Nuclear energy decoupling spins

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

In a strong magnetic field, the electron and nuclear spin vectors, 1 and S are fully decoupled and each have their axis parallel to the applied field. If 6 is the angle between the axis of the dipoles (Fig. 5) and the line joining them, and r is their separation, then the Hamiltonian representing the energy of dipolar interaction is... 

The dipolar relaxation mechanism is unique because the dipolar coupling interaction contains two spin terms involving mutual spin flips - zero quantum t J. J. t and double quantum J J < j j transitions. All other relaxation processes are limited to single spin interchange. While the decoupler is on, the spin population differences between the levels irradiated are equalized as the rate of energy input from the decoupler greatly exceeds the outflow by relaxation. In dipolar coupled systems, the availability of double and zero quantum relaxation pathways (cross-relaxation) produces non-Boltzmann spin populations in the energy levels of the observed nucleus. These perturbed populations are measured as the nuclear Overhauser effect (nOe) effect rj). The relationship is... 

Under conditions of proton decoupling there are two relaxation parameters of general interest the longitudinal relaxation time, and NOE, the nuclear Over-hauser enhancement. The third relaxation parameter, T2 or spin-spin relaxation time is not readily measurable for in decoupled systems. Both and NOE are directly related to the transition probabilities associated with nuclei changing energy levels. However, their functional dependence on transition probabilities differs and they can therefore be used in combination to resolve ambiguities. NOE has been found to be a very sensitive measure of mobility of carbon atoms of proteins and to provide reliable qualitative measures of the state of carbon atoms [3]. 

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