The theory of nuclear magnetic resonance (NMR) on a solid sample containing pairs of coupled homonuclear spins-1/2, rotating in a large magnetic field, is presented. The time dependence introduced by the sample rotation, in conjunction with the spin–spin coupling, makes it appear that each of the central two levels in the four-level system split into a pair of ‘‘virtual states.’’ Each of the eight possible single-quantum coherences between the virtual states and the two outer levels in general contribute to the spectrum, although four of these contributions are forbidden unless a rotational resonance occurs (matching of an integer multiple of the spinning speed with the difference in isotropic shifts). Analytical line shapes for the case of vanishing shift anisotropy are given and techniques for numerical simulation in the general case demonstrated. The theory of Zeeman magnetization exchange in the presence of zero-quantum dephasing is presented.

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We introduce an improved variant of the C7 pulse-sequence for efficient recoupling of spin-1/2 pair dipolar interactions in magic-angle spinning solid-state NMR spectroscopy. The tolerance of C7 toward isotropic as well as anisotropic chemical shift offsets and rf inhomogeneity is improved considerably by replacing the original basic element Cφ44̄=(2π)φ(2π)φ+π with the cyclically permuted element Cφ14̄3=(π/2)φ(2π)φ+π(3π/2)φ. The improved performance of this permutationally offset stabilized variant of C7 is analyzed by average Hamiltonian theory to fifth order, numerical simulations, and demonstrated by experiments on powder samples of doubly 13C-labeled barium oxalate hemihydrate and diammonium fumarate.

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