An efficient simulation of variable-angle spinning lineshapes for the quadrupolar nuclei with half-integer spin

A Modular Implementation for the Simulation of 1D and 2D Solid-State NMR Spectra of Quadrupolar Nuclei in the Virtual Multifrequency Spectrometer-Draw Graphical Interface

We present the implementation of the solid state (SoS)NMR module for the simulation of several 1D and 2D NMR spectra of all the elements in the periodic table in the virtual multifrequency spectrometer (VMS). This module is fully integrated with the graphical user interface of VMS (VMS-Draw) [Licari et al., J. Comput. Chem. 36, 2015, 321-334], a freeware tool which allows a user-friendly handling of structures and analyses of advanced spectroscopical properties of chemical compounds-from model systems to real-world applications. Besides the numerous modules already available in VMS for the study of electronic, optical, vibrational, vibronic, and EPR properties, here the simulation of NMR spectra is presented with a particular emphasis on those techniques usually employed to investigate solid state systems. The SoSNMR module benefits from its ability to work under both periodic and nonperiodic conditions, such that small molecules/molecular clusters can be treated, as well as extended three-dimensional systems enforcing (or not) translational periodicity. These features allow VMS to simulate spectra resulting from NMR calculations by some popular quantum chemistry codes, namely Gaussian09/16, Castep, and Quantum Espresso. The effectiveness of the SoSNMR module of VMS is examined throughout the manuscript, and applied to simulate 1D static, MAS, and VAS NMR spectra as well as 2D correlation (90°, MAS) and MQMAS spectra of active NMR nuclei embedded in different amorphous and crystalline systems of actual interest in chemistry and material science. Finally, the program is able to simulate the spectra of both the total ensemble of spin-active nuclei present in the system and of subensembles differentiated depending on the chemical environment of the first and second coordination sphere in a very general way applicable to any kind of systems.

Investigation of multiaxis molecular motion by off-magic angle spinning deuteron NMR

The relatively new deuteron NMR method of off-axis-magic angle spinning (OMAS) has been extended and used to investigate multiaxis rotational jump motion. Floquet theory is developed for simulating deuteron OMAS spectra with multisite jumps at different rates about noncoincident axes, and efficient procedures are presented for computing the sideband line shapes. It is demonstrated experimentally that reproducible adjustment of the angle between the rotor axis and the static magnetic field is feasible with precision approaching +/- 0.01 degrees. This leads to the reintroduction of a scaled, first-order quadrupole coupling that defines a new kinetic window and makes deuteron OMAS much more sensitive than ordinary magic angle spinning to motion on the kilohertz time scale. Temperature-dependent deuteron OMAS line shapes of octanoic acid/urea-d4 inclusion compound have been recorded and fitted, using least-squares procedures, to provide rates of rotation about both CN and CO bonds. The Arrhenius activation parameters for rotation about CN bonds, Ea = 60.4+/-2.4 kJ/mol and ln(A) = 24.9+/-0.3, agree well with previous values determined by selective inversion experiments. However, OMAS yields Ea = 26.3+/-0.4 kJ/mole and ln(A) = 24.9+/-0.3 for whole-body rotation about the CO bond axis in contrast to previous analysis of static quadrupole echo (QE) line shapes which gave Ea = 22.3+/-0.3 kJ/mole and ln(A) = 24.8+/-0.6 for the same sample. The underlying homogeneous linewidths of OMAS spectra are much smaller than those of QE spectra, and this provides higher precision and less systematic error in the determination of rates.

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. (Ix) is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging (Ix) over the Euler angles and simulate the 11B MAS NMR lineshapes for crystalline and vitreous B2O3. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.

23Na magic-angle spinning nuclear magnetic resonance of central and satellite transitions in the characterization of the anhydrous, dihydrate, and mixed phases of sodium molybdate and tungstate

23Na Magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra of pure phases for Na2MoO4, Na2MoO4 x 2H2O, Na2WO4, and Na2WO4 x 2H2O have led to the determination of accurate values for the quadrupole coupling parameters and isotropic chemical shifts for all Na sites. The analysis of the spectra involves a combination of simulations of the line shapes for the central transitions and the manifold of spinning sidebands for the satellite transitions. The spectral parameters for the pure phases represent a prerequisite for a correct assignment and quantitative evaluation of 23Na MAS spectra at different magnetic field strengths observed for mixtures of the anhydrous and dihydrate phases. Such phase mixtures are observed, for example, for some commercial samples of Na2MoO4 or may be generated by (i) exposure of the anhydrous phases to a humid atmosphere or (ii) gently heating the dihydrates. The quadrupole coupling parameters for the two Na sites in the dihydrates are tentatively assigned to the two crystallographically distinct Na atoms in the asymmetric unit by calculations of an approximate dependency of the electric field gradient tensor on the local geometry for the Na sites.