Coupling strength, distance dependence

The values of the mixing coefficients cos and sin depend on the coupling strength, which we can define in terms of the resonance (hopping) integral H12 measured relative to the distance Hn-H22 between AO levels, giving157 ... 

Our first step towards determining, unequivocally, the strength and the distance dependence of TB-mediated electronic coupling within saturated hydrocarbon bridges stemmed from our PES and ETS studies on the first three members of the series of totally rigid, symmetrical, polynorbomane-dienes 15(4)-15(6), where the numbers in parentheses refer to the numbers of C-C bridge bonds connecting the two double bonds (Fig. 12). The experimental studies were supplemented with... 

As mentioned earlier, KT/3-21G calculations offer a simple computational method for reliably estimating both the distance dependence and the strength of the electronic coupling element for ET in a variety of systems.39,83 In this context, one also requires a method for analysing and dissecting intra-bridge orbital interactions, and several elegant treatments are available.39,42-45,84,85,89,125-140... 

Various correlation and internuclear distance measurements are based on zero- or double quantum spin flips. The most efficient correlation methods are based on the adiabatic process, which is relatively insensitive to actual, orientation-dependent coupling strength. A double-quantum spin flip is generated by a sweep of the rf field amplitude, centred at half rotation frequency (the HORROR condition [9]). The increased rotation frequency leads to a crucial improvement in the broad-band character of the DREAM method [10]. The zero-quantum adiabatic spin flip process is considered in the next section. 

The chemical shift is the horizontal axis of a typical NMR spectrum, roughly proportional to the shielding strength at a nucleus relative to some reference substance. The spin-spin coupling term in NMR is the shift in the nuclear spin energy levels of one nucleus from its interaction with another nucleus. It is a highly distance-dependent effect and is used to map out which features in the NMR spectrum arise from adjacent nuclei. 

The distance-dependence of the near-field is quite universal [33]. When approximated to an exponential decay, the near-field coupling in the dimer system is found to have a decay length of >= 0.2 in units of the particle diameter D, regardless of the nanostructure size, shape, metal, or medium. That is, as a function of the distance s away from the nanoparticle surface, the near-field strength E can be expressed as ... 

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