Rate constant CPET

Mechanism (I). In this chapter we merge the approaches of the Interacting/ Intersecting State Model (ISM) to atom and proton transfer reactions" with treatment of electron transfer reactions by this same model. Transition-state energies and effective reaction frequencies are calculated and used to obtain the rate constants of representative CPET. 

The transition between adiabatic PT and electronically non-adiabatic CPET can also be incorporated in the adiabatic PT rate constant using the electronic nonadiabatic factor Xei, that depends on (XeiVei)/vv in the same way as IkgsI depends on pi x- Additionally, we include in the energy barrier the contributions from the reorganizations of the parts of the molecular system involved in the synchronous proton and electron transfer, and express the rate constant for nonadiabatic CPET as... 

The rate constants, kn, obtained at all pH values studied, were effectively identical. For anions lie and 2ie, the rate of reactions with O2 showed no significant change as the pH was decreased from 2 to 1. These were the first indications that the reaction is zero-order in [H+], namely, pH-independent. Solvent kinetic-isotope effect experiments were carried out in D2O at D+ concentrations corresponding to pH values of 2 and 7.2. The rate remained unchanged when the solvent H2O was replaced by D2O. That provided a second line of evidence that even at pH 2, well below the pAfa = 4.7 of protonated superoxide (HO2 ), proton transfer (PT) occurs after rate-limiting electron transfer to O2 (ETPT mechanism), rather than via concerted proton-electron transfer (CPET) [61-65], in which an electron and proton are transferred simultaneously in a single elementary step—see Sect. 12.3.2. 

CPET to dioxygen was documented [66] by reacting members from the iso-structural series of one-electron reduced donor anions, lie, 2ie, and 3ie, with O2 at [H+] values from 0.1 to 1.9 M in water. Of the three donor-anions, lie was the only POM anion to display a linear (first-order) dependence of observed rate constants, obs, on [H+] (Fig. 12.9). LiCl was used to maintain constant ionic strength, and several independent control experiments ruled out ion-association between Li+ and lie that could induce variations in bs value. (One representative set of control reactions is indicated by the black diamonds in Fig. 12.9 see caption for details). 

Figure 12.12 red curve) shows the increase in rate constants for CPET (defined as cpet[H+]) as the average distance between (lie,02) encounter pairs and H+ (x-axis) decreases with increasingly larger [H+] values. The black line corresponds to the pH-independent rate constant for the ET process for more details see the figure caption. 

Fig. 12.12 Values for (black line) and cpetCH ] (red line), both in units of M s , as a function of the radii, r, of spherical volumes that each contain one proton. These radii indicate the average distance between O2 molecules and the loci of H" " ions in solvated proton complexes. The plot of fecPEr[H ] values (red line) begins at r= 9 A, which corresponds to [H+] =0.5 M, at which CPET values clearly exceed experimental uncertainties (see Fig. 12.9), and ends at the largest [H+] value studied (1.9 M) at which r 6 A. The two rate constants, 1 bt and (tcpEr[H" ], reach parity (1.2 s ) at r = 6.5 A, within the commonly reported 5-7 A...

Finally, the rate constant for CPET, pet is still much smaller (orders of magnitude) than the diffusional cage escape rate constant, ke (Fig. 12.14). Using a steady-state approximation, with cPEr[H ] << ke, the rate expression for CPET reduces to Eq. 12.14. 

Fig. 12.14 Elementary steps for ET and CPET. Both reactions proceed via the formation of encounter pairs (lie,02). These form by diffusion at a rate equal to the bimolecular rate constant kj, and dissociate from one another with a cage-escape rate constant, kc- At large [H+], kinetically significant fractions of the (lie,02) encounter pairs form in close proximity to rapidly diffusing H+ ions, and rates for CPET (kcPET[H" ]) become competitive with those for ET (Iet) (Reprinted from ref. [66] with permission from the American Chemical Society)...

Reaction between the one electron reduced POM anions and O2 were then summarized. These studies demonstrated that at mildly acidic to neutral pH values in water, electron transfer from Keggin heteropolytungstates to O2 occurs by an outer-sphere mechanism. In these cases, the effect of Keggin-ion charge on rate constants for the reduction of O2 was shown to be significant, and was attributed to anion-anion repulsion within the successor-complex ion pairs formed between the negatively charged POM anions and 02 . This was followed by the discovery of a concerted proton-electron (CPET) pathway for electron transfer to O2 at lower pH values (< 1). 

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