Selection rules for multiple quantum NMR excitation in solids: Derivation from time-reversal symmetry and comparison with simulations and C-13 NMR experiments

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selectio n rules apply to experiments in which the effective coupling Hamiltonian us ed for multiple quantum excitation is both time-reversal invariant and time -reversible by a phase shift of the radiofrequency pulse sequence that gene rates the effective couplings. The selection rules are shown to be conseque nces of time-reversal invariance and time-reversibility and otherwise indep endent of the specific form of the effective coupling Hamiltonian. Numerica l simulations of multiple quantum NMR signal amplitudes and experimental mu ltiple quantum excitation spectra are presented for the case of a multiply C-13-labeled helical polypeptide. The simulations and experiments confirm t he selection rules and demonstrate their impact on multiple quantum C-13 NM R spectra in this biochemically relevant case.