Influence of heteronuclear dipolar interactions on magic angle spinning NMR spectra of solids containing isolated three-spin systems

Abstract

Average Hamiltonian theory (AHT) is used to predict magic angle spinning (MAS) NMR spectra arising from isolated three-spin (I = 1/2) systems consisting of two crystallographically equivalent spins (A and A′) and a third heteronuclear spin (X). Under conditions of rapid sample spinning, the theory predicts the AA′ region of the MAS NMR spectra to consist of two equally intense peaks separated by the heteronuclear indirect spin-spin coupling constant J AX = J A′X, analogous to the situation in solution NMR studies. However, under slow spinning conditions the theory indicates a general eight-peak MAS spectrum for the AA′ region. Furthermore, it is shown that the two A-spin sub-spectra which arise from the two allowed spin states of X (m X = ±1/2) are different in that one is ‘squeezed’ while the other is ‘stretched’. Qualitatively, the heteronuclear dipolar interactions between the X spin and the crystallographically equivalent spins are responsible for the different A-spin sub-spectra associated with m X = +1/2 and m X = -1/2. In accord with theory, the 199Hg satellite peaks observed in 31P MAS NMR spectra of Hg(PPh3)2(NO3)2 (A, A′ = 31P; X = 199Hg) depend on the spin state of the 199Hg nucleus. In contrast, the heteronuclear dipolar interaction does not contribute to the linewidths observed in MAS NMR spectra of heteronuclear two-spin systems.