Distance Dependence of Electronic Couplings

Consider two DNA fragments d-bib2...bm-a and d-bib2—bn a where donor and acceptor are separated by r-stacked bridges of lengths m and n, respectively. The distance dependence of the rate constant is often expressed in terms of an exponential decay parameter /i [5-9]  

In k=-/i(m+l)AR+const., where AR=3.38 A is the separation of adjacent pairs. For charge shift processes (as opposed to charge separation) between 

TTBTT 4.66X10 8.62x10 19.4x10 3.58x10 3.86x10  

AABAA 1.03X10 1.02x10 7.03x10 2.46x10 1.33x10  

We applied the effective Hamiltonian approach to DNA fragments of standard geometry with d=a=GGG, determined the effective couphng from Eq. 18, and analyzed the coupling following Eq. 24. Now, we will discuss the results for various bridge compositions (Table 7) [51]. 

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As discussed above, the first study of the distance dependence of electronic coupling associated with ET and HT applied PES, ETS and Koopmans theorem calculations to the rigid, symmetrical polynorbomane dienes 12( ), from which values of 0.88 and 1.2 bond were found for HT in the radical cations and ET in the radical anions, respectively. Although the electronic coupling could be calculated for a broad range of bridge lengths (up to 16 bonds), only the first two members of the series could be studied experimentally. It was clearly imperative to obtain an experimental determination of the distance dependence of ET rates based on more than two distances ... 

Constant reflecting distance dependence of electronic coupling... 

Composilion has a marked effect on p. Dilution can cause (i to drop by orders of magnitude. The functional dependence is often expressed in terms of an exponential dependence on intersite distance R=at m as suggested by the homogeneous lattice gas model, p c)exponential distance dependence of intersite coupling precludes observing a percolation threshold for transport. 

Fig.6 The distance dependence of electron-transfer rates in DNA hairpins [51]. The acceptor is a photoexcited derivatized stilbene (SA) or phenanthrene (PA) the electron donor is guanine (G), deazaguanine (Z), or inosine (I). The decay is much more rapid in the Z-PA couple compared to the G-SA couple because the tunneling energy is further from the bridge states in the case of Z-PA...

The distance dependence of electron transfer has been studied extensively for the homogeneous case. An approximately exponential decay of the electronic coupling has been found with the number of saturated bonds in the spacer unit (see for example [6,7]). The results presented here suggest that an exponential dependence fits also our data for heterogeneous electron transfer in ultra-high vacuum. A different result has been reported for electron transfer from Re complexes to anatase where a local triplet state can play a role [8]. 

Long-distance intervalence electron transfer is now demonstrated with metal-metal distances up to 25 A. Distance dependence of electron transfer has strong implications for the search of, for example, molecular switch devices or biosensors. The bridging ligand dicyanamidobenzene has been extensively studied, and for example, complex (18) exhibits a very strong coupling (0.32 eV) for a metal-metal distance of 19.5 A. ... 

In Equation (6.28), Hab is the electronic coupling at close contact (d°), and fi is the rate of decay of coupling with distance (d). Studies of the distance dependence of electron-transfer rates in donor-acceptor complexes, and of randomly oriented donors and acceptors in rigid matrices, have suggested 0.8 iS<1.2... 

The study of photoinduced electron transfer between molecular donors and acceptors provides a means to assess the electronic coupling provided by the DNA helix. Early applications of this method to DNA-mediated reactions utilized reactants noncovalently bound to DNA [28-30] These studies provided qualitative information concerning the efficiency and distance dependence of electron transfer, but the ambiguity associated with random distributions of reactants along the DNA helix precluded a quantitative analysis. Once chemical methods were developed for the covalent attachment of donors and acceptors to DNA [31], the distance dependence of these reactions, as well as the effects of perturbations within the intervening medium, could be systematically studied. The identification of unnatural DNA bases with appropriate photophysical and redox properties has also helped to define the extent of electronic coupling provided by the base stack [16]. 

Eng MP, Albinsson B (2006) Non-exponential distance dependence of bridge-mediated electronic coupling. Angew Chem Int Ed 45 5626—5629... 

Figure 6. Distance dependence of the interactions between two equivalent jt-type orbitals. The magnitude of the interaction, A (jt), at any given distance is approximately equal to twice the electronic coupling, Vci, for hole transfer between the two orbitals, (a) Through-space (TS) coupling. (b) Through-bond (TB) coupling. Using HF/ 3-21G theory, j8 3.0 A"1, for TS interactions, and 0.8 per bond for TB interactions in the diene series 1(n).

An important question remains to be answered although the phenomenological P value appears to be fairly insensitive to the nature of the hydrocarbon bridge, does it necessarily follow that Pei, for the distance dependence of the electronic coupling, Vd, should likewise display a similar insensitivity Extracting Vd values, and hence 3d, from experimental ET rate data is presently fraught with difficulties and uncertainties. An alternative approach to this problem is to calculate the couplings. A par-... 

We have assumed here that J can be treated as a constant. In some types of calculation, the explicit distance-dependence of the electron coupling integral must be taken into account. Little is yet known of the appropriate form of such a dependence. ... 

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