Electronic couphng

The present approach has been applied to the experiment done by Nelsen et ah, [112], which is a measurement of the intramolecular electron transfer of 2,7-dinitronaphthalene in three kinds of solvents. Since the solvent dynamics effect is supposed to be unimportant in these cases, we can use the present theory within the effective ID model approach. The basic parameters are taken from the above reference except for the effective frequency. The results are shown in Fig. 26, which shows an excellent agreement with the experiment. The electronic couphng is quite strong and the perturbative treatment cannot work. The effective frequencies used are 1200, 950, and 800 cm for CH3CN, dimethylformamide (DMF), and PrCN [113]. 

In semiclassical ET theory, three parameters govern the reaction rates the electronic couphng between the donor and acceptor (%) the free-energy change for the reaction (AG°) and a parameter (X.) related to the extent of inner-shell and solvent nuclear reorganization accompanying the ET reaction [29]. Additionally, when intrinsic ET barriers are small, the dynamics of nuclear motion can limit ET rates through the frequency factor v. These parameters describe the rate of electron transfer between a donor and acceptor held at a fixed distance and orientation (Eq. 1),... 

Both the electronic couphng matrix element and the outer-sphere component of the nuclear reorientation parameter are thought to vary with donor-acceptor separation and orientation [29, 49]. It has been shown in studies of Os and Ru-ammines bridged by polyproline spacers that the distance dependence of X can be greater than that of [50]. Dielectric continuum models of solvent reorganization predict that Xg will increase with... 

Theoretical analysis of electronic couphng in DNA [12] suggests that the limiting beta value—the values that would be accessed for donor and accep-... 

The transfer rate constant of single-step CT depends on various parameters [25, 26], but the electronic couphng Vda- is crucial for the dependence of the rate constant on the distance between a donor d and an acceptor a and on their orientation. Electronic interactions of donor and acceptor with the intervening medium, in turn, determine the couphng Vda which can be found from quantum chemical calculations on pertinent models. A number of excellent reviews discussed the quantum chemical treatment of electron transfer [27-29]. 

In line with the Franck-Condon principle, the electron transfer occurs at the seam of the crossing between diabatic (localized) states of donor and acceptor. The electronic coupHng is the off-diagonal matrix element of the Hamiltonian defined at the crossing point. 

Usually, we calculated the electronic couphngs in DNA-related systems at the Hartree-Fock level [65]. For systems like [(GC),(CG)] and [(TA),(AT)], where donor and acceptor are equivalent by symmetry, the couphng matrix element can be estimated as half of the adiabatic energy sphtting. Therefore, such symmetric systems cannot be used to compare the performance of dif-... 

Moreover, as will be shown below, electronic coupHngs are very sensitive to conformational changes of DNA fragments their magnitude can change... 

To a first approximation, the matrix element Hda is proportional to the overlap Sda for d-a distances of interest in DNA. Therefore, the couphng Vda, as given by Eq. 5, is approximately proportional to the overlap Sda- Troisi and Orlandi found an almost hnear relationship between the electronic couphng of nucleobases and the overlap of the pertinent donor and acceptor orbitals. At the level HF/3-21G, the matrix element Vda (in oV) can be estimated as —0.716 Sjj, where Sg is the overlap integral calculated between the HOMOs of the donor and acceptor sites. This approximation obviously can be very useful when combined with MD simulations of DNA fragments. However, two remarks are in order (i) the reference values of Vda should be generated with a more accurate method, e.g., based on Eq. 5 instead of Eq. 6 [32] and (ii) the very small basis set 3-2IG is insufficient for achieving satisfactory reference matrix elements (Table 1). 

Hole transfer can exhibit a pronounced directional asymmetry. For instance, the couphng matrix element 1 (G-A) in [(GC),(AT)] is about five times larger than 1 (A-G) in [(AT),(GC)]. In both systems, G and A are in the same strand with the orientations 5 -G-A-3 and 3 -A-G-5, respectively. On the other hand, very similar electronic couphngs G/A and G A, with distinct interstrand orientation of G and A, are calculated for the systems [(GC),(TA)] and [(CG),(AT)], respectively. 

Furthermore, we compare the effective electronic couphngs for stacks TBT, TTBTT, ABA, and AABAA where B=A, A, G, T, and C (Table 7) [50]. As expected, the effects of B on the couphngs provided by three- and five-... 

Electronic coupHng matrix elements for DNA-related systems are much more difficult to calculate than the coupHng of hole transfer. First, in the case of an excess electron, the one-electron approximation likely is insufficient and electron correlation is expected to play a crucial role. Second, preliminary results revealed a considerable influence of the basis set on the calculated coupling. Third, an excess electron is expected to be delocalized over several pyrimidine bases this will render the evaluation of V a even more difficult. Thus far, no rehable estimates of electronic coupling matrix elements seem to be available. 

C. Hofmann, M. Ketelaars, M. Matsushita, H. Michel, T.J. Aartsma, J. Kohler, Single-molecule study of the electronic couphngs in a circular array of molecules ... 

Micic O. I., Ahrenkiel S. P. and Nozik A. J. (2001), Synthesis of extremely small InP quantum dots and electronic couphng in their disordered sohd films , Appl. Phys. Lett. 78, 4022-4024. 

Figure 14. Downhill exciton relaxation rates as a function of energy gap between two monomers, predicted by the Forster model (open triangles), the traditional Redheld model (open circles), and the modihed Redheld model (hlled circles). In (a) the electronic couphng, Ju = lOOcm and in b) Ju =20cm . The reorganization energy, if = lOOcm and the spectral density is represented by a Gaussian correlation function with Zg = 100 fs [163],...

Figure 29. Ratio of exciton population relaxation rate (S) to the exciton pure dephasing rate (r) as a function of J/a, where J is the electronic couphng and a is the disorder, a = 150 cm for B850 of LH2. The upper curve is for = 0, and the lower curve is for Eoip = 550cm . As S/T increases, energy transfer becomes more coherent.

Electronic couphngs between pairs of the three different T1 centers have also been calculated. These centers are connected pairwise by 13 covalent and 2 hydrogen bonds, resulting in an electronic decay coupling factor of 1.7 x lO. However, in spite of this relatively short distance, intramolecular ET between these sites is not expected. The high-potential TIC is, as mentioned above, most likely in the reduced state even in the resting (as isolated) enzyme and thus not involved in ET at all. The driving force for TIA to TIB ET is very low or even... 

We note that Equations 1.1.5 and 1.1.6 were obtained in the framework of perturbation theory and are therefore strictly applicable only in the limiting case of weak electronic couphng (nonadiabatic electron-transfer regime) [14,15]. In a more general case (any Vy < 0.5A,), the thermal activation barrier also depends on electronic coupling while the prefactor is a function of the attempting nuclear frequency v (frequency for nuclear motion along the reaction coordinate) and the electronic frequency that is equal to the prefactor in Equations 1.1.5 and 1.1.6... 

Troisi, A., and Orlandi, G., The hole transfer in DNA Calculation of electron couphng between close bases, Chem. Phys. Lett., 344, 509, 2001. 

Substitution of alkyl groups increases the nonradiative decay rates by increasing the effective number of coupled states while the electronic couphng matrix element remains constant (c/ Figure 1.2) [16]. 

Few examples of mixed-metal supramolecular complexes incorporating multiple Ru(II) and Pt(II) centers have been reported. These systems use dpp or dpq BLs to couple Ru(II) and Pt(II) subunits. The BL provides electronic couphng of the bridged metals. 

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