Applications of Average Hamiltonian Theory to spin polarization transfer in magnetic resonance

Average Hamiltonian Theory (AHT) is a widely used framework for analyzing spin dynamics in magnetic resonance experiments. The application of radiofrequency or microwave pulses, together with sample spinning, renders the Hamiltonian explicitly time-dependent, complicating the description of spin-state evolution. AHT overcomes this challenge by employing the Magnus expansion to generate a time-independent effective Hamiltonian. In this review, we discuss applications of AHT to spin polarization transfer mechanisms in nucleus-nucleus, electron-nucleus, and electron-electron-nucleus spin systems. AHT analysis to obtain an effective Hamiltonian in an appropriate interaction frame followed by density matrix evolution reveals optimal conditions for polarization transfer. The expression of the final density matrix also provides insight into the efficiency of the polarization transfer mechanism and their dependencies on external as well as internal interactions. Such analysis guides the design of experimental protocols, enabling informed choices of field strength, irradiation frequency, and pulse schemes to enhance nuclear polarization and dynamic nuclear polarization (DNP) efficiency. Thus, AHT serves as a powerful tool for both interpreting and optimizing polarization transfer experiments.