Zeeman truncation in NMR. I. The role of operator commutation

Abstract

Hamiltonians are of pivotal importance for describing and analyzing NMR experiments. However, the “exact” spin Hamiltonian operators are in practice not utilized, but merely a simplified form referred to either as the “secular,” “Zeeman‐truncated,” or “high‐field” Hamiltonian. It results after accounting for the dominating role of the Zeeman interaction relative to all other, much smaller NMR interactions, such as chemical shifts, through‐bond, or through‐space spin–spin couplings. In this article and the following one, we introduce the Zeeman truncation process to newcomers to NMR by thoroughly reviewing the options available for reducing the full Hamiltonian of a spin interaction to its Zeeman‐truncated counterpart. The present paper considers time‐independent Hamiltonians, where we discuss the criteria for performing truncation, highlighting the role of operator commutation by a simple formalism that is equivalent to application of lowest‐order static perturbation theory. The validity of the approximations are illustrated by examining the explicit matrix representations of the “exact” and “Zeeman truncated” Hamiltonians, considering the NMR interactions relevant for systems of interacting spin‐1/2 nuclei. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 91–108, 2015.