Broadband homonuclear cross polarization using flip-flop spectroscopy

Abstract

We have developed a new type of pulse sequence for broadband homonuclear cross polarization (l-10), known as TOCSY or HOHAHA in the literature. Our new sequences, called FLOPSY-8 and FLOPSY16 (flip-flop spectroscopy), offer a noticeable improvement in polarization transfer efficiency for a given expenditure of RF power, and outperform commonly used windowless sequences like WALTZ-16, DIPSI-2, DIPSI-3, and MLEV-16 or MLEV-17. In this Communication we describe how the FLOPSY sequences work by a geometrical analogy with the firmly established area of composite 180” pulses, and we compare FLOPSY with the other sequences. In Fig. 1 we show the familiar rotating-frame geometrical picture for an ensemble of isolated spin-f nuclei, in which the orthogonal axes are labeled with the linear spin operators I,, I,,, and I,. The state of the spins is represented as a vector from the origin to a point on the surface of the unit sphere, and evolution under an RF field is represented as a rotation of the spin vector about a vector representing the effective field. Spin inversion is accomplished on resonance by 180” pulse, mapping 1, onto 1,. Off resonance the effective field has a nonzero z component, and complete inversion is not possible with a single elementary rotation. On the right we show an analogous picture for the zero-quantum (ZQ) manifold of a two-spin system. Here it is the average d@erence in z magnetization II, Izz which labels the z component, and the transverse components in the picture label the x and y components of ZQ coherence. The x component is familiar as the transverse part of the scalar spin-spin coupling; the y component does not normally appear as part of the high-resolution spin Hamiltonian. It is formally related to the x component by a zero-quantum phase shift, that is, a unitary transformation by the longitudinal component in the ZQ frame. The three components in the ZQ frame are easily derived by considering the single-transition (II) or fictitious spin-4 (12) operators for the flip-flop transition I+-) I -+). Provided the dynamics remain within the ZQ manifold, our geometrical picture makes it easy to understand broadband cross polarization. An on-resonance 180” pulse in the ZQ frame will invert the average difference in z magnetization. The total z magnetization remains unaffected by the ZQ rotations, so we can write