Dipolar-Coupling Model

The observed trends in plasmon coupling in a dimer can be explained by a simple model where each of the interacting particles is considered to be a point dipole [44]. In a dimer, the electric field El (or E2) felt by particle 1 (or 2) is the sum of the incident light field Eo and the near-field of the electric dipole fx.2 (or pii) on the neighboring particle, which for a dipole deca as the inverse cube of the distance d from the particle. While the assumption of a dipolar near-field is not strictly valid, as we shall see later, the dipolar- 

K is an orientation factor, which depends on the alignment of the two single-particle dipoles  

For the special case of dimer of identical particles, i.e. a homodimer, 

The coupled-particle polarizability a is maximum when the denominator vanishes. Combining with Eq. (6.1) we get the resonance condition  

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Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

The wide structural application of dipolar couplings is demonstrated by its use to validate models built by sequence homology methods. Additionally, dipolar couplings have been shown to reduce the RMSD between these models and the target structure. One example is the work reported by Chou et al., in which the RMSD of sequence homology models of the protein calmodulin, built from the structure of recoverin and parvalbumin, is reduced using heteronuclear dipolar couplings [110]. 

Fig. 11.15 Diagram showing the relative proximity of the two ligands Glp and S3P, which form a stable ternary complex with the enzyme EPSP synthase. The distance constraints were obtained from both homonuclear and heteronuclear dipolar couplings obtained using the REDOR and DRAMA pulse sequence, together with a model showing a...

CT-VPP-REDOR) or the pulse duration fp (CT-VPD-REDOR) then produces CT-REDOR curves, from which the second moment may be evaluated with distinctively superior accuracy as compared to the values obtained from a parabolic fit to the conventional REDOR data. When restricting the experiment to short dipolar evolution times, the two-spin approximation may be applied for the data analysis, which proves to be especially attractive for amorphous solids, for which the exact spin geometry is unknovm. The data presented on the model compoimds illustrate the various facets of CT-REDOR NMR spectroscopy. First application examples, namely, the evaluation of the heteronuclear Li-Ti dipolar couplings within the garnet structure of Li5La3Nb20i2, the determi-nation of the intemuclear B- P distance in frustrated Lewis pairs, the analysis of Na- F dipolar interaction in fluormica or Na- P... 

If the molecular tumbling rate is slow enough that larger electron-electron dipolar couplings are not motionally averaged, Fourier deconvolution can be used to analyze dipolar interactions in fluid solution.18 Distances in doubly spin-labelled rhodopsin were measured by Fourier deconvolution of CW line-shape changes in room temperature solution.78 The broadening function was modelled as the sum of Pake patterns from a distribution of distances. As a reference point for the distance measurements one label was attached at the cytoplasmic termination of transmembrane helix 1. The second label was attached near the cytoplasmic termination of transmembrane helix 7 or in the short helix 8. The distances and conformational flexibility in the dark state are... 

NMR is the experimental tool of choice to explore conformational properties, especially of flexible small molecules in solution [55-57], Interpretation of NMR-derived structural parameters in combination with molecular modeling usually offers a view of the accessible conformations to ligands. The most relevant structural parameters derived from NMR are interproton distances obtained from NOE or ROE experiments, dihedral angle restraints from 3J scalar coupling measurements and, recently, residual dipolar couplings (RDCs) [58],... 

Some systems cannot be well described by translational motion, so instead they require a model based on rotational diffusion. The commonly used model is one where the nuclei and radical form a bound complex, then this complex rotates to modulate dipolar coupling.74 Here, the overall correlation time consists of the rotational correlation time of the solvent complex, xT, and the exchange rate of molecules in and out of the complex, tm, where 1 /tc 1 /tr I 1 /tm. The form of this spectral density function is simpler4,25 ... 

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