Zeeman Truncation in NMR. I. The Role of Operator Commutation
2015 (English)In: Concepts in magnetic resonance. Bridging education and research, ISSN 1546-6086, E-ISSN 1552-5023, Vol. 43, no 4, 91-108 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2015. Vol. 43, no 4, 91-108 p.
NMR Hamiltonians, operator truncation, secular approximation, high-field Hamiltonian, spherical tensors
Chemical Sciences Physical Sciences Radiology, Nuclear Medicine and Medical Imaging
IdentifiersURN: urn:nbn:se:su:diva-117417DOI: 10.1002/cmr.a.21319ISI: 000353343600002OAI: oai:DiVA.org:su-117417DiVA: diva2:813911