Temperature dependence electron transfer rates

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

The donor-acceptor complexes [Ir(/r-dmpz)(CO)(PPh2 0(CH2)2R )]2 exhibit photo-induced electron-transfer rate constants of 1012s—1 and charge recombination rates slower than 2 x 10los-1 when R = pyridine and 4-phenylpyridine.534 Further studies on these complexes revealed that recombination reactions were temperature dependent and slower for the deuterated acceptors.535... 

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

A number of publications in recent years have demonstrated an active interest in the theoretical aspects of electron transfer (ET) processes in biological systems (1.-9). This interest was stimulated by the extensive experimental information regarding the temperature dependence of ET rates measured over a broad range of temperatures (10-16). The unimolecular rate of cyto-chrome-c oxidation in Chromatium (10-12), for example, exhibits the Arrhenius type dependence and changes by three orders of... 

Figure 2. Theoretical prediction for the temperature dependence of the electron transfer rate for activated and for activationless processes. Solid lines are calculated for a continuum of vibrational modes dotted lines represent the single-mode approximation (6, 8). Upper curve AE, —2000 cm 1 P, 20 and S, 20. Lower curves AE, —800 cm"1 P, 8 and S, 20.

It is too early to draw any conclusions about the insensitivity of the rate constants to the nature of the dipeptide. Differences among the peptides seem to be revealed more in the temperature dependencies of the rate constants for intramolecular electron transfer than in the magnitude of the rate constant itself. Work is in progress on the synthesis of other di-, tri-, and tetra-peptides separating Co(III) and Ru(II) in order to examine the temperature dependence of the intramolecular rate... 

Study of the Temperature Dependence of the Electron Transfer Rate... 

A meaningful comparison of kinetic data obtained in different biological systems should be based on the determination of the respective contributions of the nuclear and electronic factors. The most direct method of separating these contributions consists in the measurement of the temperature dependence of the rate over the widest available range. In the following, we distinguish between experiments performed at room temperature, which are usually interpreted by assuming that all the nuclear motions coupled to the transfer may be described classically, and experiments performed at lower temperature, in which the quantified character of particular vibrational modes may appear. 

Since the values of i/ depend on several factors noted above, in the absence of additional data such as the temperature dependence of the electron transfer rate constants for i-2 it is difficult to analyze the apparent difference between i/ for the charge separation reaction and that of the radical ion pair recombination reaction. However, the difference between these two values of u is not unreasonable given that the charge separation involves oxidation of an excited state of the donor, while radical ion pair recombination involves two ground state radicals. Small changes in the nuclear coordinates of the donor and acceptor for these two reactions should be sufficient to produce the observed difference in i/. The electronic coupling factor between ZnTPP and AQ should be different than that between ZnTPP " and AQ". 

In order to learn more about the importance of vibrational motions in the primary photochemistry, we have measured the temperature dependence of the rate of electron transfer from 1 (BPh ) to Q over the range 295 to 5 K in polyvinyl alcohol films (22) The rate increases by a factor of about two as the temperature is reduced from 295 K to 100 K, and then remains constant down to 5 K the... 

Figure 4 shows the temperature dependence of the decay kinetics measured in PVA films in the 665-nm band (triangles). Some measurements at lower temperatures in the 545-nm band are also shown (circles). The electron transfer rate constant increases by a factor of 2 as the temperature is lowered from 295 K to 100 K, at which point the rate becomes independent of temperature within experimental error. The solid curve through the experimental data in Figure 4 is a theoretical fit that will be discussed below. 

Temperature Dependence of the Kinetics. In an earlier article (22) we gave a detailed analysis of the temperature dependence of the rate of electron transfer from 1 (BPh ) to Q (Figure 4). Here we summarize some of the important considerations and discuss further the possible insights that the temperature and detection-wavelength dependence of the kinetics may give into the molecular mechanism of electron transfer and the overall charge separation process. 

Cai et al. [7e] investigated electron and hole transfer in various polynucleotide duplexes and compared them with previous results found for salmon sperm DNA, to examine the effect of base sequence on excess electron and hole transfer along the DNA 71-way at low temperature. Electron and hole transfer in DNA was found to be clearly base sequence dependent. In glassy aqueous systems (7M LiBr glasses at 77 K), excess electron-transfer rates increase in the order polydIdC-polydIdC<salmon testes DNAexcess electron and hole transfer rates increase in the order polyC-polyG<salmon testes DNATransfer distances at 1 min and distance decay constants for electron and hole transfer from base radicals to MX in polynucleotides-MX and DNA-MX at 77 K are derived and compiled in Table 3. This table clearly shows that the electron-transfer rate from donor sites decreases in... 

Base Sequence Effects on Excess Electron Transfer. Cai et al.69 investigated low temperature electron and hole transfer to intercalator trapping sites in various polynucleotide duplexes and compared them with previous results found for salmon sperm DNA. Electron and hole transfer in DNA was found to be base sequence dependent. In glassy aqueous systems (7 M LiBr, D20 glasses at 77 K), excess electron-transfer rates increase in the order polydldC-polydldC < DNA... 

Fig. 20. Temperature dependence of the electron transfer rate, kt, in the [aFe(III) p Zn] hybrid hemoglobin. Data taken from ref. 91.

There has been keen interest in determination of activation parameters for electrode reactions. The enthalpy of activation for a heterogeneous electron transfer reaction, AH X, is the quantity usually sought [3,4]. It is determined by measuring the temperature dependence of the rate constant for electron transfer at the formal potential, that is, the standard heterogeneous electron transfer rate constant, ks. The activation enthalpy is then computed by Equation 16.7 ... 

The cuprous-cupric electron transfer reaction is believed to be the rate-limiting step in the process of stress corrosion cracking in some engineering environments [60], Experimental studies of the temperature dependence of this rate at a copper electrode were carried out at Argonne. Two remarkable conclusions arise from the study reviewed here [69] (1) Unlike our previous study of the ferrous-ferric reaction [44], we find the cuprous-cupric electron transfer reaction to be adiabatic, and (2) the free energy barrier to the cuprous cupric reaction is dominated in our interpretation by the energy required to approach the electrode and not, as in the ferrous-ferric case, by solvent rearrangement. 

Numerous theoretical studies have been made with the aim of explaining the unusual temperature dependence of the electron transfer rates in the RCs of the... 

The temperature dependence of k, was investigated and reported in Ref. [266], To obtain low-temperature data, samples were prepared in a 50% glycerol-water mixture. Figure 33 presents the temperature variation of k,. One can see from this Fig. that the electron transfer rate falls smoothly from the room temperature value to a non-zero value, kt = 9 + 4 s 1, which does not vary further from 170 down to 77 K. Data in the temperature-dependent region (T > 253 K) give the value Ea 2 kcal mol 1 for the Arrhenius activation energy. 

Temperature dependences of the rate for direct photoinduced electron transfer process and reverse charge recombination reaction were studied in some works. As a rule both processes were found to be temperature dependent. However for [p(MP), a(Fe(III)P hemoglobin hybrid (M = Zn(II), Mg(II)) the rate constants of both processes were found to be temperature independent in the temperature interval 273-293 K [285],... 

The temperature dependence of the rate constant of electron transfer over large distance from the first triplet state of Zn porphyrin to Rum(NH3)5 covalently attached to histidine-33 in Zn-substituted cytc was studied in Ref. [318]. A temperature independent triplet quenching process with the rate constant 3.6 s-1, was observed at 10-100 K and tentatively attributed to electron transfer facilitated by nuclear tunneling. 

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