A general theoretical description of the influence of isotropic chemical shift in dipolar recoupling experiments for solid-state NMR

Abstract

We present a general theoretical description that allows to describe the influence of isotropic chemical shift in homonuclear and heteronuclear dipolar recoupling experiments in magic-anglespinning solid-state NMR. Through a transformation of the Hamiltonian into an interaction frame with the combined radio-frequency irradiation and the isotropic chemical shift, we determine an effective Hamiltonian to first order with respect to the relevant internal nuclear spin interactions. This unravels the essential resonance conditions for efficient dipolar recoupling.

Time-optimized pulsed dynamic nuclear polarization

“…However, this is not computationally practical, and we have chosen a value for time T , such that it is longer than both 2π/ω eff and 2π/ω m , to ensure the convergence on the value of aχfalse(italick,italiclfalse). Alternatively, the coefficients can be determined efficiently using a more advanced method introduced recently ( 31 ). The analytical description of the interaction-frame transformation and the calculation of the Fourier coefficients (Eq.…”

Single-spin vector analysis of strongly coupled nuclei in TOCSY NMR experiments

“…For dipolar couplings under magic-angle spinning, we have demonstrated that a similar representation leads to accurate simulation results. 30 However, the aim here is to simplify matters even more, so we hypothesize that the AB-spin system Hamiltonian using the effective J coupling is a good approximation for the present system. We will not use this approximation for precise numerical calculations, but we will use it to establish more qualitative measures of the performance of different pulse sequences.…”

“…A similar result was found for the much larger dipole-dipole interaction under magic-angle spinning. 30 However, convergence and the possible necessity for including higher-order terms is a concern in some cases and will be the subject of a future-ongoing-study.…”

“…Recently, we presented and proposed a strategy for handling the effect of chemical shift in the theoretical description of dipolar recoupling experiments. 30 This strategy involved handling the combined effect of rf and chemical shift for each nucleus by moving into an interaction frame that included these effects and then describing the dipolar coupling in these interaction frames. While this approach greatly simplified the description of complex pulse sequences and provides new analytical insight, it involved a number of resonance and near-resonance conditions that could complicate the description.…”

Designing broadband pulsed dynamic nuclear polarization sequences in static solids

“…Following this, a phase-alternating low-power X-inverse X (XiX)-DNP has been demonstrated recently using similar average Hamiltonian and operator-based Floquet theory design principles 30 . In this work, we further introduce an alternative design strategy based on single-spin vector effective Hamiltonian theory 31,32 , which incorporates Fourier coefficients (exploited in Floquet theory) into average Hamiltonian theory. This theoretical framework is applicable to any arbitrary periodic DNP experiments, and will here be used for designing broadband DNP experiments.…”