Nuclear spins states, energy

Nuclear magnetic resonance (NMR) spectroscopy is concerned with the energies of the nuclear spin states and the transitions that are possible between different states. To work out the energies of the states, we need to understand the interactions that affect nuclear spin state energies and to develop an appropriate Hamiltonian. 

FIGURE 13 4 An external magnetic field causes the two nuclear spin states to have different energies The difference in energy AE is proportional to the strength of the applied field... 

Energy difference between nuclear spin states (kJ/mol or kcal/mol)... 

It turns out though that there are several possible variations on this general theme We could for example keep the magnetic field constant and continuously vary the radiofrequency until it matched the energy difference between the nuclear spin states Or we could keep the rf constant and adjust the energy levels by varying the magnetic... 

Section 13 3 In the presence of an external magnetic field the +j and —5 nuclear spin states of a proton have slightly different energies... 

If the radiofrequency spectmm is due to emission of radiation between pairs of states - for example nuclear spin states in NMR spectroscopy - the width of a line is a consequence of the lifetime, t, of the upper, emitting state. The lifetime and the energy spread, AE, of the upper state are related through the uncertainty principle (see Equation 1.16) by... 

No energy difference in nuclear spin states in absence of external magnetic field... 

Nuclear magnetic resonance, NMR (Chapter 13 introduction) A spectroscopic technique that provides information about the carbon-hydrogen framework of a molecule. NMR works by detecting the energy absorptions accompanying the transitions between nuclear spin states that occur when a molecule is placed in a strong magnetic field and irradiated with radiofrequency waves. 

Clearly, if a situation were achieved such that exceeded Np, the excess energy could be absorbed by the rf field and this would appear as an emission signal in the n.m.r. spectrum. On the other hand, if Np could be made to exceed by more than the Boltzmann factor, then enhanced absorption would be observed. N.m.r. spectra showing such effects are referred to as polarized spectra because they arise from polarization of nuclear spins. The effects are transient because, once the perturbing influence which gives rise to the non-Boltzmann distribution (and which can be either physical or chemical) ceases, the thermal equilibrium distribution of nuclear spin states is re-established within a few seconds. 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

At time [Case (2)] therefore, the hj rfine energy is approximately equal to the energy difference between the S and T states and can provide the driving force for T-S mixing. Now the h3q>erfine constants and Oj are a function of both nuclear and electronic spin states and thus one particular nuclear spin state for Hj and Hj will induce the T-S mixing more readily than the other. Thus nuclear spin selection occurs during the transition between S and T manifolds. However, this would yield no... 

In a spin system with anisotropic g and A tensors, the transition probability Wba between two nuclear spin states energy levels Eb and Ea may be calculated from the coupling operator given in (3.20). For a circularly polarized rf field, B2(t)R. in (3.20) has to be replaced by Bep(t)ft with the l.h. or r.h. rotating field B t) defined in (2,1). The nuclear transition probability is then given by... 

As mentioned above, we assume that the molecular energy does not depend on the nuclear spin state For the initial rovibronic state nuclear spin functions available, for which the product function 4 i) in equation (2) is an allowed complete internal state for the molecule in question, because it obeys Fermi-Dirac statistics by permutations of identical fermion nuclei, and Bose-Einstein statistics by permutations of identical boson nuclei (see Chapter 8 in Ref. [3]). By necessity [3], the same nuclear spin functions can be combined with the final rovibronic state form allowed complete... 

---