Curious Consequences of Strong Coupling in NMR Experiments Involving Selective Pulses

Abstract

This study is concerned with the effects of applying selective pulses to systems with strong second-order scalar couplings in isotropic phase, where different transitions (rs) are associated with different transition matrix elementsF⁺_(rs). Two unusual features can be distinguished: the nutation angle (“flip angle”) depends on the matrix element of the irradiated transition (rs), and, in contrast to the behavior of an isolated spin-$\text{1}\text{2}$ system, the norm of the three single-transition operators [I^(rs)_x,I^(rs)_y,I^(rs)_z] associated with the fictitious spin-$\text{1}\text{2}$ space of the irradiated transition (rs) is generally not conserved. It is necessary to consider the single-transition operators [I^(rp)_x,I^(rp)_y,I^(rp)_z] and [I^(sq)_x,I^(sq)_y,I^(sq)_z] associated with all connected transitions (rp) and (sq) that share a common energy levelrorswith the irradiated transition (rs). If the pulse applied to the (rs) transition is sufficiently selective, the transverse componentsI^(rp)_x,I^(rp)_y,I^(sq)_x, andI^(sq)_y, can be neglected, since their expectation values remain equal to zero after application of a selective pulse to the (rs) transition, but the longitudinal componentsI^(rp)_zandI^(sq)_zacquire nonvanishing expectation values. When the selective pulse affects several transitions simultaneously, the response varies from one transition to another, depending on the matrix elements and the connectivities. These effects manifest themselves in unusual amplitudes and phases of signals excited by selective pulses, in particular in selective two-dimensional correlation spectra.