Solvent model

Implicit solvents or continuum solvents, are models in which one accepts the assumption that implicit solvent molecules can be replaced by a homogeneously polarizable medium as long as this medium, to a good approximation, gives equivalent properties. : \hat{H}^\mathrm{total}(r_\mathrm{m}) = \hat{H}^\mathrm{molecule} (r_\mathrm{m}) + \hat{V}^\text{molecule + solvent} (r_\mathrm{m}) Note here that the implicit nature of the solvent is shown mathematically in the equation above, as the equation is only dependent on solute molecule coordinates (r_\mathrm{m}) . The second right hand term \hat{V}^\text{molecules + solvent} is composed of interaction operators. These interaction operators calculate the systems responses as a result of going from a gaseous infinitely separated system to one in a continuum solution. If one is therefore modelling a reaction this process is akin to modelling the reaction in the gas phase and providing a perturbation to the Hamiltonian in this reaction. Several standard models exist and have all been used successfully in a number of situations. The Polarizable continuum model (PCM) is a commonly used implicit model and has seeded the birth of several variants. The COSMO solvation model is another popular implicit solvation model. This model uses the scaled conductor boundary condition, which is a fast and robust approximation to the exact dielectric equations and reduces the outlying charge errors as compared to PCM. The approximations lead to a root mean square deviation in the order of 0.07 kcal/mol to the exact solutions. == Explicit models ==

Explicit solvent models treat explicitly (i.e. the coordinates and usually at least some of the molecular degrees of freedom are included) the solvent molecules. This is a more intuitively realistic picture in which there are direct, specific solvent interactions with a solute, in contrast to continuum models. These models generally occur in the application of molecular mechanics (MM) and dynamics (MD) or Monte Carlo (MC) simulations, although some quantum chemical calculations do use solvent clusters. Molecular dynamics simulations allow scientists to study the time evolution of a chemical system in discrete time intervals. These simulations often utilize molecular mechanics force fields which are generally empirical, parametrized functions which can efficiently calculate the properties and motions of large systems. and the simple point charge model (SPC) of water have been used extensively. A typical model of this kind uses a fixed number of sites (often three for water), on each site is placed a parametrized point charge and repulsion and dispersion parameter. These models are commonly geometrically constrained with aspects of the geometry fixed such as the bond length or angles. Advancements around 2010 onwards in explicit solvent modelling see the use of a new generation of polarizable force fields, which are currently being created. These force fields are able to account for changes in the molecular charge distribution. A number of these force fields are being developed to utilise multipole moments, as opposed to point charges, given that multipole moments can reflect the charge anisotropy of the molecules. One such method is the Atomic Multipole Optimised Energetics for Biomolecular Applications (AMOEBA) force field. This method has been used to study the solvation dynamics of ions. and the Quantum Chemical Topology Force Field (QCTFF). Polarizable water models are also being produced. The so-called charge on spring (COS) model gives water models with the ability to polarize due to one of the interaction sites being flexible (on spring). == Hybrid models ==

Hybrid models, as then name suggests, are in the middle between explicit and implicit models. Hybrid models can usually be considered closer to one or other implicit or explicit. Mixed quantum mechanics and molecular mechanics models, (QM/MM) schemes, can be thought of in this context. QM/MM methods here are closer to explicit models. One can imagine having a QM core treatment containing the solute and may be a small number of explicit solvent molecules. The second layer could then comprise MM water molecules, with a final third layer of implicit solvent representing the bulk. The Reference Interaction Site Model (RISM) can be thought of being closer to implicit solvent representations. RISM allows the solvent density to fluctuate in a local environment, achieving a description of the solvent shell behaviour. RISM, a classical statistical mechanics methodology, has it roots in the integral equation theory of liquids (IET). By statistically modeling of the solvent, an appreciation of the dynamics of the system can be acquired. This is more useful than a static model as the dynamics of the solvent can be important in some processes. The statistical modeling is done using radial distribution function (RDF). RDF are probabilistic functions which can represent the probability of locating solvent atoms/molecules in a specific area or at a specific distance from the reference point; generally taken as the solute molecule. As the probability of locating solvent atoms and molecules from the reference point can be determined in RISM theory, solvent shell structure can be directly derived. The molecular Ornstein-Zernike equation (MOZ) is the starting point for RISM calculations. :h(r) = c(r_{1,2}) + \int \mathrm{d}r_{3} \, c(r_{1,3}) \rho (r_{3}) h(r_{2,3}) Ornstein-Zernike equation with the assumption of spherical symmetry. ρ is the liquid density, r is the separating distance, h(r) is the total correlation function, c(r) is the direct correlation function. h(r) and c(r) are the solutions to the MOZ equations. In order to solve for h(r) and c(r), another equation must be introduced. This new equation is called a closure relation. The exact closure relation is unknown, due to the so-called bridge functions exact form being unclear, we, therefore, must introduce approximations. There are several valid approximations, the first was the HyperNetted Chain (HNC), which sets the unknown terms in the closure relation to zero. Although appearing crude the HNC has been generally quite successfully applied, although it shows slow convergence and divergent behaviour in some cases. A modern alternative closure relation has been suggested the Partially Linearised HyperNetted Chain (PLHNC) or Kovalenko Hirata closure. The PLHNC partially linearises the exponential function if it exceeds its cutoff value. This causes a much more reliable convergence of the equations. The COSMO-RS model is another hybrid model using the surface polarization charge density derived from continuum COSMO calculations to estimate the interaction energies with neighbored molecules. COSMO-RS is able to account for a major part of reorientation and strong directional interactions like hydrogen bonding within the first solvation shell. It yields thermodynamically consistent mixture thermodynamics and is often used in addition to UNIFAC in chemical engineering applications. == Applications to QSAR and QSPR ==

Quantitative structure–activity relationships/quantitative structure–property relationships (QSAR/QSPR), whilst unable to directly model the physical process occurring in a condensed solvent phase, can provide useful predictions of solvent and solvation properties and activities; such as the solubility of a solute. A regression model or statistical learning model is then applied to find a correlation between the descriptor(s) and the property of interest. Once trained on some known data these model can be applied to similar unknown data to make predictions. Typically the known data comes from experimental measurement, although there is no reason why similar methods can not be used to correlate descriptor(s) with theoretical or predicted values. It is currently debated whether if more accurate experimental data was used to train these models whether the prediction from such models would be more accurate. More recently the rise of deep learning has provided many methods to generate embedded representations of molecules. == References ==