Spectroscopy from proton spin magnetization evolution in their rotating frame: A study of small tunneling splitting

The time evolution of proton Zeeman magnetization in the rotating frame at exact resonance, omega = omega(0), is evaluated for an isolated tunneling methyl group CH(3). The Fourier transform of this evolution in time is calculated and both its real and imaginary components are presented. It is shown that the real component does not depend significantly on the strength of the preparation pulse when the tunneling splitting of the methyl rotator ground state is less than 100 kHz. It is also found that the imaginary component of the transform is inversely proportional to the strength of the preparation RF pulse. This is a consequence of the partial dephasing of proton spins during the preparation pulse. The results of the calculation compare well with the experimental spectra of CH(3)CD(2)I.