Solvation sphere

ACS Symposium Series American Chemical Society Washington, DC, 1980. 

CD was utilized to obtain the solvent dependency of the conformation of the cation-lonophore complex as well as Kp s. Saturation Isotherms were plotted from linear computer fits of 1/[cation] versus 1/ArJ the slopes yielded Kjj s while extrapolation of Rq to infinite cation concentration provided the rJ s of the cation-saturated lonophore. It Is Important to note that the cation Itself is a significant vlnclnal moiety, which by virtue of Its charge, polarizability and location with respect to the chromophore of concern, can modify the rotational strength of the chromophore. 

X-ray crystallographic studies confirm that all cationic complexes of carboxylic lonophores have their llgandlng atoms oriented toward a central cavity. The extent to which this conformation would be altered in the absence of a bound cation due to the mutual electrostatic repulsion of the dipolar oxygen atoms would, in turn, be modulated by the mobility of the backbone supporting the ligands. 

We conclude that the dynamics of molecular conformation associated with sallnomycin complexatlon In all likelihood extend at least to the other naturally occurring carboxylic lonophores. The influence of lonophore environment, e.g. solvent, on lonophore conformation Is particularly significant when considering the environmental continuum encountered by an lonophore when trans-versing a biological membrane. 

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Figure 9.10 Schematic relationship between the radius Rq of an unsolvated sphere and the effective radius R of a solvated sphere or of a spherical volume excluded by an ellipsoidal particle rotating through all directions.

Methods for evaluating the effect of a solvent may broadly be divided into two types those describing the individual solvent molecules, as discussed in Section 16.1, and those which treat the solvent as a continuous medium. Combinations are also possible, for example by explicitly considering the first solvation sphere and treating the rest by a continuum model. Each of these may be subdivided according to whether they use a classical or quantum mechanical description. 

For solvent models where the cavity/dispersion interaction is parameterized by fitting to experimental solvation energies, the use of a few explicit solvent molecules for the first solvation sphere is not recommended, as the parameterization represents a best fit to experimental data without any explicit solvent present. 

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. 

Three types of methods are used to study solvation in molecular solvents. These are primarily the methods commonly used in studying the structures of molecules. However, optical spectroscopy (IR and Raman) yields results that are difficult to interpret from the point of view of solvation and are thus not often used to measure solvation numbers. NMR is more successful, as the chemical shifts are chiefly affected by solvation. Measurement of solvation-dependent kinetic quantities is often used (<electrolytic mobility, diffusion coefficients, etc). These methods supply data on the region in the immediate vicinity of the ion, i.e. the primary solvation sphere, closely connected to the ion and moving together with it. By means of the third type of methods some static quantities entropy and compressibility as well as some non-thermodynamic quantities such as the dielectric constant) are measured. These methods also pertain to the secondary solvation-sphere, in which the solvent structure is affected by the presence of ions, but the... 

An important extension of these ideas is to cases where an ion interacts with polar molecules (ion-dipole forces). In such cases the polarity of the molecule is increased because of the inductive effect caused by the ion. Polar solvent molecules that surround an ion in the solvation sphere do not have the same polarity as do the molecules in the bulk solvent. 

When an ionic compound is dissolved in a solvent, the crystal lattice is broken apart. As the ions separate, they become strongly attached to solvent molecules by ion-dipole forces. The number of water molecules surrounding an ion is known as its hydration number. However, the water molecules clustered around an ion constitute a shell that is referred to as the primary solvation sphere. The water molecules are in motion and are also attracted to the bulk solvent that surrounds the cluster. Because of this, solvent molecules move into and out of the solvation sphere, giving a hydration number that does not always have a fixed value. Therefore, it is customary to speak of the average hydration number for an ion. 

Presumably, the function of M+ is to "cushion the repulsion of the two negative ions. The larger, softer Cs+ can do this more effectively than the smaller, harder ions such as Li+ or Na+. Also, to form these bridged transition states, solvent molecules must be displaced from the solvation sphere of the cations. That process, because of their smaller sizes, would require more energy for the more strongly solvated Li+ and Na+. For the Cs+ ion, which forms effective bridges, the rate of electron exchange has been found to be linearly related to Cs+ concentration. 

In the IPCM calculations, the molecule is contained inside a cavity within the polarizable continuum, the size of which is determined by a suitable computed isodensity surface. The size of this cavity corresponds to the molecular volume allowing a simple, yet effective evaluation of the molecular activation volume, which is not based on semi-empirical models, but also does not allow a direct comparison with experimental data as the second solvation sphere is almost completely absent. The volume difference between the precursor complex Be(H20)4(H20)]2+ and the transition structure [Be(H20)5]2+, viz., —4.5A3, represents the activation volume of the reaction. This value can be compared with the value of —6.1 A3 calculated for the corresponding water exchange reaction around Li+, for which we concluded the operation of a limiting associative mechanism. In the present case, both the nature of [Be(H20)5]2+ and the activation volume clearly indicate the operation of an associative interchange mechanism (156). 

In aqueous solution, a metal complex is enclosed by several solvation spheres involving many solvent molecules. As recently shown, for mechanistic studies a reduced coordination sphere is sufficient (157,159), and therefore here inclusion of a third solvent molecule is sufficient. Addition of a third water molecule results in the exothermic formation of [Be(H20)2(L)--H20] and [Be(H20)2(LH)--H20]+, where the third hydrogen-bonded... 

Addition of a second water or ammonia molecule results in the formation of [Be(solvent)(12-crown-4)---(solvent )]2+, where the second solvent molecule, is regarded as present in the second solvation sphere and is very loosely attached ([Be(H20)(12-crown-4)---(H20)]. 3.71 A [Be(NH3)(12-crown-4) (NH3)]2+ 5.06A)... 

UCW = capped water, TW = tethered water (see text), k = force constant for restraining potential (kcal/mol/A2). b Radius (A) of solvation sphere. 1 Numbers of dynamical water molecules within solvation sphere. d Mean and standard error for the forward (i.e. 8-methyl-N5-deazapterin —> 8-methylpterin) and reverse mutation of the electrostatic force field Cutoff for protein-ligand and solvent-ligand interaction all other interactions are subject to a 9 A cutoff. 

Let us denote by R the coordinates of all the nuclei involved, those of the central ion, its ligands, and the surrounding solvation sphere, and by r the coordinates of all electrons. The Hamiltonian for the... 

Another approach to ET reactions originated in the work of Weiss and Libby, who suggested that activation energy for ET reactions in solution does not arise from the collisional-vibrational or electrostatic interaction of the solvent in the first and second solvation sphere, but rather from continuum solvent polarization fluctuation far out in solution. This approach, called continuum theory, was further developed by Kubo and Toyozawa, " Marcus, Platzmann and Erank, and by Levich and Dogo-nadze. ... 

Adsorption of Ag on the surface of PdO is also an interesting option offered by colloidal oxide synthesis. Silver is a well-known promoter for the improvement of catalytic properties, primarily selectivity, in various reactions such as hydrogenation of polyunsaturated compounds." The more stable oxidation state of silver is -F1 Aquo soluble precursors are silver nitrate (halide precursors are aU insoluble), and some organics such as acetate or oxalate with limited solubility may also be used." Ag" " is a d ° ion and can easily form linear AgL2 type complexes according to crystal field theory. Nevertheless, even for a concentrated solution of AgNOs, Ag+ does not form aquo complexes." Although a solvation sphere surrounds the cation, no metal-water chemical bonds have been observed. 

Fig. 8.16. Schematic model for ion evaporation, rsoiv is the radius of the solvation sphere, rsi the radius of the separating ion, and hi the height of the protuberance when the radius of its parabolic tip equals Reproduced from Ref. [85] by permission. Elsevier Science, 1987.

Similar measurements have given values for the fractionation factor of hydrogen-bonded complexes of the fluoride ion (Emsley et al., 1986c) and the acetate ion (Clark et al., 1988a) in acetic acid solution, [20] and [21]. For the chloride ion in acetic acid, the result (Emsley et al., 1986c) was cp = 1.26, which means that the exchangeable sites in acetic acid molecules in the solvation sphere of the chloride ion are favoured by deuterium compared to the sites in the bulk solvent. 

Figure 9.5. Schematic illustration of a distribution of functional groups on the surface of a. Groups 1 and 7 are independently solvated (there is no overlap between the solvation spheres, indicated by the dashed curves). Groups 2 and 3 are pair-correlated. Groups 4,5, and 6 are triply correlated.

The assumption of a single electron spin and a single T2 holds usually for S = 1/2 and for S > 1 in certain limits. Let us assume that the instantaneous distortions of the solvation sphere of the ion result in a transient ZFS and that the time-dependence of the transient ZFS can be described by the pseudorotation model, with the magnitude of the transient ZFS equal to At and the correlation time t . The simple picture of electron relaxation for S = 1 is valid if the Redfield condition (Att <5c 1) applies. Under the extreme narrowing conditions ((Os v 1), the longitudinal and transverse electron spin relaxation rates are equal to each other and to the low-field limit rate Tgo, occurring in Eqs. (14) and (15). The low field-limit rate is then given by (27,86) ... 

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