Theoretical description of pulse induced resonances in the homonuclear PIRATE experiment

Abstract

Rotor-synchronous π pulses applied to protons (S) enhance homonuclear polarisation transfer between two spins (I) such as 13C or 15N as long as at least a single I–S heteronuclear dipolar-coupling interaction exists. The enhancement is maximum when the chemical-shift difference Δν between two spins equals an integer multiple, n, of the pulse-modulation frequency, which is half the rotor frequency νr. This condition, applied in the Pulse Induced Resonance with Angular dependent Total Enhancement (PIRATE) experiment, can be generalised for any spacing of the pulses k/νr such that Δν. We show, using average Hamiltonian theory (AHT) and Floquet theory, that the resonance conditions promote a second-order recoupling consisting of a cross-term between the homonuclear and heteronuclear dipolar interactions in a three-spin system. The minimum requirement is a coupling between the two I spins and a coupling of one of the I spins to the S spin. The effective Hamiltonian at the resonance conditions contains three-spin operators of the form 2I1±I2∓Sz with a non-zero effective dipolar coupling. Theoretical analysis shows that the effective strength of the resonance conditions decreases with increasing values of k and n. The theory is backed by numerical simulations, and experimental results on fully labelled 13C-glycine demonstrating the efficiency of the different resonance condition for k=1,2 at various spinning frequencies.