Cluster-continuum model

J. R. Pliego and J. M. Riveros, The cluster-continuum model for the calculation of the solvation free energy of ionic species, J. Phys. Chem. A, 105 (2001) 7241-7247. 

Equation (3.21) shows that the potential of the mean force is an effective potential energy surface created by the solute-solvent interaction. The PMF may be calculated by an explicit treatment of the entire solute-solvent system by molecular dynamics or Monte Carlo methods, or it may be calculated by an implicit treatment of the solvent, such as by a continuum model, which is the subject of this book. A third possibility (discussed at length in Section 3.3.3) is that some solvent molecules are explicit or discrete and others are implicit and represented as a continuous medium. Such a mixed discrete-continuum model may be considered as a special case of a continuum model in which the solute and explicit solvent molecules form a supermolecule or cluster that is embedded in a continuum. In this contribution we will emphasize continuum models (including cluster-continuum models). 

Pratt and co-workers have proposed a quasichemical theory [118-122] in which the solvent is partitioned into inner-shell and outer-shell domains with the outer shell treated by a continuum electrostatic method. The cluster-continuum model, mixed discrete-continuum models, and the quasichemical theory are essentially three different names for the same approach to the problem [123], The quasichemical theory, the cluster-continuum model, other mixed discrete-continuum approaches, and the use of geometry-dependent atomic surface tensions provide different ways to account for the fact that the solvent does not retain its bulk properties right up to the solute-solvent boundary. Experience has shown that deviations from bulk behavior are mainly localized in the first solvation shell. Although these first-solvation-shell effects are sometimes classified into cavitation energy, dispersion, hydrophobic effects, hydrogen bonding, repulsion, and so forth, they clearly must also include the fact that the local dielectric constant (to the extent that such a quantity may even be defined) of the solvent is different near the solute than in the bulk (or near a different kind of solute or near a different part of the same solute). Furthermore... 

In addition to SMx and the cluster-continuum model, other continuum models have also been used to study reactions in liquids, including the polarized continuum model [133-135] (PCM), the conductor-like screening model (COSMO [136] and COSMO-RS [137,138]), the generalized COSMO [139] (GCOSMO) model, conductorlike PCM [140] (CPCM), and isodensity PCM [141] (IPCM). 

Figure 3.11 Application of the cluster-continuum model for basic hydrolysis of the methyl formate.

Bryantsev, V.S., Diallo, M.S., Goddard, W.A. Calculation of solvation free energies of charged solutes using mixed cluster/continuum models. J. Phys. Chem. B 2008,112(32), 9709-19. 

Kelly, Cramer, and Truhlar used the cluster-continuum model in their study of aqueous acid dissociation constants [39]. They compared the correlation between experimental pK values and the calculated acid dissociation Gibbs free energies of anions with and without an additional explicit water molecule using SM6. Note that because ol the relation between pK and AG q as shown in equation 2.1, a plot of pK, versus AG should yield a slope of 1/2.303RT. or 1/RTlnaO). 

Westphal, E. Phego, J. R., Absolute Solvation Free Eneigy of Li+ and Na+ Ions in Dimethyl Sulfoxide Solution A Theoretical Ab Initio and Cluster-Continuum Model Study. J. Chem. Phys. 2005,123(7), 074508. 

Bryantsev, V., Ceilculation of Solvation Free Energies of Ii+ and O2 Ions and Neutral lithium-Oxygen Compounds in Acetonitrile Using Mixed Cluster/Continuum Models. Theor. Chem. Acc Theory, Computation, and Modeling (Theoretica ChimicaActa) 2012,131,1-11. 

To test the models against experimentally determined red for EC, TD cycles were used. The predicted red varied between -0.95 to +1.05 V vs. Li/LF [11, 37], depending on the model. Underestimated - negative or close to zero - were obtained for the smaller [Li(EC) ] (n=l-2) super-molecules, while the cluster-continuum models and the [Li(EC) ] ( =4) super-molecule with E,ea of 1.05 V and... 

Scheme 1 The cluster-continuum model employed to investigate the reductive decomposition of solvent. Sol solvent molecules X salt anions.

But, is a continuum representation of solvent always sufficient May we neglect specific solute-solvent interactions such as H-bonds And what about reactions in which the solvent plays the role of a reactant Furthermore, do species in solution interact, e.g., a charged catalyst with its counterion, and how would this affect the catalyst s reactivity To address these and similar questions, we first have to extend the model systems considered to include an explicit representation of solvent and of those molecular species which may have an impact on reactivity. A first step in this direction is the use of cluster-continuum models in which a reduced number of explicit solvent molecules are introduced in the model. This approach has been successfully applied in computational studies of the organometallic reactivity [12-14], yet it suffers from some limitations [15]. How many solvent molecules should be explicitly included Is the first solvation sphere enough In order to mimic bulk conditicHis, models have to include enough solvent molecules to fully solvate the solute. These models, which are built to reproduce experimental densities, are generally treated as periodically repeating units in order to remove the explicit/ continuum (or vacuum) boundary. 

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