Nuclear spins spin states

Quantitative theories for the chemical shift and nuclear spin-spin interaction were developed by Ramsey (113) soon after the experimental discoveries of the effects. Unfortunately the complete treatments of these effects involve rather detailed knowledge of the electronic structures of molecules and require evaluation of matrix elements of the orbital angular momentum between ground and excited electronic states. These matrix elements depend sensitively on the behavior of the wave function near... 

The NMR observables of a substance as a liquid, solution, or in the gas phase of paramount importance to the inorganic chemist are chemical shifts and nuclear spin-spin coupling constants. In the solid state, however, these effects generally are dwarfed by anisotropic dipolar interactions so... 

Finally, spin-orbit interaction has often been considered as the cause of states of mixed permutational symmetry. There are, however, a variety of other spin interactions which may accomplish such mixing electron spin-electron spin, electron spin-nuclear spin, spin-other-orbit, and spin rotation interactions. That other such spin interactions may enhance spin-forbidden processes in organic molecules is frequently ignored, though they may be of importance.66,136... 

Nuclear spin-spin coupling constants (Jab) are among the most difficult of molecular properties to compute by ab initio methods, because of the need to include the excited states in the expression for J. In recent years, a variety of calculations have appeared using ground-state SCF-MO s, and expressing the coupling constant... 

For those familiar with NMR spectroscopy it may be helpful to realize that the ESR g-shift is comparable with the NMR chemical shift. Similarly, electron-nuclear hyperfine coupling can be compared with nuclear-nuclear spin-spin coupling in NMR. (In systems containing more than one unpaired electron per molecule, electron spin-electron spin coupling is, of course, important. For doublet-state radicals, this coupling does not arise it is of great importance in triplet state molecules and in many high-spin transition metal complexes.)... 

Since 1996, only a few reports of the use of solid-state NMR spectroscopy for the study of phospholes have appeared, the emphasis having largely been on the identification and characterization of phospholes in solution. However, a detailed DFT investigation of the one-bond phosphorus-phosphorus indirect nuclear spin-spin coupling tensor, of the phosphole tetramer 34 has been reported <2000CJC118, 2004JPC(A)4895>. The calculated... 

There are also well known isotope effects associated with odd nuclear spin, spin-electron spin coupling, e.g., [10]. Such an effect that would favor formation over even spin nuclei absent in ozone formation, presumably because the ozone formation occurs on a singlet electronic state surface While there are some 27 electronic states of an O/O2 pair that in principle could be involved in ozone formation, only the lowest singlet state of O3 is deep enough to be sufficiently long-lived to be collisionally stabilized to lead to O3 formation at atmospheric pressure. Only it was assumed [12-15] to play a significant route to O3 formation under those conditions. The "no reaction" posed by the other entrance chaimels reduced the calculated rate of O3 formation accordingly [15]. 

Figure 15.9 Mechanisms for eleciron-coupled nuclear spin-.spin interactions for luidei sL piii iilecl by one. two and three bonds. Only the lowest energy nuclear spin states are shown.

In the case of Sn—X bonds and quadmpolar nuclei X, the Sn NMR signal may be broadened without resolved splitting, as a result of scalar relaxation of the second kind. In this case, the coupling constants can be calculated, if the relaxation time of the X nucleus is known.in favorable cases, the pattern of the solid-state n Sn NMR spectra can be analyzed with respect to the isotropic indirect nuclear spin-spin coupling (e.g. in PhsSnCl,, 280 and -1-275... 

Pulse techniques have been used by Powles et al (1960, 1962) to measure temperature dependence of nuclear spin-spin coupling in molecules such as methanol and acetaldehyde, which have steady-state spectra approximating to an AX3 case (Pople etal. 1959). Hahn and Maxwell (1951, 1952) showed that modulations of echo amplitudes could be explained on the basis of scalar couplings. In the limit of weak coupling the formulae are simplified and the chemical shift modulation disappears. In a Carr-Purcell experiment the amplitude of the %th echo E (t) in an AX3 case can be shown to be... 

Fig. 4. Radio frequency spectrum of H2 in the vicinity of the proton resonance frequency [4] in first clearly observed multiple line spectra with coherent radiation. The resonance frequencies are primarily determined by the interaction of the proton magnetic moment with the external magnetic field, but the states of different mj and mj are displaced relative to each other by the different values of the nuclear spin-spin and spin rotational interaction energies [4].

Sum-over-states expression The time-independent second-order properties, such as the nuclear spin-spin coupling constant (see Eq. 13), can be expressed by means of the perturbation theory as... 

---