Quenching and Recoupling of Echo Modulations in NMR Spectroscopy

Abstract

Trains of spin echoes are normally modulated by homonuclear scalar couplings. It has long been known that echo modulations are quenched when the pulse-repetition rates are much larger than the offsets of the coupling partners, because the spin systems behave as if they consisted of magnetically equivalent spins when the offsets are suppressed. This type of quenching of the echo modulations can occur when the radio-frequency (RF) pulses are ideal, that is, when they are perfectly homogeneous, properly calibrated to induce rotations through an angle, pi, and have an RF amplitude, omega(1)=-gammaB(1), that is strong compared to the largest offset, Omega(S)=omega(0S)-omega(RF), with respect to the carrier frequency. Recently, it was discovered that echo modulations can also be quenched when the RF pulses are nonideal, that is, when they are too weak to bring about an ideal rotation of the magnetization of the coupling partners, so that the effective fields associated with the RF pulses are tilted in the rotating frame. This phenomenon typically occurs when the pulse-repetition rates are much slower than the offset of the coupling partner. Under such conditions, it turns out, however, that for certain offsets, when the phase, Phi(S) (which arises from a free precession of the magnetization of the coupling partner, S, in the pulse interval, 2tau, and the pulse length, tau(pi)), approaches a multiple of 2pi, the echo modulations are restored. However, the frequencies of these echo modulations are not simply determined by the homonuclear scalar coupling, J(IS). The Fourier transforms of the echo trains (the so-called "J spectra") reveal surprising multiplet patterns, and the amplitudes of the echo modulations depend on the offsets of the coupling partners. Herein, we present a unified theory, based on an average-Hamiltonian approach, to describe these effects for two-spin systems. Experimental evidence of echo modulations in a system of two spins is presented. Experiments with three and more spins, backed up by extensive numerical simulations, will be presented elsewhere.