Coordinating solvent 1-coordination

The effect known either as electroosmosis or electroendosmosis is a complement to that of electrophoresis. In the latter case, when a field F is applied, the surface or particle is mobile and moves relative to the solvent, which is fixed (in laboratory coordinates). If, however, the surface is fixed, it is the mobile diffuse layer that moves under an applied field, carrying solution with it. If one has a tube of radius r whose walls possess a certain potential and charge density, then Eqs. V-35 and V-36 again apply, with v now being the velocity of the diffuse layer. For water at 25°C, a field of about 1500 V/cm is needed to produce a velocity of 1 cm/sec if f is 100 mV (see Problem V-14). 

A reactive species in liquid solution is subject to pemianent random collisions with solvent molecules that lead to statistical fluctuations of position, momentum and internal energy of the solute. The situation can be described by a reaction coordinate X coupled to a huge number of solvent bath modes. If there is a reaction... 

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... 

The dependence of k on viscosity becomes even more puzzling when the time scale of motion along the reaction coordinate becomes comparable to that of solvent dipole reorientation around the changing charge distribution... 

Figure A3.8.1 A schematic diagram of the PMF along the reaction coordinate for an isomerizing solute in the gas phase (frill curve) and in solution (broken curve). Note the modification of the barrier height, the well positions, and the reaction free energy due to the interaction with the solvent.

The GLE can be derived by invoking the linear response approximation for the response of the solvent modes coupled to the motion of the reaction coordinate. 

In homopolymers all tire constituents (monomers) are identical, and hence tire interactions between tire monomers and between tire monomers and tire solvent have the same functional fonn. To describe tire shapes of a homopolymer (in the limit of large molecular weight) it is sufficient to model tire chain as a sequence of connected beads. Such a model can be used to describe tire shapes tliat a chain can adopt in various solvent conditions. A measure of shape is tire dimension of tire chain as a function of the degree of polymerization, N. If N is large tlien tire precise chemical details do not affect tire way tire size scales witli N [10]. In such a description a homopolymer is characterized in tenns of a single parameter tliat essentially characterizes tire effective interaction between tire beads, which is obtained by integrating over tire solvent coordinates. 

Electron transfer reaction rates can depend strongly on tire polarity or dielectric properties of tire solvent. This is because (a) a polar solvent serves to stabilize botli tire initial and final states, tluis altering tire driving force of tire ET reaction, and (b) in a reaction coordinate system where the distance between reactants and products (DA and... 

Calculations within tire framework of a reaction coordinate degrees of freedom coupled to a batli of oscillators (solvent) suggest tliat coherent oscillations in the electronic-state populations of an electron-transfer reaction in a polar solvent can be induced by subjecting tire system to a sequence of monocliromatic laser pulses on tire picosecond time scale. The ability to tailor electron transfer by such light fields is an ongoing area of interest [511 (figure C3.2.14). 

Measurements on copper) I) chloride show the vapour to be the dimer of formula CU2CI2, but molecular weight determinations in certain solvents such as pyridine show it to be present in solution as single molecules, probably because coordination compounds such as py -> CuCl (py = pyridine) are formed. 

However, it is common practice to sample an isothermal isobaric ensemble NPT, constant pressure and constant temperature), which normally reflects standard laboratory conditions well. Similarly to temperature control, the system is coupled to an external bath with the desired target pressure Pq. By rescaling the dimensions of the periodic box and the atomic coordinates by the factor // at each integration step At according to Eq. (46), the volume of the box and the forces of the solvent molecules acting on the box walls are adjusted. 

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. 

One approach to this problem is to use a potential of mean force (PMF), which describes he the free energy changes as a particular coordinate (such as the separation of two atoms or t torsion angle of a bond) is varied. The free energy change described by the potential of me force includes the averaged effects of the solvent. 

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

Unfortunately, the number of mechanistic studies in this field stands in no proportion to its versatility" . Thermodynamic analysis revealed that the beneficial effect of Lewis-acids on the rate of the Diels-Alder reaction can be primarily ascribed to a reduction of the enthalpy of activation ( AAH = 30-50 kJ/mole) leaving the activation entropy essentially unchanged (TAAS = 0-10 kJ/mol)" . Solvent effects on Lewis-acid catalysed Diels-Alder reactions have received very little attention. A change in solvent affects mainly the coordination step rather than the actual Diels-Alder reaction. Donating solvents severely impede catalysis . This observation justifies the widespread use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis-acid catalysed Diels-Alder reactions. 

In a Lewis-acid catalysed Diels-Alder reaction, the first step is coordination of the catalyst to a Lewis-basic site of the reactant. In a typical catalysed Diels-Alder reaction, the carbonyl oxygen of the dienophile coordinates to the Lewis acid. The most common solvents for these processes are inert apolar liquids such as dichloromethane or benzene. Protic solvents, and water in particular, are avoided because of their strong interactions wifti the catalyst and the reacting system. Interestingly, for other catalysed reactions such as hydroformylations the same solvents do not give problems. This paradox is a result of the difference in hardness of the reactants and the catalyst involved... 

The most effective Lewis-acid catalysts for the Diels-Alder reaction are hard cations. Not surprisingly, they coordinate to hard nuclei on the reacting system, typically oxygen atoms. Consequently, hard solvents are likely to affect these interactions significantly. Table 1.4 shows a selection of some solvents ranked according to their softness. Note that water is one of the hardest... 

Donor strengths, taken from ref. 207b, based upon the solvent effect on the symmetric stretching frequency of the soft Lewis acid HgBr2. Gutmann s donor number taken from ref 207b, based upon AHr for the process of coordination of an isolated solvent molecule to the moderately hard SbCL molecule in dichioroethane. ° Bulk donor number calculated as described in ref 209 from the solvent effect on the adsorption spectrum of VO(acac)2. Taken from ref 58, based on the NMR chemical shift of triethylphosphine oxide in the respective pure solvent. Taken from ref 61, based on the solvatochromic shift of a pyridinium-A-phenoxide betaine dye. 

Finally, the solvent also interacts with sites of the Lewis acid and the Lewis base that are not directly involved in mutual coordination, thereby altering the electronic properties of the complex. For example, delocalisation of charges into the surrounding solvent molecules causes ions in solution to be softer than in the gas phase . Again, water is particularly effective since it can act as an efficient electron pair acceptor as well as a donor. 

In summary, water is clearly an extremely bad solvent for coordination of a hard Lewis acid to a hard Lewis base. Hence, catalysis of Diels-Alder reactions in water is expected to be difficult due to the relative inefficiency of the interactions between the Diels-Alder reactants and the Lewis-acid catalyst in this medium. 

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