The Calculation of NMR Chemical Shifts in Periodic Systems Based on Gauge Including Atomic Orbitals and Density Functional Theory

Lithium Transport Studies on Chloride-Doped Argyrodites as Electrolytes for Solid-State Batteries

In this study, the activation energy and ionic conductivity of the Li6PS5Cl material for all-solid-state batteries were investigated using solid-state nuclear magnetic resonance (NMR) spectroscopy and electrochemical impedance spectroscopy (EIS). The results show that the activation energy values estimated from nuclear relaxation rates are significantly lower than those obtained from impedance measurements. The total ionic conductivities for long-range lithium diffusion in Li6PS5Cl calculated from EIS studies depend on the crystal size and unit cell parameter. The study also presents a new sample preparation method for measuring activation energy using temperature-dependent EIS and compares the results with the solid-state NMR data. The activation energy for a thin-film sample is equivalent to the long-range lithium dynamics estimated from NMR measurements, indicating the presence of additional limiting processes in thick pellets. Additionally, a theoretical model of Li-ion hopping based on results obtained using density-functional theory methods in comparison with experimental findings was discussed. Overall, the study emphasizes the importance of sample preparation methods in determining accurate activation energy and ionic conductivity values for solid-state lithium batteries and the significance of solid-state electrolyte thickness in new solid-state battery design for faster Li-ion diffusion.

Structural Refinement of Carbimazole by NMR Crystallography

The characterization of the three-dimensional structure of solids is of major importance, especially in the pharmaceutical field. In the present work, NMR crystallography methods are applied with the aim to refine the crystal structure of carbimazole, an active pharmaceutical ingredient used for the treatment of hyperthyroidism and Grave’s disease. Starting from previously reported X-ray diffraction data, two refined structures were obtained by geometry optimization methods. Experimental ¹H and ¹³C isotropic chemical shift measured by the suitable ¹H and ¹³C high-resolution solid state NMR techniques were compared with DFT-GIPAW calculated values, allowing the quality of the obtained structure to be experimentally checked. The refined structure was further validated through the analysis of ¹H-¹H and ¹H-¹³C 2D NMR correlation experiments. The final structure differs from that previously obtained from X-ray diffraction data mostly for the position of hydrogen atoms.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Electronic orbital response of regular extended and infinite periodic systems to magnetic fields. I. Theoretical foundations for static case

A theoretical treatment for the orbital response of an infinite, periodic system to a static, homogeneous, magnetic field is presented. It is assumed that the system of interest has an energy gap separating occupied and unoccupied orbitals and a zero Chern number. In contrast to earlier studies, we do not utilize a perturbation expansion, although we do assume the field is sufficiently weak that the occurrence of Landau levels can be ignored. The theory is developed by analyzing results for large, finite systems and also by comparing with the analogous treatment of an electrostatic field. The resulting many-electron Hamilton operator is forced to be hermitian, but hermiticity is not preserved, in general, for the subsequently derived single-particle operators that determine the electronic orbitals. However, we demonstrate that when focusing on the canonical solutions to the single-particle equations, hermiticity is preserved. The issue of gauge-origin dependence of approximate solutions is addressed. Our approach is compared with several previously proposed treatments, whereby limitations in some of the latter are identified.

Solid-state 17O NMR study of 2-acylbenzoic acids and warfarin

We report synthesis and solid-state ¹⁷O NMR characterization of four site-specifically ¹⁷O-labeled 2-acylbenzoic acids (2-RC(O)C₆H₄COOH) where R=H and CH₃): 2-[3-¹⁷O]formylbenzoic acid, 2-[1,2-¹⁷O₂]formylbenzoic acid, 2-[3-¹⁷O]acetylbenzoic acid, and 2-[1,2,3-¹⁷O₃]acetylbenzoic acid. In the solid state, both 2-formyl- and 2-acetyl-benzoic acids exist as the cyclic phthalide form each containing a five-membered lactone ring and a cyclic hemiacetal/hemiketal group. Static and magic-angle-spinning ¹⁷O NMR spectra were recorded at 14.1 and 21.1T for these compounds, from which the ¹⁷O chemical shift and nuclear quadrupolar coupling tensors were determined for each oxygen site. These results represent the first time that ¹⁷O NMR tensors are fully characterized for lactone, cyclic hemiacetal, and cyclic hemiketal functional groups. We also report solid-state ¹⁷O NMR data for the cyclic hemiketal group an anticoagulant drug, warfarin. Experimental ¹⁷O NMR tensors in these compounds were compared with computational results obtained with a periodic DFT code BAND.

Relativistic calculations of magnetic resonance parameters: background and some recent developments

This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

An improved scheme for the calculation of NMR chemical shifts in periodic systems based on gauge including atomic orbitals and density functional theory

We report here on an improved first principles method that can determine NMR shielding tensors for periodic systems. Our scheme evaluates the shielding tensor as the second derivative of the total electronic energy with respect to a nuclear magnetic moment and an external magnetic field. Both the induced current density J(α) due to the first perturbation from the nuclear magnetic moment as well as the interaction of J(α) with the second perturbation in the form of an external magnetic field are evaluated analytically. Our approach is based on Kohn–Sham density functional theory and gauge-including atomic orbitals. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn–Sham potential fully without the use of effective core potentials. The method is implemented into the periodic program BAND. The new scheme represents an improvement over a previously proposed method in that use can be made of the zero-order Kohn–Sham orbitals from a calculation based on a primitive cell instead of a supercell. Further, J(α) is evaluated analytically rather than by a finite difference approach. The improvements reduce the required computational time by up to two orders of magnitude for three-dimensional systems. Such a reduction is made possible by the fact that we are using atomic centered basis functions. The new implementation is further able to take into account scalar relativistic effects within the zero-order regular approximation. Results from calculations of NMR shielding constants based on the present approach are presented for systems with one-, two-, and three-dimensional periodicity. The reported values are compared to experiment and results from the previously proposed scheme.

Solid-state 207Pb nuclear magnetic resonance studies of adducts of 1,10-phenanthroline with lead(II) halides

Experimental and predicted 207Pb nuclear magnetic resonance (NMR) parameters of solid-state coordination complexes of lead(II) bromide, lead(II) iodide, and lead(II) chloride with 1,10-phenanthroline are reported. Structural and electronic differences between the 1:1 and 1:2 adducts are reflected by the NMR parameters. The NMR chemical shieldings of the isostructural complexes indicate that the electronic state of the lead(II) center depends on the number of ligands and the halogen anion. The NMR results suggest that the 1:2 adduct may be more stereochemically active than the 1:1 adduct.