Solvent molecules: explicit treatment

It was noted above that a continuum treatment of the solvent can be helpful, although representing certain solvent molecules explicitly may be necessary. The expressions for handling the free energy contributions in such hybrid models have been derived by Gilson et al.11... 

Ab initio MO calculations were carried out on the hydrolysis of CH3CI, with explicit consideration of up to 13 water solvent molecules. The treatments were at the HF/3-21G,HF/6-31G,HF/6-31 G orMP2/6-31 G levels. Forn > 3 three important stationary points were detected in the course of the reaction. Calculations for n = 13 at the HF/6-31 G level reproduced the experimental activation enthalpy and the secondary deuterium KIE. The proton transfer from the attacking water to the water cluster occurs after the transition state, in which O-C is 1.975 A and C-Cl is 2.500 A. 

One of the main drawbacks of continuum solvation methodologies is the lack of the treatment of exphcit solute-solvent interactions such as hydrogen bonding. Therefore, depending on the solute-solvent couple, some spectral features, strictly related to these issues, cannot be correctly reproduced. In order to overtake such hmitations, mixed discrete-continuum approaches have been developed [173-180]. In these approaches, the solute molecule is redefined so as to be composed of the target molecule plus a small number of solvent molecules explicitly interacting with the target. However, the precise definition and number of solvent molecules to be exphcitly included in order to reach physically consistent results is not obvious and depends not only on the system under study but also on... 

It is possible to go beyond the SASA/PB approximation and develop better approximations to current implicit solvent representations with sophisticated statistical mechanical models based on distribution functions or integral equations (see Section V.A). An alternative intermediate approach consists in including a small number of explicit solvent molecules near the solute while the influence of the remain bulk solvent molecules is taken into account implicitly (see Section V.B). On the other hand, in some cases it is necessary to use a treatment that is markedly simpler than SASA/PB to carry out extensive conformational searches. In such situations, it possible to use empirical models that describe the entire solvation free energy on the basis of the SASA (see Section V.C). An even simpler class of approximations consists in using infonnation-based potentials constructed to mimic and reproduce the statistical trends observed in macromolecular structures (see Section V.D). Although the microscopic basis of these approximations is not yet formally linked to a statistical mechanical formulation of implicit solvent, full SASA models and empirical information-based potentials may be very effective for particular problems. 

Summing up, small molecules are more sensihve to surface effects to influence their conformation than large biopolymers. Hence, we are convinced that conformational analyses in soluhon without explicit treatment of the solvent are arhficial and have to be taken with greatest caution. 

The weakest point of our approach is the treatment of the bulk solvent. The energies derived from an implicit solvent model like IPCM are mainly based on energy calculations on gas-phase structures and effects of explicit solvent molecules are not included. 

The last thirty years have seen a flowering of simulation techniques based on explicit treatments of solvent molecules (some references are given above). Such methods provide new insight into the reasons why continuum methods work or don t work. However they have not and never will replace continuum models. In fact, continuum models are sometimes so strikingly successful that hubris may be the most serious danger facing their practitioners. One of the goals of this present chapter will be to diffuse (but not entirely deflate ) any possible overconfidence. 

Another similar approach applies an explicit density-functional theory treatment to the solute molecules, while representing the contribution of the solvent molecules as an effective potential [105]. 

It can be seen from Table 26.1 that various methods used to model the effect of a solvent can be broadly classified into three types (1) those which treat the solvent as continuous medium, (2) those which describe the individual solvent molecules (discrete/explicit solvation), and (3) combinations of (1) and (2) treatments. The following section provides a brief introduction to continuum models. 

TvaroSka, KoS r and Hricovini in this book). One way to account for the effect of solvent on conforxnation might be to represent the molecule without environmental influences, and then explicitly include the solvent or other environmental molecules in the calculation. While avoiding built-in influences of environment is a satisfying concept, it is difficult to obtain by experiment parameters that lack those influences. Several methods have been used to study solvation effects, including continuum descriptions (24) and the explicit treatment of solvent molecules in Monte Carlo and molecular dynamics simulation. 

The solvent reaction field calculations involve several different aspects. We would like concentrate on the points required to make these models successful as well as on the facts that limit their accuracy. One of them is the shape of the molecular cavity, which can be modelled spherically or according to the real shape of the solute molecule. First, we discuss the papers in which spherical cavity models were applied. The studies utilizing the solute-shaped cavity models are collected the second group. Finally, the approaches employing explicit treatment of the first-solvation shell molecules combined with the continuum models are discussed. 

It should be recalled that the calculation of solvent effects on optical activity presents some unique problems. A chiral solute induces a chiral structure of the surrounding solvent, even when the individual solvent molecules are achiral. This means that the solvent participates in the observed optical effect not only by a modification of the geometric structure and electronic density of the solute, but that part of the observed OR or circular dichroism arises from the chiral solvent shell rather than from the solute molecule as such. This is not accounted for by the PCM, and can be rendered only by an explicit quantum mechanical treatment of at least the first solvent shell, or preferably by molecular dynamics simulations. 

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). 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

This hybrid solvation model surrounds the solute with a small number of explicit solvent molecules, and then embeds this cluster into the implicit dielectric field. Local effects are addressed by the full quantum mechanical treatment of the interaction between the solute and the few explicit solvent molecules. Long-range effects are included through the interaction of the cluster with the dielectric field. A decision is still needed as to how many explicit solvent molecules should be included within the cluster, recognizing that each additional solvent molecule increases the size of the calculation and expands the configurational space that must be explored. 

It does not appear that any attempt has been made to couple this BKO model to a means by which to calculate the CDS components of solvation, and this limits the model s accuracy, especially for solvents like water, where the CDS terms are not expected to be trivial. For water as solvent, studies have appeared that surround the solute with some small to moderate number of explicit solvent molecules, with the resulting supermolecule treated as interacting with the surrounding continuum. 23,230 Although such a treatment has the virtue of probably making the calculation less sensitive to the now-large cavity radius, it suffers from the usual explicit-solvent drawbacks of the size of the system, the complexity of the hypersurface, and the need for statistical sampling. 

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