Random Matrix Theory and Nuclear Magnetic Resonance Spectral Distributions

Abstract

The complicated ¹³C and proton NMR spectra of the cyclic tetramer of propylene oxide have been interpreted by an analysis of the spin Hamiltonian in terms of the statistical theory of energy levels (random matrix theory). Predicted Poisson and Wigner spectral distributions (corresponding physically to uncorrelated and correlated spin energy levels of the propylene oxide tetramer) are confirmed experimentally. This success of the random matrix analysis suggests that, in general, qualitative chemically significant information about the internal correlation of a system can be extracted from NMR spectra (especially ¹³C NMR spectra) too complicated to analyze in any other way. Such an analysis seems particularly suitable to test the suggestion that certain biopolymers exist in coherent or correlated states.