ChemInform Abstract: Symmetry in NOE Spectra

Abstract

In this note, we address a problem connected with the understanding and interpretation of different experiments to measure the NOE. It is well known that a steadystate NOE enhancement, measured by observing a resonance A while irradiating a resonance B (denoted A{ B}), is quantitatively different from the reverse enhancement B(A), measured by observing B while irradiating A (I). In a 2D NOESY spectrum, however, the two symmetry-related cross peaks linking A and B are quantitatively identical (2).’ Also, the cross peak at (wl = bA, w2 = &) necessarily corresponds to an enhancement of the type B{ A} in that it represents magnetization which was transferred from A to B during the mixing time 7, while the cross peak at (wi = &, w2 = 6,) necessarily corresponds to its reverse, A(B). In view of this, it appears contradictory that the 2D experiment should be symmetrical when the 1D experiment is not. It is the resolution of this apparent contradiction which forms the subject of this note. It has been supposed that this difference originates in the two-dimensional nature of the NOESY experiment, or alternatively that typical values of T are too short to allow measurable intensity differences between symmetry-related cross peaks to develop. Neither explanation is correct. The true explanation is that the appropriate one-dimensional analogy for a NOESY experiment is not the steady-state NOE experiment, but rather the transient NOE experiment; this, like the NOESY experiment, is fully symmetrical, in the sense that A{ B} = B(A) for all values of 7. Although this analogy has been pointed out before (2), and the theory presented below is not new, it is our experience that the implications for the appearance of NOE spectra can be somewhat confusing. Also, the inherent symmetry of the transient NOE experiment (which is, after all, still a selective irradiation experiment) seems not to be widely appreciated. In what follows, we therefore develop these points, first descriptively and then in more formal terms. Fundamentally, the difference in symmetry between the steady-state and transient experiments arises from the presence or absence of selective irradiation during NOE evolution in the two cases. In the steady-state experiment, enhancements develop during a period of continuous selective irradiation of the target resonance. By complete contrast, in the transient experiment, the target resonance is rapidly inverted (or sat-