Unraveling multi-spin effects in rotational resonance nuclear magnetic resonance using effective reduced density matrix theory

A perspective on the relative merits/demerits of time-propagators based on Floquet theorem

The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iH̄t defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrödinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed.

Determination of the relative orientation between 15N-1H dipolar coupling and 1H chemical shift anisotropy tensors under fast MAS solid-state NMR

In this work, we have proposed a proton-detected three-dimensional (3D) ¹⁵N-¹H dipolar coupling (DIP)/¹H chemical shift anisotropy (CSA)/¹H chemical shift (CS) correlation experiment to measure the relative orientation between the ¹⁵N-¹H dipolar coupling and the ¹H CSA tensors under fast magic angle spinning (MAS) solid-state NMR. In the 3D correlation experiment, the ¹⁵N-¹H dipolar coupling and ¹H CSA tensors are recoupled using our recently developed windowless C-symmetry-based C3₃¹-ROCSA (recoupling of chemical shift anisotropy) DIPSHIFT and C3₃¹-ROCSA pulse-based methods, respectively. The 2D ¹⁵N-¹H DIP/¹H CSA powder lineshapes extracted using the proposed 3D correlation method are shown to be sensitive to the sign and asymmetry of the ¹H CSA tensor, a feature that allows the determination of the relative orientation between the two correlating tensors with improved accuracy. The experimental method developed in this study is demonstrated on a powdered U-¹⁵N L-Histidine.HCl·H₂O sample.

Bimodal Floquet theory of phase-modulated heteronuclear decoupling experiments in solid-state NMR spectroscopy

A prescription based on bimodal Floquet theory is proposed to describe the nuances of phase-modulated supercycled decoupling experiments in solids. The frequency dependent interaction frames relevant to a particular supercycle are identified to facilitate faster convergence of perturbation corrections to the derived effective Hamiltonians. In contrast to silico-based methods, the proposed analytic method offers an attractive platform for faster optimization of experiments in solids. Additionally, the relevance of supercycling at ultrafast spinning conditions is also discussed.

On the equivalence between different averaging schemes in magnetic resonance

Evolution of quantum mechanical systems under time-dependent Hamiltonians has remained a challenging problem of interest across all disciplines. Through suitable approximations, different averaging methods have emerged in the past for modeling the time-evolution under time-dependent Hamiltonians. To this end, the development of analytic methods in the form of time-averaged effective Hamiltonians has gained prominence over other methods. In particular, the advancement of spectroscopic methods for probing molecular structures has benefited enormously from such theoretical pursuits. Nonetheless, the validity of the approximations and the exactness of the proposed effective Hamiltonians have always remained a contentious issue. Here, in this report, we reexamine the equivalence between the effective Hamiltonians derived from the Magnus formula and Floquet theory through suitable examples in magnetic resonance.