms per water molecule but have different parameters for the Lennard-Jones potential and partial charges. The SPC/E model, in particular, has successfully reproduced various water properties, including the density and structure of liquid water.
   • Lennard-Jones Potential: The SPC models also utilize the Lennard-Jones potential to describe the van der Waals interactions between water molecules. The parameters are adjusted to reproduce various properties of water, including the radial distribution function.
   • Charges: The SPC models assign partial charges to the oxygen and hydrogen atoms in a manner that reproduces the dipole moment and electric field properties of water. These charges are carefully chosen to ensure an accurate representation of the water molecule.
2. The TIP3P (Transferable Intermolecular Potential 3 Points) model developed by Prof. W. Jorgensen and collaborators at Yale University (USA) [4] is another widely-used water model. As the SPC model, it represents water molecules as three atoms: two hydrogen atoms and one oxygen atom. The oxygen atom has a partial negative charge, while each hydrogen atom has a partial positive charge. The model also includes harmonic bond stretching and angle bending terms to describe the covalent bonds and bond angles within water molecules.
   • Bond Stretching: The TIP3P model assumes harmonic bond stretching between oxygen and hydrogen atoms. The equilibrium bond length is typically set to 0.9572 Å, and the force constant represents the stiffness of the bond.
   • Angle Bending: The TIP3P model employs harmonic angle bending terms to describe the HOH angle. The equilibrium angle is typically set to 104.52 degrees, corresponding to the tetrahedral geometry of water.
   • Lennard-Jones Potential: The model uses the Lennard-Jones potential to describe the van der Waals interactions between water molecules. The parameters for the potential are chosen to reproduce the experimentally observed properties of water, such as the density and vaporization enthalpy.
   • Charges: The oxygen atom in the TIP3P model carries a partial negative charge, while each hydrogen atom has a partial positive charge. The charges are usually chosen to reproduce the dipole moment and electric field properties of water.
3. The TIP4P model extends the TIP3P model by explicitly including a virtual site, referred to as the “dummy” or “massless” site, in addition to the three atoms. This dummy site is located along the HOH angle bisector and represents the lone pair of electrons on the oxygen atom. The TIP4P model improves the description of water properties, particularly the hydrogen bonding behavior.
   • Dummy Sites: The TIP4P model introduces a virtual site, referred to as the dummy or massless site, to represent the lone pair of electrons on the oxygen atom. This allows for a more accurate representation of the hydrogen bonding behavior in water.
   • Electrostatics: The TIP4P model includes a positive charge located on the dummy site, which balances the negative charge on the oxygen atom. This ensures that the model reproduces the correct dipole moment of water.
4. Flexible Models: While rigid water models, such as TIP3P and SPC/E, assume fixed bond lengths and bond angles, flexible models introduce additional degrees of freedom by allowing parameter variations. Flexible water models, such as TIP5P and TIP4P/2005, consider the anharmonicity of bond stretching and angle bending, providing a more accurate description of water’s vibrational behavior.
   • Anharmonicity: Flexible water models, such as TIP4P/2005 and TIP5P, introduce anharmonic terms to account for the deviations from the harmonic behavior of bond stretching and angle bending. This allows for a more accurate representation of water’s vibrational properties.
   • Improved Parameters: Flexible models often incorporate refined parameters to better reproduce experimental data, such as vibrational spectra and thermodynamic properties, beyond what can be achieved with rigid models.
5. Polarizable Models: Classical force fields typically assume fixed atomic charges on water molecules. However, water is a polar molecule whose charge distribution changes in response to its local environment. Polarizable models have been developed to capture the dynamic nature of water’s charge distribution. Polarizable force fields, such as the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field, allow the partial charges on water molecules to vary with the atomic positions and local electric fields.
   • Drude Oscillators: Polarizable models, such as the AMOEBA force field, employ Drude oscillators to represent the fluctuating charge distributions in water. A Drude oscillator consists of a heavy atom (representing the oxygen atom) and a lighter particle (representing the hydrogen atom) connected by a harmonic bond.
   • Atomic Multipole Moments: Polarizable models use atomic multipole moments, including dipoles, quadrupoles, and higher-order moments, to describe the charge distribution of water molecules. The moments are allowed to vary with the positions of the atoms, capturing the dynamic nature of water’s charge distribution.

These model are the most communely used water models used in molecular dynamics simulations an din particular in simulation of biomolecular systems. The choice of model depends on the research question and the desired level of accuracy required for the simulation.

REFERENCES

1. Rahman, A. and Stillinger, F.H., 1971. Molecular dynamics study of liquid water. The Journal of Chemical Physics, 55(7), pp.3336-3359.
2. A. Rahman (1964). “Correlations in the Motion of Atoms in Liquid Argon”. Physical Review. 136: A405-A411.
3. Guillot, B., 2002. A reappraisal of what we have learnt during three decades of computer simulations on water. Journal of molecular liquids, 101(1-3), pp.219-260.
4. H. J. C. Berendsen, J. R. Grigera and T. P. Straatsma, The missing term in effective pair potentials, Journal of Physical Chemistry 91 (1987) 6269-6271.
5. Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W. and Klein, M.L., 1983. Comparison of simple potential functions for simulating liquid water. The Journal of chemical physics, 79(2), pp.926-935.