Outer sphere, entropy

Reductions of various Co(ni) complexes by Fe(II) have been studied under high pressures . The motivation for performing such experiments resides in the possibility that the volume of activation (AF ), like the entropy of activation, might be a criterion for distinguishing between inner- and outer-sphere reactions. For reactions of the type... 

The rate sequence is determined by the entropy term and correlates with the oxidation potential of the chelate complex, indicating an outer-sphere electron transfer. 

There are two other mechanistic possibilities, halogen atom abstraction (HAA) and halonium ion abstraction (EL), represented in Schemes 4.4 and 4.5, respectively, so as to display the stereochemistry of the reaction. Both reactions are expected to be faster than outer-sphere electron transfer, owing to stabilizing interactions in the transition state. They are also anticipated to both exhibit antiperiplanar preference, owing to partial delocalization over the C—C—Br framework of the unpaired electron in the HAA case or the electron pair in the EL case. Both mechanisms are compatible with the fact that the activation entropies are about the same as with outer-sphere electron donors (here, aromatic anion radicals). The bromine atom indeed bears three electron pairs located in two orthogonal 4p orbitals, perpendicular to the C—Br bond and in one s orbital. Bonded interactions in the transition... 

DR. JACK VRIESENGA (Syracuse University) You pointed out the dangers involved in extracting entropies and enthalpies from NMR data, not only as a result of the cross-correlation between the two, but also their correlation to other NMR parameters. I thought it might be useful for you to comment on the effect of pressure on the other NMR parameters, besides the kinetic control For example, you commented about the role played by the outer-sphere relaxation in the interpretation of NMR relaxation data. How would this be affected by pressure ... 

The extent to which the radicals react according to Eqs. 6 or 7 depends on the nature of Ri, Ra, and R3. If Ri = Rj = H and R3 = H through NO2, the ratio (6) (7) > 20. The addition reactions observed with these systems are characterized by strongly negative activation entropies, which can be rationalized in terms of immobilization of water molecules by the positive charge at C in the transition state [15]. That the transition state for addition has pronounced electron-transfer character concluded from the fact [15] that the rate constants for addition depend on the reduction potential of the nitrobenzene in a way describable by the Marcus relation for outer-sphere electron transfer. 

On the basis of the very negative activation entropies, the transition states for the addition are highly ionic, i.e. there is a large degree of electron transfer in the transition state as with the hydroxyalkyl radicals (Sect. 2.1.1). In support of this is the fact that the rate constants for addition depend on the reduction potentials of the nitrobenzenes, varied by the substituent R3 in a way describ-able by the Marcus equation for outer-sphere electron transfer [19]. 

Often, it is difficult to distinguish definitely between inner sphere and outer sphere complexes in the same system. Based on the preceding discussion of the thermodynamic parameters, AH and AS values can be used, with cation, to obtain insight into the outer vs. inner sphere nature of metal complexes. For inner sphere complexation, the hydration sphere is disrupted more extensively and the net entropy and enthalpy changes are usually positive. In outer sphere complexes, the dehydration sphere is less disrupted. The net enthalpy and entropy changes are negative due to the complexation with its decrease in randomness without a compensatory disruption of the hydration spheres. 

A model has been considered for Sn2 reactions, based on two interacting states. Relevant bond energies, standard electrode potentials, solvent contribntions (nonequi-librinm polarization), and steric effects are included. Applications of the theory are made to the cross-relation between rate constants of cross- and identity reactions, experimental entropies and energies of activation, the relative rates of Sn2 and ET reactions, and the possible expediting of an outer sphere ET reaction by an incipient SN2-type interaction (Marcus, 1997). 

Relaxation of complicated ligands may occur as a step in both pathways. Diebler and Eigen 461 indicated the ways in which such mechanisms could be analysed using fast reaction methods. Several studies of Ln(III) complex formation and of the formation of Ln(III) mixed complexes have been analysed. Generally the dissociative mechanism is considered to dominate and we are then concerned with the water exchange rate. Several studies have shown that the rate decreases from La(III) to Lu(III) but there seems to be a minimum rate around Tm(III). This is also seen in the rate of rotation of ligands on the surface of the ions, Fig. 7. There may be a small crystal field term, or another contribution to a tetrad -like effect from the 4f electron core. However in the hydrate the precise relationship between the inner and outer sphere water may also be important as we saw when we discussed the heat and entropy of complex ion formation. 

The AAH (a-a) value is — 11.8 kJ mol 1 for [Co(alamp)(py)]+ and —5.6 kJ mol 1 for [Co((R,R)-promp)(H20)]+. These values are largely compensated by the AASJ(a-a) value. Interestingly, the AH value linearly depends on the AS value. This result shows that the enthalpy-entropy compensation certainly occurs in the reaction. The compensation is discussed, as follows Since this reaction involves outer-sphere-type electron transfer, the activation enthalpy is necessary to bring the reactants close enough together to allow electron transfer and to break up the hydration shell of the reactants. The entropy term contains the contribution due to rearrangement of the solvent molecules. As a result, the enthalpy-entropy compensation occurs in the reaction. 

Some general observations on the energies and entropies of activation of redox reactions which proceed by bridged activated complexes are in order. These quantities, even for the few systems for which they have been determined, cover the range 4 to 14 kcal and —20 to —45 e.u. respectively. The ranges overlap with those for the outer-sphere activated complexes and, except possibly in extreme cases, it is not safe to use the magnitude of these quantities as diagnostic of mechanism. The comparison of AS for the process... 

For ASexp = 3 5, we obtain an estimate of 65-75% of outer sphere for EuBrO (HBrC, pKa = -2.3). However, such a calculation of simple additive entropies is probably too naive to be of much value. Morris, et al (14) have used similar reasoning to assign predominant outer sphere character to ScC10 2 an(i ScBrO"5. ... 

J/m/K. The agreement between the nmr estimates and those from equation (1) add weight to the estimates in Table III. In Figure 2 the variation of log i and log 0 as functions of pKa reflect the vital role of ligand basicity in the inner-outer sphere competition. These curves indicate that the cross-over from predominantly outer sphere to predominantly inner sphere occurs near pKa values of 2. However, since the enthalpy and entropy changes for inner sphere complexation are larger than for outer sphere formation, both AH and AS would still be endothermic (characteristic of inner sphere reaction). 

---