Nuclear spin-waves, multiple quantum NMR, and the benzene ring

Abstract

In the description of multiple quantum NMR spectra of spin \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$2$}}\) coupled nuclear spin systems, the interpretation is greatly simplified by subdividing the Hamiltonian ℋ (=ℋ1+ℋ2), where ℋ1 is a suitable combination of the constants of the motion. In this paper, a useful connection is established between (i) the discrete Fourier transform, (ii) the Bloch theorem for translationally invariant systems, and (iii) the nuclear spin dynamics of the benzene ring. In particular, it is shown that multiple quantum NMR experiments, performed at room temperature, can be used to probe the nuclear spin-wave excitations (∼10−7 K) of the benzene ring.