Discrete solvent models

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

From Table 3-9 one learns that the continuum-only results are only for water in reasonable agreement with experiment. In contrast, the discrete solvent model leads, even in this very limited version, to shifts that compare well with experiment. Notice also that going from water to MeCN and CCI4, the dispersion is of increasing importance MeCN has an appreciable dipole moment but is also more polarizable than water, especially along the CN triple bond, while for CCI4 the polarizability is the only parameter of importance. 

The fast component is clearly related to electronic polarization, Pfast = Pd, while the slow component, connected to nuclear motions of the solvent molecules, is often called the orientational polarization (Pslow = Pot), or inertial component (PsioW = Pin)- This simplified model has been developed and applied by many authors we shall recall here Marcus (see the papers already quoted), who first had the idea of using Psiow as a dynamical coordinate. For description of solvent dynamical coordinates in discrete solvent models see Warshel (1982) and other papers quoted in Section 9. 

This method deserves further comments. It is a method addressed to describe the main features of a chemical reaction in solution, not paying much attention to fine details, but aiming at simplicity and versatility. It introduces in the discrete solvent model several concepts of capital importance, used, until that time, only for reaction in vacuo or for reactions in solution described at the basic continuum level. 

This relatively well detailed description of Warshel s activity (many points have been omitted for the sake of brevity) should permit to get an appreciation of some basic features of the discrete solvent models leading to effective Hamiltonians. A partitioning of the molecular assembly under the form of a Hartree product, 5, is almost compulsory. The description of solvent molecules (and of the interactions they have with the solute) is reduced to simple terms. The description of the energetic properties of the... 

As remarked in the previous subsection, discrete solvent models require the use of statistical procedures to properly describe solvent effects. In exposing the evolution of Warshel s methodologies in Subsection 9.1 several times we indicated the use of computer simulations, and the devices introduced in the model to reduce the number of discrete components, which are objects of the simulation, and hence the computational times. 

Experimental reports on liquid-phase molecular dipole moments are scarce, because of the natural difficulty of a direct measurement. Theoretical reports can be found only for the pyridine-water clusters [67, 68]. Here, we investigate the solute polarization by the solvent that implies an increase in its dipole moment. This is obtained using continuum and discrete solvent models. The continuum approach uses the polarized continuum model [69] (PCM), while the discrete solvent model uses the solvent molecules treated as point charges only. The iterative polarization is... 

An extension of this approximation to the case of chemical reactions has been proposed by Warshel within the framework of discrete solvent models, and by Hynes and co-workers within the continuum ones. In a proton transfer reaction, the diabatic states are either taken to be the neutral and ionic forms of valence bond states for a hydrogen bonded complex or are replaced by hypothetical charge distributions in which the charges appropriate to the reactant or product... 

Wihlin P, Schimmelpfennig B, Wahlgren U, Grenthe I, VaUet V. On the combined use of discrete solvent models and continuum descriptions of solvent effects in ligand exchange reactions a case study of the uranyl(VI) aquo ion. Theor Chem Acc. 2009 124 377-384. 

Claverie P, J P Daudey, J Lmglet, B Pullman, D Piazzola and M J Huron 1978. Studies of Solvent Effects. I. Discrete, Continuum and Discrete-Continuum Models and Their Comparison for Some Simple Cases NH, CH3OH and substituted NH4. Journal of Physical Chemistry 82 405-418. 

The mixed solvent models, where the first solvation sphere is accounted for by including a number of solvent molecules, implicitly include the solute-solvent cavity/ dispersion terms, although the corresponding tenns between the solvent molecules and the continuum are usually neglected. Once discrete solvent molecules are included, however, the problem of configuration sampling arises. Nevertheless, in many cases the first solvation shell is by far the most important, and mixed models may yield substantially better results than pure continuum models, at the price of an increase in computational cost. 

Another method that has been applied by our group to the study of enzymatic reactions is the Effective Fragment Potential (EFP) method [19]. The EFP method (developed at Mark Gordon s group at Iowa State University) allows the explicit inclusion of environment effects in quantum chemical calculations. The solvent, which may consist of discrete solvent molecules, protein fragments or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which can include some... 

The discrete protonation states methods employing implicit solvent models in both MD and MC steps have significantly lower computational cost. Dlugosz and... 

Claverie, P. Daudey, J.P. Langlet, J. Pullman, B. Piazzola, D. Huron, M.J., Studies of solvent effects. 1. Discrete, continuum, and discrete-continuum models and their comparison for some simple cases NH4, CH3OH, and substituted NH4, J. Phys. Chem. 1978, 82, 405-418... 

Based on the discrete solvent approach, a perturbed hard fluid model was developed to study dissociation reactions [227], In this model, the solute-solvent interactions are... 

This volume of Modem Aspects covers a wide spread of topics presented in an authoritative, informative and instructive manner by some internationally renowned specialists. Professors Politzer and Dr. Murray provide a comprehensive description of the various theoretical treatments of solute-solvent interactions, including ion-solvent interactions. Both continuum and discrete molecular models for the solvent molecules are discussed, including Monte Carlo and molecular dynamics simulations. The advantages and drawbacks of the resulting models and computational approaches are discussed and the impressive progress made in predicting the properties of molecular and ionic solutions is surveyed. 

Table 7 compares free energies of hydration125 produced by the two types of solvent models that have been presented discrete molecular and continuum. The discrete molecular involved classical force field molecular dynamics (MD) and a free energy perturbation (FEP) technique whereby the solute molecule is annihilated to dummy atoms, so that absolute AGhydration are obtained the continuum were SCRF/PCM calculations, with Claverie-Pierotti Gcavilatlon and Floris-Tomasi Gvdw. The... 

Free Energies of Hydration Predicted by Discrete Molecular (MD/FEP) and Continuum (SCRF/PCM) Solvent Models, in kcal/mole.g... 

General Comments Discrete Molecular and Continuum Solvent Models... 

For ionic as for molecular solutes (Section III.3), some studies have applied the discrete molecular model to the solvent in the immediate environment of the solute, and treated the remainder as a continuum. This can in principle help to deal with the problem of inner-shell structure as well as that of long-range effects. Thus Straatsma and Berendsen used the Bom equation to correct simulation-obtained free energies of hydration for six monatomic ions.174 This helped in some instances but not in others. 

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