Accurate analysis and perspectives for systematic design of magnetic resonance experiments using single-spin vector and exact effective Hamiltonian theory

Aimed at fundamental understanding and design of advanced magnetic resonance experiments on basis of Hamiltonians, we describe highly convergent and exact effective Hamiltonian methods which alleviate important deficits of current less accurate methods. This involves single-spin vector effective Hamiltonian theory (SSV-EHT) to first order in the interaction frame of rf and chemical shift offsets as well as exact effective Hamiltonian theory (EEHT) being an exact approach to average Hamiltonian theory not relying on interaction frame transformations. Bringing these methods together, we present tools to analyze challenging experiments in need of considering large static components in Hamiltonian (e.g., offsets) while economizing with radiofrequency irradiation power. It is demonstrated how the two complementary tools may provide important new insight into the detailed effective Hamiltonians of advanced NMR experiments, noting that the methods are by no means restricted to NMR. This is demonstrated for isotropic mixing in liquid-state NMR and dipolar recoupling in solid-state NMR where insight into the delicate interplay between bilinear two-spin and linear single-spin terms in the effective Hamiltonian may increase understanding of determinants for broadband excitation and the formation of recoupling resonances. Furthermore, we demonstrate how simple products single-spin effective Hamiltonians may be used as generators of multiple-spin effective Hamiltonians and though this a new approach to density operator calculations for large multiple-spin systems.