FT NMR of nonequilibrium states of complex spin systems. II. Weakly coupled systems

Since the Fourier transform NMR spectrum of a nonequilibrium state may be different from the slow-passage spectrum, a theory is developed which describes the phenomenon in any weakly coupled system, including those with magnetic equivalence. Liouville space techniques are used to derive simple expressions for the line intensities as a function of flip angle, in terms of Legendre polynomials. The theory uses F² representations directly and is applicable to any weakly coupled system. The results are tabulated for A_mX_n systems, m,n = 1, 2, 3, and 6. The theory is still applicable when. the weak coupling approximation starts to break down and line intensities are perturbed. It is shown that if the nonequilibrium intensities are corrected by a simple factor, as in the equilibrium case, these systems may be treated as if they were weakly coupled. In practice, the theory may be used to extrapolate to the slow-passage, zero flip angle spectrum. Furthermore, different parts of a degenerate line may be separated by means of the flip angle dependence. As an illustration, a nonequilibrium state was created among the protons in ethyl acetate. The experimental flip angle dependence of its spectra is well represented by the theory.