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The magic of water: How to simulate the mystery of water with computational chemistry?
Water, as one of the most important substances on earth, its unique physical and chemical properties are essential to the existence of life. Since the rise of computational chemistry, scientists have been working to use mathematical models to simulate the behavior of water. These models not only predict the physical properties of water, but also provide insights into how water reacts in different environments and its role in living organisms.
"The properties of water are closely related to its molecular structure, which can be simulated and predicted using computational chemistry methods."
Water models in computational chemistry are mainly used to simulate water molecule aggregates, liquid water and aqueous solutions. These models are based on quantum mechanics, molecular mechanics, experimental data, or a combination of these methods. To mimic the specific properties of water molecules, researchers have developed several types of models, which can generally be categorized in three ways: (i) the number of interaction points, called “sites”, (ii) the rigid or flexible, and (iii) whether the model includes polarization effects.
In the simulation of water, a common approach is to use an explicit solvent model, that is, a model based on specific molecules. As an alternative to these explicit models, implicit solvent models are available, which use a continuum model to treat the behavior of water. An example of this area includes the COSMO solvent model or the polarizable continuum model (PCM), or even some mixed solvent models.
Simple water model
The rigid model is considered the simplest model for water and relies on non-bonded interactions. In these models, bond interactions are handled implicitly via global constraints. Electrostatic interactions are modeled based on Coulomb's law, while repulsive and dispersion forces are described using Lennard-Jones potentials. These potential models, such as TIP3P (Transferable Three-Point Molecular Potential) and TIP4P, are represented as:
E = ∑(kC * qi * qj / rij) + (A / rOO^12) - (B / rOO^6)
Where kC is the electrostatic constant, qi and qj are the partial charges relative to the electron charge, and rij is the distance between the two atoms. In many water models, the Lennard-Jones term applies only to interactions between oxygen atoms. The geometrical parameters of various water models, such as OH distance and HOH angle, vary according to the model.
Two- and three-dimensional models
The two-site model is based on the familiar three-site SPC model and is able to predict the dielectric properties of water using site-renormalized molecular fluid theory. The three-dimensional model corresponds to the three atoms of the water molecule, with each site having a charge. The three-dimensional model is computationally efficient and is widely used in many molecular dynamics simulations.“The commonly used three-dimensional models, such as TIP3P, perform well in calculating specific heat performance.”
For example, the SPC/E model adds a polarization correction to the potential energy function, making the resulting water density and diffusion constant better than the SPC model. The TIP3P model is widely used in the CHARMM force field, and slight modifications are made to the original model to make it more suitable for the simulation of biological molecules.
Flexible vs. Rigid ModelsThe flexible SPC water model is a reparameterized three-dimensional water model. Unlike the rigid SPC model, the flexible model can correctly describe the density and dielectric constant of water in molecular dynamics simulations. This model is implemented in several computational programs, such as MDynaMix and Abalone.
Higher-order water models
The four-site model improves the charge distribution of water molecules by adding a dummy atom near the oxygen atom of the three-site model. The earliest such model can be traced back to the Bernal–Fowler model in 1933. Although the model was historically important, it did not reproduce the key properties of water very well.
The TIP4P model is widely used in computational chemistry software and plays a key role in the simulation of biomolecular systems, while new water models such as the OPC model can more accurately describe the electrical properties of water.
The development of the five- and six-position models
Although the five-bit model has a high computational cost, it has gradually made progress in recent years with the introduction of the TIP5P model. The five-bit model better reproduces the geometry of the water dimer and is able to accurately capture the experimental data. The six-bit model incorporates all the features of past models into the data and is designed specifically for studying water and ice systems.
"In computational chemistry, the simulation of water is not only a technical challenge, but also a key to understanding the workings of life."
Computational costs and future prospects
The computational cost of the water model increases with the number of sites. For molecular dynamics simulations, as the number of sites increases, the number of interatomic distances that need to be calculated also increases. However, the development of these models is not just a mathematical narrative, but a microcosm of how water actually behaves in nature. As technology advances, will we be able to find models that reveal more mysteries of water in the near future?
