Effective Hamiltonian and 1H-14N cross polarization/double cross polarization at fast MAS

Unravelling the mechanism of polarization transfer from spin-1/2 to spin-1 system in solids

An analytic theory based on the concept of "effective-fields" is proposed to explain the mechanism of polarization transfer from spin I = 1/2 to spin S = 1 in non-rotating (static) solids. Employing an isolated two-spin model system, the matching conditions responsible for polarization transfer in cross-polarization (CP) experiments are identified and described in terms of the single-transition operators. In contrast to other existing treatments, the polarization transfer among spins is quantified through analytic expressions highlighting the individual contributions emerging from all plausible CP matching conditions. The interplay between the CP matching conditions observed in experiments is outlined in both isotropic and anisotropic systems and verified through comparison between simulations based on analytic and exact numerical methods. The predictions emerging from the analytic theory are verified over a wide range of experimentally relevant parameters and could be beneficial in the optimization of the CP experiments.

Satellite-transition double cross-polarization HETCOR under fast MAS

Double-cross polarization to the satellite-transitions (STs) of half-integer quadrupolar nuclei is demonstrated using proton-detected heteronuclear correlation (HETCOR) under fast magic-angle spinning (MAS). By placing the rf frequency away from the central-transition (CT) and selective to the STs, average Hamiltonian theory shows a scaled effective rf field with a phase equal to the complex ST spinning sideband being irradiated. Such an effective rf field can excite and spinlock STs but the phase spread usually leads to signal cancellation in one-step excitation or cross polarization experiments. The cancellation does not occur for two-step double cross-polarization (DCP) HETCOR experiments, therefore high efficiencies can be obtained. With careful magic-angle calibration, ST and double-quantum ST (DQST) HETCOR experiments are demonstrated with the ³⁵Cl nuclei in histidine·HCl·H₂O. These experiments provide additional information over the commonly observed CT spectra and near isotropic resolution in the case of DQST of spin S = 3/2 quadrupolar nuclei.

Effective Hamiltonian and spin dynamics in fast MAS TRAPDOR-HMQC experiments involving spin-3/2 quadrupolar nuclei

We present a theoretical and numerical description of the spin dynamics associated with TRAPDOR-HMQC (T-HMQC) experiment for a ¹H (I) - ³⁵Cl (S) spin system under fast magic angle spinning (MAS). Towards this an exact effective Hamiltonian describing the system is numerically evaluated with matrix logarithm approach. The different magnitudes of the heteronuclear and pure S terms in the effective Hamiltonian allow us to suggest a truncation approximation, which is shown to be in excellent agreement with the exact time evolution. Limitations of this approximation, especially at the rotary resonance condition, are discussed. The truncated effective Hamiltonian is further employed to monitor the buildup of various coherences during TRAPDOR irradiation. We observe and explain a functional resemblance between the magnitude of different terms in the truncated effective Hamiltonian and the amplitudes of various coherences during TRAPDOR irradiation, as function of crystallite orientation. Subsequently, the dependence of the sign (phase) of the T-HMQC signal on the coherence type generated is investigated numerically and analytically. We examine the continuous creation and evolution of various coherences at arbitrary times, i.e., at and between avoided level crossings. Behavior between consecutive crossings is described analytically and reveals 'quadrature' evolution of pairs of coherences and coherence interconversions. The adiabatic, sudden, and intermediate regimes for T-HMQC experiments are discussed within the approach established by A. J. Vega. Equations as well as numerical simulations suggest the existence of a driving coherence which builds up between consecutive crossings and then gets distributed at crossings among other coherences. In the intermediate regime, redistribution of the driving coherence to other coherences is almost uniform such that coherences involving S-spin double-quantum terms may be efficiently produced.