respect toIandS. This operator evolves under theJIRandJSRscalar
coupling interactions but not under theJISscalar coupling interaction.
Evolution under theJIRscalar coupling interaction is given by
4 IySxRz )
2 JIRtIzRz
4 IySxRzcosðJIRtÞ 2 IxSxsinðJIRtÞ: ½ 2 : 260 Evolution of multiple-quantum coherences under the scalar coupling
interaction proceeds at the sum and difference frequencies of the passive
scalar coupling constants in a manner analogous to the chemical shift
evolution. For example, consider the zero-quantum term ZQISy ¼
1
2 ð^2 IySx^2 IxSyÞ evolving under the passive coupling effects JIR and
JSRfor a timet,
ZQISy )
2 JIRtIzRzþ 2 JSRtSzRz
ZQISy cosðÞKISt 2ZQISxRzsinðÞKISt,
½ 2 : 261 in whichKIS¼|JSR–JIR| is known as thezero-quantum splitting, and
2ZQISxRz¼^12 ð 2 IxSxþ 2 IySyÞRz: ½ 2 : 262 2.7.6 COHERENCETRANSFER ANDGENERATION OF
MULTIPLE-QUANTUMCOHERENCE
Coherence transfer is a vital effect in multidimensional NMR
spectroscopy, and, most notably, an effect that cannot be described
in the Bloch model. Suppose that an antiphase component, 2IxSz,of
the density operator has been generated in some manner. As will be
discussed later, antiphase operators can be produced by the use of a spin
echo pulse sequence. The effect of applying a 90ypulse to both spins is
2 IxSz!
2 Iy 2 I
zSz!
2 Sy 2 I
zSx: ½^2 :^263 The original antiphase coherence on theIspin (containing a single
transverse operator) is converted to antiphase coherence on theSspin.
Coherence has been transferred from one spin to another under the
influence of the rf pulse.
In contrast, application of a 90xto both spins gives
2 IxSz )
2 ðIxþSxÞ 2 I
xSy: ½^2 :^264 92 CHAPTER 2 THEORETICALDESCRIPTION OFNMR SPECTROSCOPY