Solvation shell, first

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

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. 

The analysis of recent measurements of the density dependence of has shown, however, that considering only the variation of solvent structure in the vicinity of the atom pair as a fiinction of density is entirely sufficient to understand tire observed changes in with pressure and also with size of the solvent molecules [38]. Assuming that iodine atoms colliding with a solvent molecule of the first solvation shell under an angle a less than (the value of is solvent dependent and has to be found by simulations) are reflected back onto each other in the solvent cage, is given by... 

Chambers C C, G D Hawkins, C J Cramer and D G Tmlilar 1996. Model for Aqueous Solvation Ba sed on Class IC Atomic Charges and First Solvation Shell Effects. Journal of Physical Chemistry 100 16385-16398. 

The energy of solvation can be further broken down into terms that are a function of the bulk solvent and terms that are specifically associated with the first solvation shell. The bulk solvent contribution is primarily the result of dielectric shielding of electrostatic charge interactions. In the simplest form, this can be included in electrostatic interactions by including a dielectric constant k, as in the following Coulombic interaction equation ... 

Modem understanding of the hydrophobic effect attributes it primarily to a decrease in the number of hydrogen bonds that can be achieved by the water molecules when they are near a nonpolar surface. This view is confirmed by computer simulations of nonpolar solutes in water [15]. To a first approximation, the magnimde of the free energy associated with the nonpolar contribution can thus be considered to be proportional to the number of solvent molecules in the first solvation shell. This idea leads to a convenient and attractive approximation that is used extensively in biophysical applications [9,16-18]. It consists in assuming that the nonpolar free energy contribution is directly related to the SASA [9],... 

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. 

The substituent effects on the H-bonding in an adenine-uracil (A-U) base pair were studied for a series of common functional groups [99JPC(A)8516]. Substitutions in the 5 position of uracil are of particular importance because they are located toward the major groove and can easily be introduced by several chemical methods. Based on DFT calculation with a basis set including diffuse functions, variations of about 1 kcal/mol were found for the two H-bonds. The solvent effects on three different Watson-Crick A-U base pairs (Scheme 100) have been modeled by seven water molecules creating the first solvation shell [98JPC(A)6167]. 

Thus the coefficient can be evaluated from and aY- The approximate value of p (= 9.4 X 10 molecules m ) is obtained from the density of bulk water by assuming that the thickness of the first solvation shell equals the diameter (0.28 nm) of a water molecule,... 

This indicates that the polarity of a medium is a long-range property that goes much further than the first solvation shell and therefore involves the two adjacent bulk media properties. This result is, however, valid for compounds the solvation of which is not determined by specific interactions with the first solvent shell, but rather by long-range forces like dipole interactions. The solvation of DEPNA was determined by molecular dynamics too and similar conclusions were drawn [82]. 

Contrary to earlier expectations (see Dorfman, 1965), Hentz and Kenney-Wallace (1972, 1974) failed to find any correlation between s and Emax. Actually, there is a better correlation of matrix polarity with the spectral shift from e(to e upon solvation and the time required to reach the equilibrium spectrum (Kevan, 1974). Furthermore, Hentz and Kenney-Wallace point out that emax is smaller f°r alcohols with branched alkyl groups, the spectrum being sensitive to the number, structure, and position of these groups relative to OH. Clearly, a steric effect is called for, and the authors claim that a successful theory must not rely too heavily on continuum interaction as appeared in the earlier theories ofjortner (1959,1964). Instead, the dominant interaction must be of short range, and probably the spectrum is determined by optimum configuration of dipoles within the first solvation shell. 

The actual evaluations of Edd, II, and EHH are complex. Note that for Edd, CKJ uses Buckingham s (1957) prescription for the number of dipoles in the first solvation shell and considers both the thermally averaged dipole moment and the induced moment. The polarization energy is obtained from Land and O Reilly (1967). 

The chemical shieldings were then recalculated in this same system using the QM/MM method [10], To this end, each molecule was considered individually. The water molecule of interest and its first solvation shell were treated quantum mechanically, whereas the surrounding water molecules were taken into account with an empirical force field representation (MM molecules). The first solvation shell was defined via a distance criterion on the oxygen-oxygen distance. As a threshold, the first minimum of the O-O pair correlation function was taken this occurs at 3.5 A [93]. All... 

For a water molecule with its first solvation shell only, chemical shielding differs considerably from the complete ab initio calculation. Although this discrepancy is not completely removed by the inclusion of the electrical field of the remaining molecules through the QM/MM approach, it is strongly reduced. 

The vertical excitation energies were calculated for different configurations of a QM/MM trajectory using the approximate ROKS [27] method as well as TDDFT. The effect of the size of the quantum region was tested systematically by including (i) only the solute in the quantum region or (ii) the solute and its first solvation shell (defined as the 12 water molecules closest to the acetone molecule). 

Using the ROKS method a blue shift of 0.23 eV (experimental value 0.21 eV [94]) is calculated for the case in which only acetone itself is included in the QM region. Addition of the first solvation shell has only a tiny effect (a shift of 0.03-0.04 eV) indicating that the solvent shift is basically converged with respect to... 

A subject not treated here is the use of distance-dependent effective dielectric constants as a way to take account of the structure in the dielectric medium when a solute is present. This subject has recently been reviewed [120], In the approaches covered in the present chapter, deviations of the effective dielectric constant from the bulk value may be included in terms of physical effects in the first solvation shell, as discussed in Section 2.2. 

Another, related effect leading to non-bulk response in the first hydration shell is electrostriction[131], which is the change in solvent density due to the high electric fields in the first solvation shell of an ion. 

Although entropy cannot be strictly localized, some contributing factors to the solvent entropy change induced by the solute are localized in the first solvent shell, and contributions to the entropy of mixing that are proportional to the number of solvent molecules in the first solvation shell might sometimes... 

We summarize this section by emphasizing that we have identified a host of effects, and we have seen that they are mainly short-range effects that are primarily associated with the first solvation shell. A reasonable way to model these effects quantitatively is to assume they are proportional to the number of solvent molecules in the first hydration shell with environment-dependent proportionality constants. 

Finally we address the issue of contributions. In our view it is unbalanced to concentrate on a converged treatment of electrostatics but to ignore other effects. As discussed in section 2.2, first-solvation-shell effects may be included in continuum models in terms of surface tensions. An alternative way to try to include some of them is by scaled particle theory and/or by some ab initio theory... 

Unfortunately, as it is well known, in liquid water one water molecule, solute or solvent, is characterized by being connected to other molecules of water, creating a complex network. It is also known that this network is of two main types clatrate-like or hydrophyllic type. The two have different characterizations in the first solvation shell, thus generate a different electric field on the solute. 

The second example concerns the lithium ion, either considered in a cluster of water molecules or in aqueous solution. The idealized solution at infinite dilution of a lithium ion (without counter-ion) predicts six molecules of water in the first solvation shell if one uses pair-wise 2-body interactions, but the same type of computation predicts four molecules of water when 3-body effects are included. The computations were performed at room temperature. We have performed cluster computations for the Li fTO), system, with n = 1,2,3,4,5 and 6, using a density functional program developed in our laboratory. When we compute the most stable configuration for the pentamer complex Li+( starting from the most stable config-... 

Starting from a Li+ surrounded by 5 water molecules (all in the first solvation shell), we have started a DFT Molecular Dynamics simulation, with a time step of 0.5 femtoseconds. In Fig. 6 we report a plot of the system at four different times. To better visualize the evolution of the cluster geometry, we have drawn, in Fig. 6, a fictitious bond between the ion and the water oxygen, if the distance is below 2.535 A. 

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