Solvent models

In computational chemistry, a solvent model is a computational method that accounts for the behavior of solvated condensed phases. Solvent models enable simulations and thermodynamic calculations applicable to reactions and processes which take place in solution. These include biological, chemical and environmental processes. Such calculations can lead to new predictions about the physical processes occurring by improved understanding. In computational chemistry, a solvent model is a computational method that accounts for the behavior of solvated condensed phases. Solvent models enable simulations and thermodynamic calculations applicable to reactions and processes which take place in solution. These include biological, chemical and environmental processes. Such calculations can lead to new predictions about the physical processes occurring by improved understanding. Solvent models have been extensively tested and reviewed in scientific literature. The various models can generally be divided into two classes, explicit and implicit models, all of which have their own advantages and disadvantages. Implicit models are generally computationally efficient and can provide a reasonable description of the solvent behavior, but fail to account for the local fluctuations in solvent density around a solute molecule. The density fluctuation behavior is due to solvent ordering around a solute and is particularly prevalent when one is considering water as the solvent. Explicit models are often less computationally economical, but can provide a physical spatially resolved description of the solvent. However, many of these explicit models are computationally demanding and can fail to reproduce some experimental results, often due to certain fitting methods and parametrization. Hybrid methodologies are another option. These methods incorporate aspects of implicit and explicit aiming to minimize computational cost while retaining at least some spatial resolution of the solvent. These methods can require more experience to use them correctly and often contain post-calculation correction terms. 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. No explicit solvent molecules are present and so explicit solvent coordinates are not given. Continuum models consider thermally averaged and usually isotropic solvents, which is why only a small number of parameters can be used to represent the solvent with reasonable accuracy in many situations. The main parameter is the dielectric constant (ε), this is often supplemented with further parameters, for example solvent surface tension. The dielectric constant is the value responsible for defining the degree of polarizability of the solvent. Generally speaking, for implicit solvents, a calculation proceeds by encapsulating a solute in a tiled cavity (See the figure below). The cavity containing the solute is embedded in homogeneously polarizable continuum describing the solvent. The solute's charge distribution meets the continuous dielectric field at the surface of the cavity and polarizes the surrounding medium, which causes a change in the polarization on the solute. This defines the reaction potential, a response to the change in polarization. This recursive reaction potential is then iterated to self-consistency. Continuum models have widespread use, including use in force field methods and quantum chemical situations. In quantum chemistry, where charge distributions come from ab initio methods (Hartree-Fock (HF), Post-HF and density functional theory (DFT)) the implicit solvent models represent the solvent as a perturbation to the solute Hamiltonian. In general, mathematically, these approaches can be thought of in the following way: 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 m ) {displaystyle (r_{mathrm {m} })} . The second right hand term V ^ molecules + solvent {displaystyle {hat {V}}^{ ext{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. Top: Four interaction operators generally considered in the continuum solvation models. Bottom: Five contributing Gibbs energy terms from continuum solvation models. The interaction operators have a clear meaning and are physically well defined. 1st - cavity creation; a term accounting for the energy spent to build a cavity in the solvent of suitable size and shape as to house the solute. Physically, this is energy cost of compressing the solvents structure when creating a void in the solvent. 2nd term - electrostatic energy; This term deals with the polarization of the solute and solvent. 3rd term - an approximation for the quantum mechanical exchange repulsion; given the implicit solvent this term can only be approximated against high level theoretical calculations. 4th term - quantum mechanical dispersion energy; can be approximated using an averaging procedure for the solvent charge distribution. These models can make useful contributions when the solvent being modelled can be modelled by a single function i.e. it is not varying significantly from the bulk. They can also be a useful way to include approximate solvent effects where the solvent is not an active constituent in the reaction or process. Additionally, if computer resources are limited, considerable computational resources can be saved by evoking the implicit solvent approximation instead of explicit solvent molecules. Implicit solvent models have been applied to model the solvent in computational investigations of reactions and to predict hydration Gibbs energy (ΔhydG).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 model is based on the Poisson-Boltzmann equation, which is an expansion of the original Poisson's equation. Solvation Models (SMx) and the Solvation Model based on Density (SMD) have also seen wide spread use. SMx models (where x is an alphanumeric label to show the version) are based on the generalized Born equation. This is an approximation of Poisson's equation suitable for arbitrary cavity shapes. The SMD model solves the Poisson-Boltzmann equation analogously to PCM, but does so using a set of specifically parametrised radii which construct the cavity. 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 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 system., Parametrization is often to a higher level theory or experimental data. MC simulations allow one to explore the potential energy surface of a system by perturbing the system and calculating the energy after the perturbation. Prior criteria are defined to aid the algorithm in deciding whether to accept the newly perturbed system or not. In general, force field methods are based on similar energy evaluation functionals which usually contain terms representing the bond stretching, angle bending, torsions and terms for repulsion and dispersion, such as the Buckingham potential or Lennard-Jones potential. Commonly used solvents, such as water, often have idealized models generated. These idealized models allow one to reduce the degrees of freedom which are to be evaluated in the energy calculation without a significant loss in the overall accuracy; although this can lead certain models becoming useful only in specific circumstances. Models such as TIPXP (where X is an integer suggesting the number of sites used for energy evaluation) 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.