Rotary echo nutation NMR

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields. Since RF fields are limited by hardware, they seldom dominate the other interactions of these nuclei and so the spectra show unusual dependence on the pulse width used. The theory is tested with (23)Na NMR nutation spectra of a single crystal of sodium nitrate, in which the RF is comparable with the quadrupole coupling and is not necessarily on resonance with any of the transitions. Both the intensity and phase of all three transitions are followed as a function of flip angle. This provides a more rigorous trial than a powder sample where many of the details are averaged out. The formalism is based on a symbolic approach which encompasses all the published results, yet is easily implemented numerically, since no explicit spin operators or their commutators are needed. The classic perturbation results are also easily derived. There are no restrictions or assumptions on the spin of the nucleus or the relative sizes of the interactions, so the results are completely general, going beyond the standard first-order treatments in the literature.

Calculation of pulsed NMR signal in I = 3/2 quadrupolar spin system

The rf pulse response of I = 3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4 X 4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding pi/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.

Transverse relaxation times of spin 3/2 nuclei in the quadrupole nutation NMR experiment

Transverse relaxation times in the rotating frame of quadrupolar nuclei with half-integer spins are inversely proportional to the linewidth of quadrupole nutation NMR spectra. We apply fictitious spin -1/2 operators to I = 3/2 nuclei to derive correlations between the transitions of a multi-level system which affect nuclear relaxation. When omega rf << omega Q, all possible multiple-quantum transitions contribute to the transverse quadrupolar relaxation time in the rotating frame T2Qp. When omega rf >> omega Q, two of the three single-quantum transitions do not contribute. In the low-temperature region (outside the extreme narrowing limit), the contribution of double- and triple-quantum coherences to T2Qp goes through a minimum for omega rf << omega Q, while the triple-quantum coherence appears at zero frequency and corresponds to a short transverse relaxation time for omega rf >> omega Q.