Solvents coordinating

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. 

The reduced probability distribution does not depend explicitly on the solvent coordinates Y, although it incorporates the average influence of the solvent on the solute. The operation symbolized by Eq. (4) is commonly described by saying that the solvent coordinates Y have been integrated out. In a system at temperature T, the reduced probability has the form... 

Outer sphere electron transfer (e.g., [11-19,107,160-162]), ion transfer [10,109,163,164] and proton transfer [165] are among the reactions near electrodes and the hquid/liquid interface which have been studied by computer simulation. Much of this work has been reviewed recently [64,111,125,126] and will not be repeated here. All studies involve the calculation of a free energy profile as a function of a spatial or a collective solvent coordinate. 

Examine atomic charges and display electrostatic potential maps for ammonium and trimethylammonium ions (protonated ammonia and trimethylamine, respectively). How many acidic hydrogens are there in each Assuming that solvent coordinates to acidic hydrogens, how many solvation sites are there in each ... 

Solvent coordination numbers of metal ions in solution. S. F. Lincoln, Coord. Chem. Rev., 1971, 6, 309-329 (133). 

Fig. 1 Relative energy comparison between neutral and solvent coordinated cationic species, associated with counter anion CF [A], Br [B], and I [C].

Figure 2.4 Adiabatic potential energy E q) for various values of A at equilibrium. The solvent coordinate q has been normalized so that the initial state corresponds to = 0 and the final state to = 1. The reorganization energy was taken as A = 1 eV.

Figure 2.7 Potential energy surface for the adsorption of an iodide ion on Pt(lll) [Schmickler, 1995] as a function of the solvent coordinate q and the distance x from the electrode.

Figure 2.9 Model potential energy surface for combined electron and proton transfer. is the solvent coordinate for electron transfer and Q2 that for proton transfer. (See color insert.)...

From the given Hamiltonian, adiabatic potential energy surfaces for the reaction can be calculated numerically [Santos and Schmickler 2007a, b, c Santos and Schmickler 2006] they depend on the solvent coordinate q and the bond distance r, measured with respect to its equilibrium value. A typical example is shown in Fig. 2.16a (Plate 2.4) it refers to a reduction reaction at the equilibrium potential in the absence of a J-band (A = 0). The stable molecule correspond to the valley centered at g = 0, r = 0, and the two separated ions correspond to the trough seen for larger r and centered at q = 2. The two regions are separated by an activation barrier, which the system has to overcome. 

The crystal structure of the n-BugSu cation 6+ CB Mei2 , prepared according to Scheme 2.4, B (Section 2.1.2.3), was recently reported by Michl et al. Although n-BusSn in 6 CBnMei2 lacked solvent coordination, it appeared to be weakly... 

Since the most direct evidence for specihc solvation of a carbene would be a spectroscopic signature distinct from that of the free carbene and also from that of a fully formed ylide, TRIR spectroscopy has been used to search for such car-bene-solvent interactions. Chlorophenylcarbene (32) and fluorophenylcarbene (33) were recently examined by TRIR spectroscopy in the absence and presence of tetrahydrofuran (THF) or benzene. These carbenes possess IR bands near 1225 cm that largely involve stretching of the partial double bond between the carbene carbon and the aromatic ring. It was anticipated that electron pair donation from a coordinating solvent such as THF or benzene into the empty carbene p-orbital might reduce the partial double bond character to the carbene center, shifting this vibrational frequency to a lower value. However, such shifts were not observed, perhaps because these halophenylcarbenes are so well stabilized that interactions with solvent are too weak to be observed. The bimolecular rate constant for the reaction of carbenes 32 and 33 with tetramethylethylene (TME) was also unaffected by THF or benzene, consistent with the lack of solvent coordination in these cases. °... 

NMR measurements also provide information on the coordination of the ligands in the uranyl polymers. Solid-state I c-NMR confirms the coordination modes of the carboxylate ligands to the uranyl ion that is, both monodentate and bidentate carboxylate coordination modes are evident. The uranyl dicarboxyl ate polymers which possess two moles of coordinated DMSO exhibit two carbon-13 carbonyl resonances, one at about 175 ppm downfield from tetramethylsilane (TMS) and one at about 185 ppm. The polymers which possess only one mole of coordinated DMSO exhibit only the carbonyl peak near 185 ppm. Based on other known coordination compounds, the 175 ppm peak can be assigned to monodentate carboxylate and the 185 ppm peak to bidentate carboxylate. Thus, 7-coordination predominates in the polymers with either one or two moles of solvent coordinated to the uranyl ion, which is consistent with the infrared results reported elsewhere (5). 

Ni(cyclam)l2+ gives smaller coordination equilibrium constants than the open chain analogue, [Ni(2,3,2-tet)] +. A comparative study of donor solvent coordination to Ni11 complexes of 2,3,2-tet, cyclam, the smaller [12]aneN4, and [14]aneS4 has been performed.1594... 

V 1s n) is the normalized thermal distribution of configurations of the distinguished molecule in isolation [10], i.e., the required marginal distribution. The remaining set of brackets here indicates the average over solvent coordinates. The second set of brackets are not written on the right here because the averaging over solute coordinates is explicitly written out. This last formula is... 

Enhanced decarboxylation in polar solvents may be due to stabilization of polar transition states and/or solvent coordination to the metal (20). Coordination of solvent or ligands may aid decarboxylation by weakening metal-oxygen bonding (10). It also reduces the electrophilicity of the metal, the consequences of which are considered later. 

Most cations are strongly solvated, since their radii are small, and the free energy of solvation is approximately proportional to z2/r +, where ze0 is the cation charge in coulombs and r+ its ionic radius. The result of this is that even if the charge on the electrode is negative, there is usually little tendency for these cations to shed their water molecules and adsorb directly on the metal surface. Thus, the distance of closest approach of cations is determined by the radius of the inner solvent coordination sphere, and if the metal surface itself constitutes a plane, then the cation nuclei, at the distance of closest approach, will also constitute a plane termed the outer Helmholtz plane (OH P). 

Fig. 11 Free energy plot for an atom-transfer reaction in solution. Diffusive motion along the solvent coordinate opens the opportunity for a favourable atom transfer.

Solvation Thermodynamics and the Treatment of Equilibrium and Nonequilibrium Solvation Effects by Models Based on Collective Solvent Coordinates... 

There are two major approaches to including nonequilibrium effects in reaction rate calculations. The first approach treats the inability of the solvent to maintain its equilibrium solvation as the system moves along the reaction coordinate as a frictional drag on the reacting solute system.97, 100 The second approach adds one or more collective solvent coordinate to the nuclear coordinates of the solute.101 107 When these solvent coordinates are... 

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