Solvent models, cluster continuum

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 interesting combined use of discrete molecular and continuum techniques was demonstrated by Floris et al.181,182 They used the PCM to develop effective pair potentials and then applied these to molecular dynamics simulations of metal ion hydration. Another approach to such systems is to do an ab initio cluster calculation for the first hydration shell, which would typically involve four to eight water molecules, and then to depict the remainder of the solvent as a continuum. This was done by Sanchez Marcos et al. for a group of five cations 183 the continuum model was that developed by Rivail, Rinaldi et al.14,108-112 (Section III.2.ii). Their results are compared in Table 14 with those of Floris et al.,139 who used a similar procedure but PCM-based. In... 

COSMO models [27-30] were compared with the SM approach [22] by Klamt [43] and by Cramer and Truhlar [44]. A very recent paper by Klamt and coworkers [45] shows that improved calculated pKa values are obtained for the limited domain of strong to moderately weak acids by a cluster-continuum method in which the acid and conjugate base are each associated with one or a few solvent molecules and this cluster is then continuum-calculated with COSMO-RS. The authors point out, however, that for the calculation of pKa a consistent and generally applicable method is still lacking . This paper clarifies the problem raised in [41]. The matter is under study.1... 

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... 

Table 1 Mean unsigned errors in absolute aqueous solvation free energies of ions and ion-water clusters, with a single water molecule, for various continuum solvent models [12,25]...

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

Mean Unsigned Errors in Absolute Aqueous Solvation Gibbs Free Energies of Ions and Ion-Water Clusters, with a Single Water Molecule, for Various Continuum Solvent Models... 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

Jellium, and the other continuum descriptions of the solid, have the problem of exactly defining the boundary surface. This is the analog of the problem of the definition of the cavity boundary for solutes in bulk solvents, occurring in continuum solvation methods (see Section 8.7.3). The only difference is that there are more experimental data for solutes than for liquid/solid surfaces to have hints about the most convenient modeling. The few accurate ab-initio calculations on liquid/metal systems are of little help, because in order to reach an acceptable accuracy, one is compelled to reduce the solid to a small cluster, too small to describe effects with a large length scale. 

We believe that we are at the stage where the models used and methods applied to solvent reduction are so elaborate, and the computational resources so vast, that any further development should be directed into converging towards a preferred DFT functional, a preferred cluster size to model a surface, and choosing a cluster-continuum approach for a selected type of super-molecule. Thus with some kind of standardization within the field, chosen based on careful comparisons with... 

That hydration of the carbonyl group is a concerted process has been challenged by detailed calculations using a variety of basis sets and a cluster continuum solvent model the stepwise route consistently emerged ca 8 kcal moP lower than the concerted. ... 

The cluster-continuum moder iUuslrated in scheme 1 was used to simulate the most common electrolytes of LIBs. The supra-molecular cluster applied to the inner ring (scheme 1) incorporates the mutual effect between salt and solvent molecules by including the first solvation shell of the salt. Due to the minor effect that the salt anion XT has on the reductive behavior of solvent molecules coordinated with Li, XT and the surrounding solvent molecules are not discussed in the current chapter. The bulk solvent effect in the second ring of scheme 1 is treated by polarized continuum models, such as PCM, conductor-like PCM (CPCM), isodensity PCM (IPCM), and self-consistent isodensity PCM (SCl-PCM), which were developed on the basis of the Onsager reaction field theory and are recognized to provide reliable results for systems without specific interactions such as hydrogen bond. 

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. 

In a general theory of solutions, McMillan and Mayer demonstrated the formal equivalence between the pressure of a gas and the osmotic pressure of a solution. Hence the ratio of the osmotic pressure O of a dilute solution to the concentration (number density) p of the solute can be expanded in a power series in p and the coefficients of the series can be expressed, as in the theory of a real gas, in terms of cluster integrals determined by intermolecular potential energy functions. The only difference is, as already mentioned, that in the solution these potentials are effective potentials of average force, which include implicitly the effects of the solvent, modelled as a continuum. 

The two avenues above recalled, namely ab-initio computations on clusters and Molecular Dynamics on one hand and continuum model on the other, are somewhat bridged by those techniques where the solvent is included in the hamiltonian at the electrostatic level with a discrete representation [13,17], It is important to stress that quantum-mechanical computations imply a temperature of zero K, whereas Molecular Dynamics computations do include temperature. As it is well known, this inclusion is of paramount importance and allows also the consideration of entropic effects and thus free-energy, essential parameters in any reaction. 

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