The Heteronuclear Multiple-Quantum Correlation Experiment: Perspective from Classical Vectors, Nonclassical Vectors, and Product Operators

Abstract

It is usually accepted that most 2D-NMR experiments cannot be approached using classical models. Instructors argue that Product Operators (PO) or density matrix formalisms are the only alternative to get insights into complex spin evolution for experiments involving Multiple-Quantum Coherence, such as the Heteronuclear Multiple-Quantum Correlation (HMQC) technique. Nevertheless, in recent years, several contributions have been published to provide vectorial descriptions for the HMQC taking PO formalism as the starting point. In this work we provide a graphical representation of the HMQC experiment, taking the basic elements of Bloch’s vector model as building blocks. This description bears an intuitive and comfortable understanding of spin evolution during the pulse sequence, for those who are novice in 2D-NMR. Finally, this classical vectorial depiction is tested against the PO formalism and nonclassical vectors, conveying the didactic advantage of shedding light on a single phenomenon from different perspectives. This comparative approach could be useful to introduce PO and nonclassical vectors for advanced upper-division undergraduate and graduate education.