The Flexibility of SIMPSON and SIMMOL for Numerical Simulations in Solid-and Liquid-State NMR Spectroscopy

 Addressing the need for numerical simulations in the design and interpretation of advanced solid- and liquid-state NMR experiments, we present a number of novel features for numerical simulations based on the SIMPSON and SIMMOL open source software packages. Major attention is devoted to the flexibility of these Tcl-interfaced programs for numerical simulation of NMR experiments being complicated by demands for efficient powder averaging, large spin systems, and multiple-pulse rf irradiation. These features are exemplified by fast simulation of second-order quadrupolar powder patterns using crystallite interpolation, analysis of rotary resonance triple-quantum excitation for quadrupolar nuclei, iterative fitting of MQ-MAS spectra by combination of SIMPSON and MINUIT, simulation of multiple-dimensional PISEMA-type correlation experiments for macroscopically oriented membrane proteins, simulation of Hartman-Hahn polarization transfers in liquid-state NMR, and visualization of the spin evolution under complex composite broad-band excitation pulses.     

Third-order effect in solid-state NMR of quadrupolar nuclei

The theory and experimental observation of the third-order effect in solid-state NMR of quadrupolar nuclei are presented. The third-order effect consists of spherical harmonic terms up to rank l=6 and shifts NMR frequencies between two spin states that are not symmetric such as satellite transitions. Two-dimensional satellite transition magic-angle spinning experiment averages both the first and the second-order quadrupolar interactions making the quantitative measurement of the third-order effect possible. The third-order quadrupolar effect in andalusite has been measured at 11.7 T and its powder patterns are fitted with numerical simulations.     

Solid-state nuclear magnetic resonance in the rotating tilted frame

Recent methodological advances have made it possible to measure fine structure on the order of a few hertz in the nuclear magnetic resonance (NMR) spectra of quadrupolar nuclei in polycrystalline samples. Since quadrupolar couplings are often a significant fraction of the Zeeman coupling, a complete analysis of such experimental spectra requires a theoretical treatment beyond first-order. For multiple pulse NMR experiments, which may include sample rotation, the traditional density matrix approaches for treating higher-order effects suffer from the constraint that undesired fast oscillations (i.e., multiples of the Zeeman frequency), which arise from allowed overtone transitions, can only be eliminated in numerical simulations by employing sampling rates greater than 2I times the Zeeman frequency. Here, we present a general theoretical approach for arbitrary spin I that implements an analytical "filtering" of undesired fast oscillations in the rotating tilted frame, while still performing an exact diagonalization. Alternatively, this approach can be applied using a perturbation expansion for the eigenvalues and eigenstates, such that arbitrary levels of theory can be explored. The only constraint in this approach is that the Zeeman interaction remains the dominant interaction. Using this theoretical framework, numerical simulations can be implemented without the need for a high sampling rate of observables and with significantly reduced computation times. Additionally, this approach provides a general procedure for focusing on the excitation and detection of both fundamental and overtone transitions. Using this approach we explore higher-order effects on a number of sensitivity and resolution issues with NMR of quadrupolar nuclei.     

Improved excitation schemes for multiple-quantum magic-angle spinning for quadrupolar nuclei designed using optimal control theory

We have investigated the use of optimal control theory for the design of improved multiple-quantum excitation schemes for the popular multiple-quantum magic-angle spinning NMR experiment for quadrupolar nuclei with half-integer quadrupolar spin. The advantage of the new low-power experiments, termed OCFASTER, is demonstrated by sensitivity improvements approaching 50% for 87Rb in RbClO4 and RbNO3 as compared to FASTER and standard strong-pulse excitation schemes.     

Efficient symmetry-based homonuclear dipolar recoupling of quadrupolar spins: double-quantum NMR correlations in amorphous solids

We report novel symmetry-based pulse sequences for exciting double-quantum (2Q) coherences between the central transitions of half-integer spin quadrupolar nuclei in the NMR of rotating solids. Compared to previous 2Q-recoupling techniques, numerical simulations and 23Na and 27Al NMR experiments on Na2SO4 and the open-framework aluminophosphate AlPO-CJ19 verify that the new dipolar recoupling schemes display higher robustness to both radio-frequency field inhomogeneity and to spreads in resonance frequencies. These advances allowed for the first demonstration of 2Q-recoupling in an amorphous solid for revealing its intermediate-range structural features, in the context of mapping 27Al-27Al connectivities between the aluminium polyhedra (AlO4, AlO5 and AlO6) of a lanthanum aluminate glass (La0.18Al0.82O1.5).     

A composite pulse sequence for the broadband excitation in overtone N NMR spectroscopy

In this Letter, a composite π/2 pulse sequence,  135, for the broadband excitation in overtone NMR spectroscopy of spin S=1 quadrupolar nuclei is proposed. The performances of single and composite π/2 pulses against resonance offset and rf field inhomogeneity are compared based on the results from ¹⁴N overtone experiments on a single crystal sample of N-acetyl-D,L-valine. The results reveal that the  135 composite π/2 pulse is less sensitive to the pulse imperfections and it will be useful in the design of multidimensional overtone NMR experiments.     

Satellite transitions acquired in real time by magic angle spinning (STARTMAS): "ultrafast" high-resolution MAS NMR spectroscopy of spin I=3/2 nuclei

The satellite transitions acquired in real time by magic angle spinning (STARTMAS) NMR experiment combines a train of pulses with sample rotation at the magic angle to refocus the first- and second-order quadrupolar broadening of spin I=3/2 nuclei in a series of echoes, while allowing the isotropic chemical and quadrupolar shifts to evolve. The result is real-time isotropic NMR spectra at high spinning rates using conventional MAS equipment. In this paper we describe in detail how STARTMAS data can be acquired and processed with ease on commercial equipment. We also discuss the advantages and limitations of the approach and illustrate the discussion with numerical simulations and experimental data from four different powdered solids.     

Solid‐state NMR Spectroscopy of Quadrupolar Nuclei in Inorganic Chemistry

We here review the principles and applications of solid‐state NMR spectroscopy of quadrupolar nuclei, with a special emphasis on structural studies of inorganic solids. Most NMR‐observable nuclei have spin I > 1/2, and possess a quadrupole moment. The resulting quadrupolar interaction severely broadens the resonances, but also encapsulates valuable information about the symmetry of the electronic surroundings of the observed nucleus. The effect of the quadrupolar interaction, as well as that of the chemical shift and dipolar interaction, on solid‐state NMR spectra is examined in this article. To regain good resolution, specifically designed NMR techniques exist to remove the quadrupolar broadening, i.e. overtone and MQMAS spectroscopy, the principles of which are outlined here. In addition, the possibility of distance measurements via the dipolar interaction using the REDOR technique is discussed. The combined information derived from distance measurements, quadrupolar and chemical shift parameters can be helpful for determination of the crystal structure, or for detection of impurity phases, as illustrated by surveying a number of case studies covering spin I = 1, 3/2, 5/2 and 7/2.     

Hydrophilic domain structure in polymer exchange membranes: Simulations of NMR spin diffusion experiments to address ability for model discrimination

We detail the development of a flexible simulation program (NMR_DIFFSIM) that solves the nuclear magnetic resonance (NMR) spin diffusion equation for arbitrary polymer architectures. The program was used to explore the proton (¹H) NMR spin diffusion behavior predicted for a range of geometrical models describing polymer exchange membranes. These results were also directly compared with the NMR spin diffusion behavior predicted for more complex domain structures obtained from molecular dynamics (MD) simulations. The numerical implementation and capabilities of NMR_DIFFSIM were demonstrated by evaluating the experimental NMR spin diffusion behavior for the hydrophilic domain structure in sulfonated Diels‐Alder Poly(Phenylene) (SDAPP) polymer membranes. The impact of morphology variations as a function of sulfonation and hydration level on the resulting NMR spin diffusion behavior were determined. These simulations allowed us to critically address the ability of NMR spin diffusion to discriminate between different structural models, and to highlight the extremely high fidelity experimental data required to accomplish this. A direct comparison of experimental double‐quantum‐filtered ¹H NMR spin diffusion in SDAPP membranes to the spin diffusion behavior predicted for MD‐proposed morphologies revealed excellent agreement, providing experimental support for the MD structures at low to moderate hydration levels. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 62–78     

High resolution 3D exchange NMR spectroscopy and the mapping of connectivities between half-integer quadrupolar nuclei

A novel approach to the determination of structure and potential dynamics in the solid-state NMR spectroscopy of half-integer quadrupolar nuclei is proposed and demonstrated. The new experiment combines into a single three-dimensional sequence, 2D multiple-quantum magic-angle-spinning NMR and 2D exchange NMR protocols. The result separates for each inequivalent chemical site its spin-diffusion powder line shape to proximate homonuclei. A peculiar feature of the experiment is the asymmetry it displays in the individual 2D powder patterns, resulting from its encoding of isotropic shifts before the mixing period. The resulting spectra facilitate the interpretation of the structural and dynamic features for the individual sites; experimental applications of this new method to relative geometry determinations in 23Na-23Na spin pairs are presented, and the quantitative evaluation of the resulting data is briefly discussed.     

Effective Floquet Hamiltonians for dipolar and quadrupolar coupled N-spin systems in solid state nuclear magnetic resonance under magic angle spinning

Spin dynamics under magic angle spinning has been studied using different theoretical approaches and also by extensive numerical simulation programs. In this article we present a general theoretical approach that leads to analytic forms for effective Hamiltonians for an N-spin dipolar and quadrupolar coupled system under magic angle spinning (MAS) conditions, using a combination of Floquet theory and van Vleck (contact) transformation. The analytic forms presented are shown to be useful for the study of MAS spin dynamics in solids with the help of a number of simulations in two, three, and four coupled, spin-1/2 systems as well as spins in which quadrupolar interactions are also present.     

Effective Floquet Hamiltonian for spin I = 1 in magic angle spinning NMR using contact transformation

Contact transformation is an operator transformation method in time-independent perturbation theory which is used successfully in molecular spectroscopy to obtain an effective Hamiltonian. Floquet theory is used to transform the periodic time-dependent Hamiltonian, to a time-independent Floquet Hamiltonian. In this article contact transformation method has been used to get the analytical representation of Floquet Hamiltonian for quadrupolar nuclei with spin I = 1 in the presence of an RF field and first order quadrupolar interaction in magic angle spinning NMR experiments. The eigenvalues of contact transformed Hamiltonian as well as Floquet Hamiltonian have been calculated and a comparison is made between the eigenvalues obtained using the two Hamiltonians.     

Selective double-quantum nmr in solids

A simple method for selective double-quantum NMR in solids is described. The spin system is first prepared in a state having only dipolar, or quadrupolar, order. Selective excitation and detection of double-quantum coherence is then achieved by the 90°_x,y-t-45°_y pulse sequence.     

Semi‐analytical description of the S = 9/2 quadrupole nutation NMR experiment: multinuclear application to 113In and 115In in indium phosphide

The density matrix of a spin S = 9/2 excited by a radiofrequency pulse is calculated. The interaction involved during the excitation of the spin system is first‐order quadrupolar. Consequently, the results are valid for any ratio of the quadrupolar coupling ω_Q to the pulse amplitude ω₁. The behavior of the central transition intensities versus the pulse length is discussed. The ¹¹⁵In and ¹¹³In nuclei in a powdered sample of indium phosphide (InP) are used to illustrate the results. It is found that the ratio of the quadrupolar coupling constants determined in this work is in excellent agreement with the ratio of the quadrupole moments of the two nuclei. Copyright © 2015 John Wiley & Sons, Ltd.     

Homonuclear Selective One-Dimensional Gradient NMR Experiments in the Structure Determination of Natural Diterpene Derivatives

Summary.  The solution structure of two natural diterpene derivatives, the secondary metabolites esulatin-A and esulatin-B of Euphorbia esula, was investigated by homonuclear NMR experiments. Since the spectral dispersion of the ¹H NMR spectra at 500 MHz was sufficient to separate several skeletal protons of the title compounds, they were selectively excited with a double pulsed field gradient spin-echo (DPFGSE) sequence using 180°Gaussian pulses sandwiched between sine shaped gradients. With the use of selective excitation, scalar as well as dipolar interactions of the selected spins were monitored through one-dimensional (1D) COSY, TOCSY, and NOESY experiments. The chemical shifts of the coupling partners could be accurately extracted from the 1D COSY and TOCSY spectra recorded with high digital resolution. The selective TOCSY experiment provided an excellent opportunity to identify spins belonging to the same scalarly coupled spin system. The solution state conformation was investigated by selective gradient enhanced NOESY experiments. Proton–proton distances were evaluated from the cross-relaxation rates obtained from a quantitative analysis of the NOESY spectra recorded with different mixing times. The NMR derived distances were compared to the results of solid state X-ray diffraction measurements. Corresponding author. E-mail: pforgo@chem.u-szeged.hu Received November 21, 2001. Accepted (revised) January 9, 2002     

Ultra‐wideline 27Al NMR Investigation of Three‐ and Five‐Coordinate Aluminum Environments

Ultra‐wideline ²⁷Al NMR experiments are conducted on coordination compounds with ²⁷Al nuclei possessing immense quadrupolar interactions that result from exceptionally nonspherical coordination environments. NMR spectra are acquired using a methodology involving frequency‐stepped, piecewise acquisition of NMR spectra with Hahn‐echo or quadrupolar Carr–Purcell Meiboom–Gill (QCPMG) pulse sequences, which is applicable to any half‐integer quadrupolar nucleus with extremely broad NMR powder patterns. Despite the large breadth of these central transition powder patterns, ranging from 250 to 700 kHz, the total experimental times are an order of magnitude less than previously reported experiments on analogous complexes with smaller quadrupolar interactions. The complexes examined feature three‐ or five‐coordinate aluminum sites: trismesitylaluminum (AlMes₃), tris(bis(trimethylsilyl)amino)aluminum (Al(NTMS₂)₃), bis[dimethyl tetrahydrofurfuryloxide aluminum] ([Me₂‐Al(μ‐OTHF)]₂), and bis[diethyl tetrahydrofurfuryloxide aluminum] ([Et₂‐Al(μ‐OTHF)]₂). We report some of the largest ²⁷Al quadrupolar coupling constants measured to date, with values of C_Q(²⁷Al) of 48.2(1), 36.3(1), 19.9(1), and 19.6(2) MHz for AlMes₃ , Al(NTMS₂)₃ , [Me₂‐Al(μ‐OTHF)]₂ , and [Et₂‐Al(μ‐OTHF)]₂ , respectively. X‐ray crystallographic data and theoretical (Hartree–Fock and DFT) calculations of ²⁷Al electric field gradient (EFG) tensors are utilized to examine the relationships between the quadrupolar interactions and molecular structure; in particular, the origin of the immense quadrupolar interaction in the three‐coordinate species is studied via analyses of molecular orbitals.     

Dipolar and Scalar Couplings in Solid State NMR of Quadrupolar Nuclei

Summary.  Most NMR-active nuclei found in the periodic table have a quadrupole moment. In combination with a nonsymmetric electron distribution a strong NMR-active interaction results, which very often overshadows the dipolar and scalar couplings. This article aims at reviewing how these interactions manifest themselves in quadrupolar NMR and how they can be exploited for resonance assignment and structure elucidation, in spite of the presence of a strong quadrupolar interaction. E-mail: alexej.jerschow@nyu.edu Received April 16, 2002; accepted May 15, 2002     

Rapid Acquisition of 14N Solid‐State NMR Spectra with Broadband Cross Polarization

Nitrogen is an element of utmost importance in chemistry, biology and materials science. Of its two NMR‐active isotopes, ¹⁴N and ¹⁵N, solid‐state NMR (SSNMR) experiments are rarely conducted upon the former, due to its low gyromagnetic ratio (γ) and broad powder patterns arising from first‐order quadrupolar interactions. In this work, we propose a methodology for the rapid acquisition of high quality ¹⁴N SSNMR spectra that is easy to implement, and can be used for a variety of nitrogen‐containing systems. We demonstrate that it is possible to dramatically enhance ¹⁴N NMR signals in spectra of stationary, polycrystalline samples (i.e., amino acids and active pharmaceutical ingredients) by means of broadband cross polarization (CP) from abundant nuclei (e.g., ¹H). The BR oadband A diabatic IN version C ross‐ P olarization ( BRAIN–CP ) pulse sequence is combined with other elements for efficient acquisition of ultra‐wideline SSNMR spectra, including W ideband U niform‐ R ate S mooth‐ T runcation ( WURST ) pulses for broadband refocusing, C arr– P urcell M eiboom– G ill ( CPMG ) echo trains for T₂‐driven S/N enhancement, and frequency‐stepped acquisitions. The feasibility of utilizing the BRAIN–CP/WURST–CPMG sequence is tested for ¹⁴N, with special consideration given to (i) spin‐locking integer spin nuclei and maintaining adiabatic polarization transfer, and (ii) the effects of broadband polarization transfer on the overlapping satellite transition patterns. The BRAIN–CP experiments are shown to provide increases in signal‐to‐noise ranging from four to ten times and reductions of experimental times from one to two orders of magnitude compared to analogous experiments where ¹⁴N nuclei are directly excited. Furthermore, patterns acquired with this method are generally more uniform than those acquired with direct excitation methods. We also discuss the proposed method and its potential for probing a variety of chemically distinct nitrogen environments.     

Broadband excitation of quadrupolar order by modified jeener-broekaert sequences

Modified Jeener-Broekaert experiments are proposed for use in NMR spectroscopy of spins S = 1 nuclei in anisotropic phase. The new pulse sequences provide efficient creation of quadrupolar order over a wide range of values of the quadrupolar splitting. Experiments and computer simulations show that the new sequences can be used even under non-ideal experimental conditions.     

Quadrupolar nuclear magnetic resonance spectroscopy in solids using frequency-swept echoing pulses

The acquisition of ideal powder line shapes remains a recurring challenge in solid-state wideline nuclear magnetic resonance (NMR). Certain species, particularly quadrupolar spins in sites associated with large electric field gradients, are difficult to excite uniformly and with good efficiencies. This paper discusses some of the opportunities that arise upon departing from standard spin-echo excitation approaches and switching to echo sequences that use low-power, frequency-swept radio frequency (rf) pulses instead. The reduced powers demanded by such swept rf fields allow one to excite spins in different crystallites efficiently and with orientation-independent pulse angles, while the large bandwidths of interest that are needed by the measurement can be covered, thanks to the use of broadband frequency sweeps. The fact that the spins' evolution and ensuing dephasing starts at the beginning of such rf manipulation calls for the use of spin-echo sequences; a number of alternatives capable of providing the desired line shapes both in the frequency and in the time domains are introduced and experimentally demonstrated. Sensitivity- and lineshape-wise these experiments are competitive vis-a-vis current implementations of wideline quadrupolar NMR based on hard rf pulses; additional opportunities that may derive from these ideas are also briefly discussed.