Through-space distance dependence

Through-space distance dependence 9 The influence of the medium 11 Electron transfer and electron transport 12 The superexchange mechanism 15... 

ET rate constants in these systems decreased from a value of k i = 3.6 X 10 s for 36 to ka 50 s" for 39. Analysis of the activation parameters for these reactions demonstrated that solvent reorganization effects have a signiflcant effect in governing the distance dependence of intramolecular ET rates and that the electronic factor in these systems follows an attenuation factor of P = 0.68 A" using the through-space distance estimate of 3.12 A per residue. Unfortunately, accurate values for AH and A5 could not be obtain for the n = 4 compound (39), which was not included in the analysis. Interestingly, Schanze and Cabana [49] observed a nearly identical distance dependence of the activation parameters for ka occurring between a rhenium bipyiidyl electron acceptor and a (di-methylamino)benzoate donor across zero to two proline residues. 

Independent molecules and atoms interact through non-bonded forces, which also play an important role in determining the structure of individual molecular species. The non-bonded interactions do not depend upon a specific bonding relationship between atoms, they are through-space interactions and are usually modelled as a function of some inverse power of the distance. The non-bonded terms in a force field are usually considered in two groups, one comprising electrostatic interactions and the other van der Waals interactions. 

Rotational-echo double-resonance (REDOR)(75,79) is a new solid-state NMR technique which is sensitive to through-space carbon-nitrogen interactions between selectively 13C and 15N-enriched sites separated by up to 5A (20-22). The parameter directly measured in a REDOR experiment is the heteronuclear dipolar coupling constant DCN, which is in itself proportional to the inverse third power of the intemuclear distance, rCN. It is this dependence on (icn)3 which accounts both for REDOR s ability to accurately measure short distances and its insensitivity to longer-range interactions. As a technique which can probe, in detail, intermolecular interactions over a distance range of 5A, REDOR is well suited to studying the distribution of small selectively-labeled molecules in polymer delivery systems. 

An alternative approach is that adopted by Horrocks and co-workers, where the aromatic residues in metal-binding proteins are used as sensitizers. Since the distance between the metal and the donor is effectively fixed, this provides a rigid scaffold for the experiment, and the absence of a directly conjugated pathway between the metals means that Forster (through space) energy transfer can be assumed. The r-6 distance-dependence of this means that the extent of sensitized emission from the lanthanide ion provides information on the spatial relationship between the metal-ion binding site (lanthanide ions often bind at Ca2+ sites) and nearby aromatic residues. 58-60... 

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).

In summary, electron transfer dynamics, mediated through saturated hydrocarbon bridges and proteins, displays a surprisingly weak distance dependence behaviour (/J = 0.8-12 A 1), compared to that predicted for a pure through-space mechanism (P 3.0 A1). 

The dipolar-coupling Hamiltonian (TTy) describes the through-space coupling between two nuclear spins l and Ij. The dipolar coupling has an rk- dependence, and is key to the determination of internuclear distances in both solid-state and solution-state NMR. The high-field truncated form of the dipolar Hamiltonian is given by... 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

More recently, the concept of the molecular lipophilicity potential (MLP), initially introduced by Audry and coworkers (2), has attracted increasing attention. The method involves mapping the local lipophilicity at points in 3D space around a chemical compound through the use of a parametrized fragmental system coupled to an empirical distance function. Despite the absence of any physical basis for the distance-dependent functions introduced, and the difficulties inher-... 

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