Simulating multipulse NMR spectra of polycrystalline solids in the frequency domain.

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated.

Rapid simulation of two-dimensional spectra with correlated anisotropic dimensions.

A new algorithm has been developed to simulate two-dimensional (2D) spectra with correlated anisotropic frequencies faster and more accurately than previous methods. The technique uses finite-element numerical integration on the sphere and an interpolation scheme based on the Alderman-Solum-Grant algorithm. This method is particularly useful for numerical calculations of joint probability distribution functions involving quantities with a parametric orientation dependence. The technique's efficiency also allows for practical least-squares fitting of experimental 2D solid-state nuclear magnetic resonance (NMR) datasets. The simulation method is illustrated for select 2D NMR methods, and a least-squares analysis is demonstrated in the extraction of paramagnetic shift and quadrupolar coupling tensors and their relative orientation from the experimental shifting-d echo 2H NMR spectrum of a NiCl2 · 2D2O salt.

Statistical learning of NMR tensors from 2D isotropic/anisotropic correlation nuclear magnetic resonance spectra.

Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state nuclear magnetic resonance (NMR) spectrum containing multiple overlapping anisotropic subspectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the truncated singular value decomposition and the smooth least absolute shrinkage and selection operator based regularization methods, which (a) stabilize the solution and (b) promote sparsity and smoothness in the solution. We also propose an unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this article, we provide the details of the linear-inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic and experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.

Understanding multi-quantum NMR through secular approximation.

With the development of technology and improved understanding of nuclear spin-spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between "Secular-Approximation" (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.

Concept of effective Hamiltonians for transitions in multi-level systems.

Employing the concept of effective Hamiltonians, an analytical theory is introduced to describe transitions in a multi-level system in nuclear magnetic resonance (NMR) spectroscopy. Specifically, the discussion is centered towards the treatment of selective and non-selective excitations in static quadrupolar spin (I > 1/2) systems. To this end, effective radiofrequency (RF) Hamiltonians based on the spherical tensor formalism are proposed for describing transitions in both integral (I = 1, 2 and 3) and half-integral (I = 3/2, 5/2 and 7/2) quadrupolar spins. The optimum conditions desired for selective excitation in a multi-level system are derived pedagogically from first principles and presented through analytical expressions. Employing suitable model systems, the derived optimum conditions are substantiated through rigorous numerical simulations based on the spherical tensor formalism. The theory presented provides a framework for describing selective and non-selective RF pulses and could improve our understanding of multiple-pulse experiments involving quadrupolar nuclei.

Core Scientific Dataset Model: A lightweight and portable model and file format for multi-dimensional scientific data.

The Core Scientific Dataset (CSD) model with JavaScript Object Notation (JSON) serialization is presented as a lightweight, portable, and versatile standard for intra- and interdisciplinary scientific data exchange. This model supports datasets with a p-component dependent variable, {U0, …, Uq, …, Up-1}, discretely sampled at M unique points in a d-dimensional independent variable (X0, …, Xk, …, Xd-1) space. Moreover, this sampling is over an orthogonal grid, regular or rectilinear, where the principal coordinate axes of the grid are the independent variables. It can also hold correlated datasets assuming the different physical quantities (dependent variables) are sampled on the same orthogonal grid of independent variables. The model encapsulates the dependent variables' sampled data values and the minimum metadata needed to accurately represent this data in an appropriate coordinate system of independent variables. The CSD model can serve as a re-usable building block in the development of more sophisticated portable scientific dataset file standards.