Nuclear coupling

In order to describe nuclear spin-spin coupling, we need to include electron and nuclear spins, which are not present in the non-relativistic Hamilton operator. A relativistic treatment, as shown in Section 8.2, gives a direct nuclear-nuclear coupling term (eq. (8.33)). 

However, the nuclear-nuclear coupling constant also has an influence, since changing its sign changes the assignment of the lines in the spectrum. 

In addition to nuclear-coupled instability, the reactor designer must consider a number of flow instabilities. A discussion of various instabilities is given in Chapter 6. Only those instability modes of interest in BWR technology are mentioned here ... 

Chemical shift, nuclear coupling constants, relaxation times... 

Here, A is the nearly isotropic nuclear coupling constant, I is the nuclear spin (Iun = I), and m is the particular nuclear spin state. It may be observed that the zero field splitting term D has a second-order effect which must be considered at magnetic fields near 3,000 G (X-band). In addition to this complication nuclear transitions for which Am = 1 and 2 must also be considered. The analysis by Barry and Lay (171) of the Mn2+ spectrum in a CsX zeolite is shown in Fig. 35. From such spectra these authors have proposed that manganese is found in five different sites, depending upon the type of zeolite, the primary cation, and the extent of dehydration. 

Galperin M, Ratner MA, Nitzan A, Troisi A (2008) Nuclear coupling and polarization in molecular transport junction beyond tunneling to function. Science 319 1056... 

These are the equations on which a number of approximations are carried out to obtain approximate model solutions. In particular, the Bom-Oppenheimer (BO) frame allows for a useful separation between nuclear and electronic motion [49-52]. See also Park s book where some interesting elementary examples are analyzed concerning electro-nuclear coupling effects[53]. 

The electronic-nuclear coupling in molecules is also detected in the other partial Legendre-transformed representation H(/r, Q), which defines the combined Hessian G of Equation 30.27. Its first diagonal derivative,... 

Electronic-Nuclear Coupling Constants for H202 and CIF3... 

Let us now examine these electronic-nuclear coupling effects in more detail. The moderating exchange of electrons between the molecule and its hypothetical electron reservoir determines the effects of the electronic-nuclear coupling in the open molecular systems. Let us assume the initial electronic and geometric equilibria in such an initially open system p° = p.rej and F° = 0. The LeChatelier stability criteria of these two (decoupled) facets of the molecular structure requires that the conjugate forces A/jl(AN) or AFS(AQS) created by the primary electronic (AN> 0) or nuclear AQs > 0 displacements,... 

However, due to the electron-nuclear coupling in molecules a given displacement in one aspect of the molecular structure creates forces in the complementary aspect ... 

This section begins with a very brief summary of some of the technical issues associated with NMR special calculations. Subsequent subsections address the various utilities of modem methods for predicting chemical shifts and nuclear coupling constants. 

Finally, we note that there are some situations, of which the dynamical Jahn-Teller and Renner-Teller effects are the classic examples, where the nuclear coupling terms are important in any electronic basis 18). Adiabatic potential surfaces may still be defined but the resulting molecular eigenstates cannot be identified with any one surface. 

Jtj The sign of the nuclear-nuclear coupling constant giving rise to the multiplet. 

We deal first with electronic-nuclear coupling in systems with few atoms, and therefore few degrees of freedom for nuclear motions, so that we can concentrate on the first mentioned challenge. The structure and properties of a molecule in stationary states are well described within the Born-Oppenheimer picture in which the disparity in masses of nuclei and the electron, with mn me and the similarity of Coulomb forces on nuclei and electrons, Fn Fe, mean that within a short time interval At, changes in velocities satisfy Avn — Fn/(mnAt) Ave = Fnj(mnAt) so that an interaction involving small velocities to begin with, and lasting a short time, would be described by slow nuclei. The well known Born-Oppenheimer prescription is then to construct the electronic Hamiltonian Hq for fixed nuclear positions Q = (Ri,. ..,Rn), to calculate electronic states Q) for electron... 

In addition to the main hyperfine components discussed above, weak satellite lines are frequently detected, which correspond to transitions normally considered to be forbidden. Under certain circumstances the selection rule, that there is no change in orientation of the nuclear spin as the electron spin changes, breaks down, and simultaneous electron-nuclear transitions can occur. These are especially strong if the electron-nuclear coupling is very anisotropic and is comparable in magnitude to the direct interaction between the external field and the nucleus, which will, in general, have a different direction from that of the anisotropic interaction. Under these conditions the nucleus is affected by both fields, and quantum restrictions break down. 

In general, any satisfactory theoretical calculation of a nuclear coupling constant requires reliable calculation of the molecular wavefunction. As a consequence, a realistic approximation to the actual charge distribution in the carbohydrate molecule must presumably enter any theoretical model that attempts to provide a quantitative interpretation of solvent effects. The simplest treatments, and those that have been proposed most frequently to account for the solvent effect in the absence of specific effects, are those in which the solvent is treated as a continuum surrounding the solute molecule. Several different models where the solvent dependence of coupling interactions is related to the polarity of the medium have been proposed.78-79 The solvation theory80,81 has been successfully used within the FPT formalism to interpret the effect of solvent on Jc H and 3/CH. On the basis of this model, the Hamiltonian of a particular molecule includes the solvent-solute interaction term //so,v ... 

The positions of the 13C NMR lines in Crt 0 ions are mainly determined by the Fermi contact electron-13C nuclear coupling... 

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