Quadrupole Coupling Research Articles

Evaluating the motional timescales contributing to averaged anisotropic interactions in MAS solid-state NMR

Abstract. Dynamic processes in molecules can occur on a wide range of timescales, and it is important to understand which timescales of motion contribute to different parameters used in dynamics measurements. For spin relaxation, this can easily be understood from the sampling frequencies of the spectral-density function by different relaxation-rate constants. In addition to data from relaxation measurements, determining dynamically averaged anisotropic interactions in magic-angle spinning (MAS) solid-state NMR allows for better quantification of the amplitude of molecular motion. For partially averaged anisotropic interactions, the relevant timescales of motion are not so clearly defined. Whether the averaging depends on the experimental methods (e.g., pulse sequences) or conditions (e.g., MAS frequency, magnitude of anisotropic interaction, radio-frequency field amplitudes) is not fully understood. To investigate these questions, we performed numerical simulations of dynamic systems based on the stochastic Liouville equation using several experiments for recoupling the dipolar coupling, chemical-shift anisotropy or quadrupolar coupling. As described in the literature, the transition between slow motion, where parameters characterizing the anisotropic interaction are not averaged, and fast motion, where the tensors are averaged leading to a scaled anisotropic quantity, occurs over a window of motional rate constants that depends mainly on the strength of the interaction. This transition region can span 2 orders of magnitude in exchange-rate constants (typically in the microsecond range) but depends only marginally on the employed recoupling scheme or sample spinning frequency. The transition region often coincides with a fast relaxation of coherences, making precise quantitative measurements difficult. Residual couplings in off-magic-angle experiments, however, average over longer timescales of motion. While in principle one may gain information on the timescales of motion from the transition area, extracting such information is hampered by low signal-to-noise ratio in experimental spectra due to fast relaxation that occurs in the same region.

A global rho-axis method for fitting asymmetric tops with one methyl internal rotor and two 14N nuclei: Application of BELGI-2N to the microwave spectra of four methylimidazole isomers.

A number of internal rotation codes can deal with the combination of one or two internal rotors with one 14N quadrupole nucleus, but once it comes to two 14N nuclei, no such code is available even for the case of one internal rotor. We present here the extension of our internal rotor program called BELGI-2N using the rho-axis method global approach to deal with compounds containing one methyl rotor and two weakly coupling 14N nuclei. To test our new code, we applied it to the microwave data recorded for N-methylimidazole, 2-methylimidazole, 4-methylimidazole, and 5-methylimidazole using a chirped-pulse Fourier transform microwave spectrometer in the 7.0-18.5GHz frequency range. Compared to the previously published study, BELGI-2N was able to (i) significantly increase the number of assigned and fitted lines, (ii) fit the complete datasets considering both the internal rotation and the 14N nuclear quadrupole coupling effects simultaneously, and (iii) achieve standard deviations within the measurement accuracy for all methylimidazole isomers.

Electric Field Gradient in Chiral and Tetrahedral Molecules within High-Order LRESC Formalism.

In this work, we present the electric field gradient (EFG) given by the linear response elimination of the small component (LRESC) scheme up to the 1/c4 order (c is the speed of light in vacuum) in CHFClX (X = Br, I, At) chiral molecules, together with CHF2Br and CH2FX (X = Br, I, At) tetrahedral systems. The former could be good candidates for further parity violation studies, especially when heavy atoms are surrounding. In this context, the LRESC scheme demonstrates effective applicability to large tetrahedral and chiral molecules that incorporate heavy elements, with relativistic effects playing a crucial role. The LRESC results of EFG exhibit an excellent agreement with those calculated at the four-component level, giving differences of only hundredths order in a.u. (atomic units) for the bromine nucleus and less than 0.1 a.u. for the iodine nucleus. Regarding the other nuclei, for the chiral molecules, there is a heavy atom effect on the light atom (HALA) for chlorine and fluorine atoms as the substituent halogen atom becomes heavier. Furthermore, the electronic part of the EFG for the central carbon and the fluorine nuclei presents an important dependence with the environment in the molecules under study. With accurate calculations of the EFG and tabulated nuclear quadrupole moment, the nuclear quadrupole coupling constant is obtained within the LRESC scheme, including for the first time correlation effects on the spin-dependent corrections with this methodology, providing results close to the experimental ones for Cl, Br, and I atoms. At the Hartree-Fock level, the differences are around 6% for Br and I nuclei, and at the density functional theory level with the LDA and PBE0 functionals, the differences are no more than 2%.

The effect of microsolvation on the structure, nuclear quadrupole coupling, and internal rotation: The methyl carbamate⋯(H2O)1-3 complexes.

Microsolvation of the carbamate moiety delivers precise information on complexation effects on the N-C=O backbone and is of relevance to the peptide bond functionality. In this context, the mono-, di-, and trihydrated complexes of methyl carbamate have been studied in molecular expansion by high-resolution microwave spectroscopy, using chirped-pulse and Fabry-Perot resonator Fourier transform microwave instruments covering the frequency range from 2 to 18GHz. From the rotational constants of the parent and the 18Ow substituted monoisotopologues, accurate values have been derived for the geometries of the hydrogen bond interactions. The nuclear quadrupole coupling constant χcc of the nitrogen nucleus provides a direct measure of complexation changes and decreases with the degree of hydration, whereas the hindered internal rotation barrier increases slightly with microsolvation. Both tendencies could have a common origin in the π-cooperative inductive effects as the microsolvation series progresses. All transitions are split by the internal rotation of the methyl top and the nuclear quadrupole coupling, and in the largest cluster, they are additionally split by an inversion motion.

Rotational spectrum, structure, and quadrupole coupling of cyclopropylchloromethyldifluorosilane.

Cyclopropylchloromethyldifluorosilane, c-C3H5SiF2CH2Cl, has been synthesized, and its rotational spectrum has been recorded by chirped-pulse Fourier transform microwave spectroscopy. The spectral analysis of several isotopologues indicates the presence of two distinct conformations in the free-jet expansion, which are interconvertible through a rotation of the chloromethyl group. A partial substitution structure is presented for the lower energy conformation and is compared to the equilibrium structure obtained from quantum chemical calculations. Additionally, the presence of the chlorine nucleus leads to the rotational transitions splitting into multiple hyperfine components and χaa, a measure of the electric field gradient along the a axis, is unusually small at merely +0.1393(73) MHz. Various common abinitio and density functional theory methods fail to predict good quadrupole coupling constants (in the principal axis system) that adequately reproduce the observed hyperfine splitting, although diagonalizing the quadrupole coupling tensor from the principal axis system into a nucleus-centered axis system reveals that, overall, these methods calculate reasonably the electric field gradient about the chlorine nucleus. Finally, a total of nine electric dipole forbidden, quadrupole allowed transitions are observed in the rotational spectra of the parent species of the higher energy conformation and the 37Cl isotopologue of the lower energy conformation. These include those of x-type (no change in parity of Ka or Kc), which, to our knowledge, is the first time such transitions have been observed in a chlorine-containing molecule.

Anti‐Coronavirus Activity of Certain Herbacetin Derivatives, A Theoretical Study

AbstractFlavonoids are natural products commonly found in the human diet with anti‐viral activity. The electrochemical activity of flavonoids is effective in their inhibitory properties. Herbacetin is an anti‐coronavirus drug from the flavonoid family. To understand structure‐electrochemical activity relations, ab initio calculations on some selected herbacetin derivatives were carried out using Gaussian 09 in B3LYP/6‐311G*. The effect of the position and type of the various substituents in the ring A of the flavone backbone are considered. The oxygen charge density of the hydroxyl group on C8 (O8) in the considered herbacetins was compared using nuclear quadrupole coupling constants (NQCC) calculations. Results showed that the presence of the amino group in the ortho position of O8 has the most significant effect on increasing the charge density of the O8 atom (O8‐NQCC=9.23 MHz). Based on the proposed mechanism of these drugs, ortho‐amino herbacetin is expected to show a significant anti‐coronavirus effect. Comparison of calculated O8‐NQCCs of tangeretin and nobiletin with herbacetin shows that with the replacement of OH with OCH3, the charge density of oxygen atoms decreases (about 2 MHz). Therefore tangeretin and nobiletin have a lower drug effect than herbacetin. Natural bond orbital (NBO) results are in agreement with calculated NQCCs.

Experimental Evidence for Non‐Fermi‐Contact J Coupling Across Chalcogen Bonds in Ionic Salt Cocrystal Polymorphs

AbstractA pair of novel polymorphic ionic cocrystals of 3,4‐dicyanotelluradiazole and tetraphenylphosphonium bromide are synthesized and are characterized by single‐crystal XRD. Strong and directional non‐covalent chalcogen bonds (ChB) between Te and Br are analyzed via solid‐state NMR to reveal large and anisotropic J(125Te,79/81Br) coupling tensors, providing unequivocal evidence for non‐Fermi contact contributions across ChBs. Along with large 79/81Br quadrupolar couplings for the Br− anions, these data provide new tools to characterize chalcogen bonds and to differentiate between ChB polymorphs.

Experimental Evidence for Non-Fermi-Contact J Coupling Across Chalcogen Bonds in Ionic Salt Cocrystal Polymorphs.

A pair of novel polymorphic ionic cocrystals of 3,4-dicyanotelluradiazole and tetraphenylphosphonium bromide are synthesized and are characterized by single-crystal XRD. Strong and directional non-covalent chalcogen bonds (ChB) between Te and Br are analyzed via solid-state NMR to reveal large and anisotropic J(125Te,79/81Br) coupling tensors, providing unequivocal evidence for non-Fermi contact contributions across ChBs. Along with large 79/81Br quadrupolar couplings for the Br- anions, these data provide new tools to characterize chalcogen bonds and to differentiate between ChB polymorphs.

Multinuclear Residual Quadrupolar Couplings for Structure and Assignment.

Most stable isotopes have a nuclear spin >1/2, but the quadrupole interaction poses challenge on their detection by nuclear magnetic resonance (NMR). On the other hand, the quadrupole interaction is a rich source of structural information that may be exploited for solution NMR in the form of residual quadrupolar couplings (RQCs) of weakly oriented samples. While 2H RQCs are now well established for structure verification and enantiomeric discrimination of organic molecules, we will in this article highlight some recent work on RQCs of other nuclei (especially 7Li and 11B).

Accurate Experimental Structure of 1-Chloronaphthalene.

The structure of isolated 1-chloronaphthalene has been investigated in a supersonic expansion by high-resolution chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy in the 2-8 GHz frequency range. Accurate values of the rotational, centrifugal distortion, and nuclear quadrupole coupling constants for the only availabe conformer have been determined. The intensity of the spectrum allowed us to observe all the heavy atoms isotopologues in natural abundance, determining their rotational constants. From the extensive experimental dataset we derived accurate structures for 1-chloronaphthalene using different methodologies and compared with related compounds.

17O Solid-State NMR Spectroscopy of Lipid Membranes.

Despite the limitations posed by poor sensitivity, studies have reported the unique advantages of 17O based NMR spectroscopy to study systems existing in liquid, solid, or semisolid states. 17O NMR studies have exploited the remarkable sensitivity of quadrupole coupling and chemical shift anisotropy tensors to the local environment in the characterization of a variety of intra- and intermolecular interactions and motion. Recent studies have considerably expanded the use of 17O NMR to study dynamic intermolecular interactions associated with some of the challenging biological systems under magic angle spinning (MAS) and aligned conditions. The very fast relaxing nature of 17O has been well utilized in cellular and in vivo MRS (magnetic resonance spectroscopy) and MRI (magnetic resonance imaging) applications. The main focus of this Review is to highlight the new developments in the biological solids with a detailed discussion for a few selected examples including membrane proteins and nanodiscs. In addition to the unique benefits and limitations, the remaining challenges to overcome, and the impacts of higher magnetic fields and sensitivity enhancement techniques are discussed.

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.

Formic Acid-Ammonia Heterodimer: A New Δ-Machine Learning CCSD(T)-Level Potential Energy Surface Allows Investigation of the Double Proton Transfer.

The formic acid-ammonia dimer is an important example of a hydrogen-bonded complex in which a double proton transfer can occur. Its microwave spectrum has recently been reported and rotational constants and quadrupole coupling constants were determined. Calculated estimates of the double-well barrier and the internal barriers to rotation were also reported. Here, we report a full-dimensional potential energy surface (PES) for this complex, using two closely related Δ-machine learning methods to bring it to the CCSD(T) level of accuracy. The PES dissociates smoothly and accurately. Using a 2d quantum model the ground vibrational-state tunneling splitting is estimated to be less than 10-4 cm-1. The dipole moment along the intrinsic reaction coordinate is calculated along with a Mullikan charge analysis and supports the mildly ionic character of the minimum and strongly ionic character at the double-well barrier.

Hyperfine-resolved rotational spectroscopy of HCNH.

The rotational spectrum of the molecular ion HCNH+ is revisited using double-resonance spectroscopy in an ion trap apparatus, with six transitions measured between 74 and 445GHz. Due to the cryogenic temperature of the trap, the hyperfine splittings caused by the 14N quadrupolar nucleus were resolved for transitions up to J = 4 ← 3, allowing for a refinement of the spectroscopic parameters previously reported, especially the quadrupole coupling constant eQq.

Exploring the properties of the VB− defect in hBN: optical spin polarization, Rabi oscillations, and coherent nuclei modulation

Optically active point defects in semiconductors have received great attention in the field of solid-state quantum technologies. Hexagonal boron nitride, with an ultra-wide band gap Eg = 6 eV, containing a negatively charged boron vacancy ( VB− ) with unique spin, optical, and coherent properties presents a new two-dimensional platform for the implementation of quantum technologies. This work establishes the value of VB− spin polarization under optical pumping with λ ext = 532 nm laser using high-frequency (ν mw = 94 GHz) electron paramagnetic resonance (EPR) spectroscopy. In optimal conditions polarization was found to be P ≈ 38.4%. Our study reveals that Rabi oscillations induced on polarized spin states persist for up to 30–40 μs, which is nearly two orders of magnitude longer than what was previously reported. Analysis of the coherent electron–nuclear interaction through the observed electron spin echo envelope modulation made it possible to detect signals from remote nitrogen and boron nuclei, and to establish a corresponding quadrupole coupling constant C q = 180 kHz related to nuclear quadrupole moment of 14N. These results have fundamental importance for understanding the spin properties of boron vacancy.

Ammonia – Formic acid complex: internal rotation analysis, calculations, and new microwave measurements

New analysis and spectra are reported for the gas-phase ammonia-formic acid complex. Calculations to determine the theoretical barrier to internal rotation were conducted and led to the new internal rotation analysis of the dimer. Using the new analysis and calculations, 12 new lines were measured and assigned and included in the present analysis. This is the first internal rotation analysis for this complex. The measurements were made in the 7–22 GHz range using two Flygare-Balle type pulsed beam Fourier transform microwave (FTMW) spectrometers. The complex was analyzed as a hindered rotor and 20 A and 16 E state transitions were fit with the XIAM5 program. The rotational constants were determined to have the following values: A = 11970.19(9) MHz, B = 4331.479(4) MHz, and C = 3227.144(4) MHz. Rotational constants, quadrupole coupling constants, and internal rotor parameters were fit to the spectrum. Double resonance was used to verify line assignments and access higher frequencies. The barrier to internal rotation was found to be 195.18(7) cm−1. High level calculations are in good agreement with experimental values. The calculated V3 barrier values range from 168.3 to 212.8 cm−1.

Experimental nuclear quadrupole resonance and computational study of the structurally refined topological semimetal TaSb2

The local electric field gradients and magnetic dynamics of TaSb2 have been studied using Sb121, Sb123, and Ta181 nuclear quadrupole resonance (NQR) with density functional theory (DFT) calculations using XRD-determined crystal structures. By measuring all structurally expected 13 NQR lines, the nuclear quadrupole coupling constant (νQ) and asymmetric parameter (η) for Ta, Sb(1), and Sb(2) sites were obtained. These values are all in good agreement with the presented DFT calculations. Principal axes of the electric field gradients was determined for a single-crystal sample by measuring the angular dependencies of NMR frequency under a weak magnetic field. The unusual temperature dependence of η(T) of Sb(2) hints at the suppressed thermal expansion along the a axis. Spin-lattice relaxation rate (1/T1T) measurements reveal an activated-type behavior and an upturn below 30 K. Neither the low-temperature upturn nor the high-temperature activation-type behaviors are reproduced by the calculated 1/T1T based on the calculated density of states (DOS). On the other hand, the agreement between the calculated DOS and specific heat measurements indicates that the band renormalization is small. This fact indicates that TaSb2 deviates from the simple semimetal scenario, and magnetic excitations are not captured by Fermi liquid theory. Published by the American Physical Society 2024

Polar covalent apex-base bonding in borapyramidanes probed by solid-state NMR and DFT calculations.

Pyramidane molecules have attracted chemists for many decades due to their regular shape, high symmetry and their correspondence in the macroscopic world. Recently, experimental access to a number of examples has been reported, in particular the rarely reported square pyramidal bora[4]pyramidanes. To describe the bonding situation of the nonclassical structure of pyramidanes, we present solid-state Nuclear Magnetic Resonance (NMR) as a versatile tool for deciphering such bonding properties for three now accessible bora[4]pyramidane and dibora[5]pyramidane molecules. 11 B solid-state NMR spectra indicate that the apical boron nuclei in these compounds are strongly shielded (around -50 ppm vs. BF3 -Et2 O complex) and possess quadrupolar coupling constants of less than 0.9 MHz pointing to a rather high local symmetry. 13 C-11 B spin-spin coupling constants have been explored as a measure of the bond covalency in the borapyramidanes. While the carbon-boron bond to the -B(C6 F5 )2 substituents of the base serves as an example for a classical covalent 2-center-2-electron (2c-2e) sp2 -carbon-sp2 -boron σ-bond with 1 J(13 C-11 B) coupling constants in the order of 75 Hz, those of the boron(apical)-carbon(basal) bonds in the pyramid are too small to measure. These results suggest that these bonds have a strongly ionic character, which is also supported by quantum-chemical calculations.

The EFG Rosetta Stone: translating between DFT calculations and solid state NMR experiments.

We present a comprehensive study on the best practices for integrating first principles simulations in experimental quadrupolar solid-state nuclear magnetic resonance (SS-NMR), exploiting the synergies between theory and experiment for achieving the optimal interpretation of both. Most high performance materials (HPMs), such as battery electrodes, exhibit complex SS-NMR spectra due to dynamic effects or amorphous phases. NMR crystallography for such challenging materials requires reliable, accurate, efficient computational methods for calculating NMR observables from first principles for the transfer between theoretical material structure models and the interpretation of their experimental SS-NMR spectra. NMR-active nuclei within HPMs are routinely probed by their chemical shielding anisotropy (CSA). However, several nuclear isotopes of interest, e.g.7Li and 27Al, have a nuclear quadrupole and experience additional interactions with the surrounding electric field gradient (EFG). The quadrupolar interaction is a valuable source of information about atomistic structure, and in particular, local symmetry, complementing the CSA. As such, there is a range of different methods and codes to choose from for calculating EFGs, from all-electron to plane wave methods. We benchmark the accuracy of different simulation strategies for computing the EFG tensor of quadrupolar nuclei with plane wave density functional theory (DFT) and study the impact of the material structure as well as the details of the simulation strategy. Especially for small nuclei with few electrons, such as 7Li, we show that the choice of physical approximations and simulation parameters has a large effect on the transferability of the simulation results. To the best of our knowledge, we present the first comprehensive reference scale and literature survey for 7Li quadrupolar couplings. The results allow us to establish practical guidelines for developing the best simulation strategy for correlating DFT to experimental data extracting the maximum benefit and information from both, thereby advancing further research into HPMs.

Understanding Cu(i) local environments in MOFs via63/65Cu NMR spectroscopy.

The field of metal-organic frameworks (MOFs) includes a vast number of hybrid organic and inorganic porous materials with wide-ranging applications. In particular, the Cu(i) ion exhibits rich coordination chemistry in MOFs and can exist in two-, three-, and four-coordinate environments, which gives rise to many structural motifs and potential applications. Direct characterization of the structurally and chemically important Cu(i) local environments is essential for understanding the sources of specific MOF properties. For the first time, 63/65Cu solid-state NMR has been used to investigate a variety of Cu(i) sites and local coordination geometries in Cu MOFs. This approach is a sensitive probe of the local Cu environment, particularly when combined with density functional theory calculations. A wide range of structurally-dependent 63/65Cu NMR parameters have been observed, including 65Cu quadrupolar coupling constants ranging from 18.8 to 74.8 MHz. Using the data from this and prior studies, a correlation between Cu quadrupolar coupling constants, Cu coordination number, and local Cu coordination geometry has been established. Links between DFT-calculated and experimental Cu NMR parameters are also presented. Several case studies illustrate the feasibility of 63/65Cu NMR for investigating and resolving inequivalent Cu sites, monitoring MOF phase changes, interrogating the Cu oxidation number, and characterizing the product of a MOF chemical reaction involving Cu(ii) reduction to Cu(i). A convenient avenue to acquire accurate 65Cu NMR spectra and NMR parameters from Cu(i) MOFs at a widely accessible magnetic field of 9.4 T is described, with a demonstrated practical application for tracking Cu(i) coordination evolution during MOF anion exchange. This work showcases the power of 63/65Cu solid-state NMR spectroscopy and DFT calculations for molecular-level characterization of Cu(i) centers in MOFs, along with the potential of this protocol for investigating a wide variety of MOF structural changes and processes important for practical applications. This approach has broad applications for examining Cu(i) centers in other weight-dilute systems.