Eigen mechanism

The Homogeneous Case. Margerum (1978) and Hering and Morel (1990) have elaborated on mechanisms and rates of metal complexation reactions in solution. In the Eigen mechanism, formation of an outer-sphere complex between a metal and a ligand is followed by a rate limiting loss of water from the inner coordination sphere of the metal, Thus, for a bivalent hexaaqua metal ion... 

The second statement has to do with the notion that in the Eigen mechanism for proton transfer there must be intermediate ion pairs. The reference to the unpublished work of Kreevoy and Liang (3) reflects the impact of their studies on some of our own recent work surveyed below. In fact, there is an extensive published literature concerning phenol-amine complexes in which the existence of the intermediates in equation 2 has been established in different organic solvents. One of the oldest such papers is that of Bell and Barrow (11) going back to 1959. Others include Hudson and co-workers (12) in 1972, and Baba and co-workers (13) in 1969. 

The effect of exchange of lactic, mandelic and sulfosalicylic acids on the relaxation of solvent protons gave rate constants (k) of exchange from 1.73 to 0.701 mol-1 s-1.642 Kinetics of complex formation with mandelic (HMDA) and vanillomandelic acids (HVMDA) gave rate constants (1.09 x 103 and 1.13 x 103 mol-1 s 1 for MDA- and VMDA ) consistent with a dissociative (Eigen) mechanism.438 As in the case of oxalic and malonic acids (Section 33.5.5.5.ii Table 27), species with coordinated hydroxyl are labilized. 

Scheme 11.7 The Eigen mechanism for proton transfer from the substrate HS to the base B.

Another approach used to interpret curvature of Br0nsted plots has been given by Murdoch (1972). This model, which incorporates Marcus theory, shows that the diffusive steps (10a, c) of the three-stage Eigen mechanism can also influence curvature. It is shown mathematically that increased difficulty of diffusion has the same... 

The values for the rate constant 0 are nearly the same for the mixed complexes when L = picolinate, sulfosalicylate and 8-oxyquinoline-5-sulfonate indicating and hence it appears that they fit Model 1 (i.e.) Diebler-Eigen mechanism involving a dissociative pathway. This is true in the case of lighter lanthanides. In the case of heavier lanthanides,... 

The advancement of the theoretical description of ion-pairing was marked by the distinction between internal (or contact or tight) and external (or solvent separated, loose) ion-pairs. Eigen and Tamm [63,64] proposed a stepwise formation of the contact ion-pair while the formation of the solvent separated ion-pair is diffusion-controlled, the elimination of the solvent molecnles to form the contact ion-pair was the slowest stage. Ultrasonic absorption data snpported the so-called Eigen mechanism represented in Figure 2.1. 

For labile complexes, it is often quite difficult to distinguish between inner and outer sphere complexes. To add to this confusion is the fact that formation constants for such labile complexes when determined by optical spectrometry are often lower than those of the same system determined by other means such as potentiometry, solvent extraction, etc. This has led some authors to identify the former as "inner sphere" constants and the latter as "total" constants. However, others have shown that this cannot be correct even if the optical spectrum of the solvated cation and the outer sphere complex is the same (4, 7). Nevertheless, the characterization and knowledge of the formation constants of outer sphere complexes are important as such complexes play a significant role in the Eigen mechanism of the formation of labile complexes (8) This model describes the formation of complexes as following a sequence ... 

This result is compatible with relaxation measurements (see Chap. 2, Vol. 1). On the Eigen mechanism, in principle, two relaxation times (tj, and Tj) should be observed, given by [6, 7]... 

More elaborately, complex formation can be viewed as in Fig. 2 (the detailed kinetic implications of this refinement to the basic Eigen mechanism are covered by Benton and Moore [71]). It is reasonable to relate the rate coefficient for the dissociative slow stage with that for solvent exchange, since breaking of a metal ion—solvent bond is involved in both processes. 

It has been usual to assume that the lanthanide ions undergo complex-ing by the Eigen mechanism (p. 250). Step k2 is a composite process involving loss of water from the coordination shell of the lanthanide ion... 

Bronsted and Pedersen [20] indicated that the rate constant for proton transfer from acid to a base cannot continue to increase in accord with a linear Bronsted law but must be limited by an encounter rate. This prediction was confirmed by Eigen s school [21] who showed that changed from 1 to zero as the p/f of the donor acid fell below that of the acceptor base (Fig. 5). Eigen [21] considered the following scheme (sometimes called the Eigen mechanism) for proton transfer from HX to Y where reactions in brackets occur in the encounter complex (Eqn. 28). The overall rate constants are given in Eqns. 29 and 30. 

Fig. 6. Deprotonation of acetylacetone by bases [21]. The points fall below the line predicted by the classical Eigen mechanism [21] and are correlated by a Marcus type equation.

The interpretation of the ultrasound relaxation data is based on the assumption that the rate-controlling step is the loss of water from the cation solvation shell via the Eigen mechanism of complex formation (Eigen and Tamm 1962)... 

Figure 8. Two solutions for the ordinary kinetic equations of the Eigen mechanism [3], eq 1 (dashed curves), as compared with the exact numerical solution for the Smoluchowski equation (full curves). Both models have the same /Cj and /Cr, but different values for the complex separation rate constant in the kinetic scheme were employed (a) giving the same area or (b) the same initial transient behavior as compared with the exact solution for the R OH decay [10b].

The complexation reactions usually proceed by the Eigen mechanism (Diebler and Eigen 1959, Eigen 1963, Eigen and Tamm 1962). This mechanism involves two steps, the rapid formation of an outer-sphere association complex (i.e., an ion pair) and the subsequent rate-determining step in which the ligand displaces one or more water molecules. 

The values of log/Cj and 0gk2 are 8.85 and 7.70, respectively. Similar conclusions were reached for the tartrate (Yun and Bear 1976), anthranilate (Silber et al. 1969) and picolinate (Erikson et al. 1987) complexation and for mixed-complex formation involving Ln (EDTA)(X) where X is a picolinate (Ekstrom et al. 1980) or a 5-sulfosalicylate anion (Ekstrom et al. 1981). The kinetic parameters for the overall reactions of these systems (Erikson et al. 1987) were consistent with the Diebler - Eigen mechanism (diebler and Eigen 1959, Purdie and Farrow 1973),... 

Kq3 0.3 dm ol l. Since k is known to be lO s", our data indicate a value for Kqs of 0.8 dm mol calculated from eqn. 9. This indicates that the kinetic results are consistent with the Eigen mechanism, but with considerable charge delocalisation in the murexide anion. 

Murdoch [53] derives an equation similar to the Marcus equation, equation 11, by the application of Hammond s postulate to the Eigen mechanism... 

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