Water exchange correlation

In these equations, the symbols have their customary meanings (see Toth et al. in this volume for an excellent review of the topic), and the correlation times given in Eq. (3) have the following typical values at 50 MHz in water Tle (electron spin-lattice relaxation time) =10 ns, T2e (electron spin-spin relaxation time) = 1 ns, rm (inner sphere water exchange correlation time) = 130 ns [3], and rR = 60 ps. These values, in the context of Eq. (1 - 3), show why rotational dynamics control relaxivity for such chelates. 

The dependence of the DFT results on the basis set used to expand the Kohn-Sham orbitals is illustrated in Table 4.3, which collects equilibrium geometry properties of water dimer obtained with the same exchange-correlation functional (B88/P86) but with different basis sets. 

Table 4.3. Water dimer properties the interaction energy (Ei t) in kcal/mol, the intermolecular distance (R00) in A, and the dipole moment p. in Debye, calculated using the B88/P86 exchange-correlation functional and different basis sets.

Femandez-Serra, M. V. Ferlat, G. Artacho, E., Two exchange-correlation functionals compared for first-principles liquid water, Los Alamos Eprint archive cond-mat/0407724, 2004... 

Figure 3 Effect of the water exchange rate, kex, and the rotational correlation time, rR, on inner-sphere proton relaxivity. The plot was simulated for a particular value of the longitudinal electron spin relaxation rate, 1/Tie — 5.28xlOss 1. The marketed contrast agents all have relaxivities around 4—5mM 1s 1 in contrast to the theoretically attainable values over lOOrnM-1 s 1, and this is mainly due to their fast rotation...

Figure 6 Effect of the increased rotational correlation time on the proton relaxivity of MP2269, a Gd111 chelate capable of noncovalent protein binding (Scheme 2). The lower NMRD curve was measured in water, whereas the upper curve was obtained in a 10%w/v bovine serum albumin solution in which the chelate is completely bound to the protein. The rotational correlation times calculated are rR=105ps in the nonbound state, and rR= 1,000 ps in the protein-bound state (t=35°C). For this chelate, the water exchange...

Fig. 2. Calculated relaxivities as a function of the water exchange rate for various proton Larmor frequencies and rotational correlation times, tr. The simulations have been performed by using the common Solomon-Bloembergen-Morgan theory of paramagnetic relaxation.

Since it has been reported that in the inner-sphere SOD catal5rtic pathway (Scheme 5) the water-exchange process is the rate-limiting one, the inner-sphere catalytic rate constants is were correlated with the water-exchange rate constants on [Mn(H20)6l (22,31). However, it seems that it is not possible to draw a direct correlation between these rate constants. Firstly, is (which is pH independent) according to the observed rate law for dismutation of superoxide (V — —d[02 ]/ d = [Mn][02 ] H[H+]+ ind>, ind 2kis, ku = 2kos/KJ has the unit... 

The interchange character of the water-exchange mechanism of the studied seven-coordinate complexes can be a reason why there is no clear correlation between their rates for the exchange process and the energies required for the dissociation of the coordinated water molecule. AE is also not possible to correlate with the catalytic rate constants published in the literature. 

The rate at which solvent molecules are exchanged between the primary solvation shell of a cation and the bulk solvent is of primary importance in the kinetics of complex formation from aquocations. In both water exchange and complex formation, a solvent molecule in the solvated cation is replaced with a new molecule (another water molecule or a ligand). Therefore, strong correlations exist between the kinetics and mechanisms of the two types of reactions. 

Although OH reacts at near-diffusion-controlled rates with inorganic anions [59], there seems to bean upper limit of ca. 3 x 10 dm mol sec in the case of simple hydrated metal ions, irrespective of the reduction potential of M"". Also, there is no correlation between the measured values of 43 and the rates of exchange of water molecules in the first hydration shell of, which rules out direct substitution of OH for H2O as a general mechanism. Other mechanisms that have been proposed are (i) abstraction of H from a coordinated H2O [75,76], and (ii) OH entering the first hydration shell to increase the coordination number by one, followed by inner-sphere electron transfer [77,78]. Data reported [78] for M" = Cr, for which the half-life for water exchange is of the order of days, are consistent with mechanism (ii) ... 

Dale Margerum Ralph Wilkins has mentioned the interesting effect of terpyridine on the subsequent substitution reaction of the nickel complex. I would like to discuss this point—namely the effect of coordination of other ligands on the rate of substitution of the remaining coordinated water. However, before proceeding we should first focus attention on the main point of this paper-which is that a tremendous amount of kinetic data for the rate of formation of all kinds of metal complexes can be correlated with the rate of water substitution of the simple aquo metal ion. This also means that dissociation rate constants of metal complexes can be predicted from the stability constants of the complexes and the rate constant of water exchange. The data from the paper are so convincing that we can proceed to other points of discussion. 

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