Quadrupolar Parameters Research Articles

Natural abundance oxygen-17 solid-state NMR of metal organic frameworks enhanced by dynamic nuclear polarization.

The 17O resonances of zirconium-oxo clusters that can be found in porous Zr carboxylate metal-organic frameworks (MOFs) have been investigated by magic-angle spinning (MAS) NMR spectroscopy enhanced by dynamic nuclear polarization (DNP). High-resolution 17O spectra at 0.037% natural abundance could be obtained in 48 hours, thanks to DNP enhancement of the 1H polarization by factors ε(1H) = Swith/Swithout = 28, followed by 1H → 17O cross-polarization, allowing a saving in experimental time by a factor of ca. 800. The distinct 17O sites from the oxo-clusters can be resolved at 18.8 T. Their assignment is supported by density functional theory (DFT) calculations of chemical shifts and quadrupolar parameters. Protonation of 17O sites seems to be leading to large characteristic shifts. Hence, natural abundance 17O NMR spectra of diamagnetic MOFs can thus be used to probe and characterize the local environment of different 17O sites on an atomic scale.

The distribution of the electron density and spin density in the interplanar areas CuFeS2by NMR63,65Cu in a local field

Chalcopyrite CuFeS2is a known semiconductor mineral with a wide range of unique physical and chemical properties. These materials can be used as elements of solar batteries, coherent and incoherent sources of polarized radiation, in photovoltaic, thermoelectric and spintronic devices. Despite the relatively large number of studies on CuFeS2, many questions about its magnetic and electronic properties, are still outstanding. In this paper we were carried out studies of the distribution of the electron density and spin density in the nuclei of iron and copper in the semiconductor mineral CuFeS2. Special attention was devoted to interrelation of electronic and spin subsystems of the compound. The results of studies of the compound obtained in NMR63,65Cu local field at low temperatures were used to perform the corresponding analysis. The cluster approach was used. The biggest cluster had Cu9Fe10S28-4formula. Calculations were carried out in the framework of restricted self-consistent Hartree - Fock with open shells (SCF-LCAO-ROHF), MINI basis. The calculations were made with the “foundation” on the quadrupole parameters (quadrupole νQ frequency and the asymmetry parameter of the electric field gradient tensor η), obtained from the experiment. Study of electron density maps were performed for the regions containing chains of Fe-S-Cu and S-Fe-S for the different layers of metals and sulfur atoms. It is shown that the nature of the connection of iron atoms belonging to neighboring layers with sulfur atoms of the intermediate layer is different, which is reflected on the electron density distribution.

Octupole correlations in light actinides from the interacting boson model based on the Gogny energy density functional

The quadrupole-octupole coupling and the related spectroscopic properties have been studied for the even-even light actinides $^{218-238}$Ra and $^{220-240}$Th. The Hartree-Fock-Bogoliubov approximation, based on the Gogny-D1M energy density functional, has been employed as a microscopic input, i.e., to obtain (axially symmetric) mean-field potential energy surfaces as functions of the quadrupole and octupole deformation parameters. The mean-field potential energy surfaces have been mapped onto the corresponding bosonic potential energy surfaces using the expectation value of the $sdf$ Interacting Boson Model (IBM) Hamiltonian in the boson condensate state. The strength parameters of the $sdf$-IBM Hamiltonian have been determined via this mapping procedure. The diagonalization of the mapped IBM Hamiltonian provides energies for positive- and negative-parity states as well as wave functions which are employed to obtain transitional strengths. The results of the calculations compare well with available data from Coulomb excitation experiments and point towards a pronounced octupole collectivity around $^{224}$Ra and $^{226}$Th.

Ligand Control of 59Co Nuclear Spin Relaxation Thermometry.

Studying the correlation between temperature-driven molecular structure and nuclear spin dynamics is essential to understanding fundamental design principles for thermometric nuclear magnetic resonance spin-based probes. Herein, we study the impact of progressively encapsulating ligands on temperature-dependent 59Co T1 (spin–lattice) and T2 (spin–spin) relaxation times in a set of Co(III) complexes: K3[Co(CN)6] (1); [Co(NH3)6]Cl3 (2); [Co(en)3]Cl3 (3), en = ethylenediamine); [Co(tn)3]Cl3 (4), tn = trimethylenediamine); [Co(tame)2]Cl3 (5), tame = triaminomethylethane); and [Co(dinosar)]Cl3 (6), dinosar = dinitrosarcophagine). Measurements indicate that 59Co T1 and T2 increase with temperature for 1–6 between 10 and 60 °C, with the greatest ΔT1/ΔT and ΔT2/ΔT temperature sensitivities found for 4 and 3, 5.3(3)%T1/°C and 6(1)%T2/°C, respectively. Temperature-dependent T2* (dephasing time) analyses were also made, revealing the highest ΔT2*/ΔT sensitivities in structures of greatest encapsulation, as high as 4.64%T2*/°C for 6. Calculations of the temperature-dependent quadrupolar coupling parameter, Δe2qQ/ΔT, enable insight into the origins of the relative ΔT1/ΔT values. These results suggest tunable quadrupolar coupling interactions as novel design principles for enhancing temperature sensitivity in nuclear spin-based probes.

Ruppeiner geometry of isotropic Blume–Emery–Griffiths model

With the aid of Ruppeiner thermodynamic metric defined on a two-dimensional phase space of dipolar (m) and quadrupolar (q) order parameters, we derive an expression for the Ricci scalar (R) in the isotropic Blume–Emery–Griffiths model. Temperature dependence of R is investigated for various values of bilinear to biquadratic ratio (r). Its behavior near the continuous/discontinuous phase transition temperatures and a tricritical point is presented. It is found that in addition to the divergence singularity and finite jumps connected with the phase transitions, there are field-dependent broad extrema in the Ricci scalar.

Neuro-fuzzy modeling of deformation parameters for fusion-barriers

The fusion-barrier distribution is very sensitive to the structure of the colliding nuclei such as nuclear quadrupole and hexadecapole deformation parameters and their signs. If the nuclei that enter the fusion reaction are deformed, the barrier problem becomes complicated. Therefore the deformation parameters are taken into account in the calculations. In this study, Neuro-Fuzzy approach, ANFIS, method has been used for the estimation of ground-state quadrupole (ε2) and hexadecapole (ε4) deformation parameters for the nuclei. According to the results, the method is suitable for this task and one can confidently use it to obtain the data that is not available in the literature.

Neutrino oscillation in the q-metric

We investigate neutrino oscillation in the field of an axially symmetric space-time, employing the so-called q-metric, in the context of general relativity. Following the standard approach, we compute the phase shift invoking the weak and strong field limits and small deformation. To do so, we consider neutron stars, white dwarfs and supernovae as strong gravitational regimes whereas the solar system as weak field regime. We argue that the inclusion of the quadrupole parameter leads to the modification of the well-known results coming from the spherical solution due to the Schwarschild space-time. Hence, we show that in the solar system regime, considering the Earth and Sun, there is a weak probability to detect deviations from the flat case, differently from the case of neutron stars and white dwarfs in which this probability is larger. Thus, we heuristically discuss some implications on constraining the free parameters of the phase shift by means of astrophysical neutrinos. A few consequences in cosmology and possible applications for future space experiments are also discussed throughout the text.

Testing the Kerr nature of supermassive and intermediate-mass black hole binaries using spin-induced multipole moment measurements

The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects []. Here, we apply the idea proposed in reference [] to binary systems composed of supermassive and intermediate-mass black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be ⩽0.1 for almost 3% of the total supermassive binary black hole population which is detectable by LISA whereas it is ∼46% for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity. We find that errors on both the quadrupole and octupole moment parameters can be estimated to be ⩽1 for ∼2% and ∼50% of the population respectively for LISA and DECIGO detectors. Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10% precision.

A Practical Review of NMR Lineshapes for Spin-1/2 and Quadrupolar Nuclei in Disordered Materials.

NMR is a powerful spectroscopic method that can provide information on the structural disorder in solids, complementing scattering and diffraction techniques. The structural disorder in solids can generate a dispersion of local magnetic and electric fields, resulting in a distribution of isotropic chemical shift δiso and quadrupolar coupling CQ. For spin-1/2 nuclei, the NMR linewidth and shape under high-resolution magic-angle spinning (MAS) reflects the distributions of isotropic chemical shift, providing a rich source of disorder information. For quadrupolar nuclei, the second-order quadrupolar broadening remains present even under MAS. In addition to isotropic chemical shift, structural disorder can impact the electric field gradient (EFG) and consequently the quadrupolar NMR parameters. The distributions of quadrupolar coupling and isotropic chemical shift are superimposed with the second-order quadrupolar broadening, but can be potentially characterized by MQMAS (multiple-quantum magic-angle spinning) spectroscopy. We review analyses of NMR lineshapes in 2D DQ–SQ (double-quantum single-quantum) and MQMAS spectroscopies, to provide a guide for more general lineshape analysis. In addition, methods to enhance the spectral resolution and sensitivity for quadrupolar nuclei are discussed, including NMR pulse techniques and the application of high magnetic fields. The role of magnetic field strength and its impact on the strategy of determining optimum NMR methods for disorder characterization are also discussed.

Theoretical and Experimental Study on the Transmission Loss of a Side Outlet Muffler

Vibration and noise reduction methods are important research directions in many industries. Mufflers are widely used in pipelines to reduce noise and vibration transmission. A theoretical analysis is conducted to determine the noise reduction mechanism of a muffler with a side outlet, and the results are verified with experiments. The quadrupole parameters of the muffler are obtained using transfer matrix analysis, and sensitivity analysis of the quadrupole parameters is conducted. The influence of the side outlet location on the transmission loss of the muffler is investigated experimentally using an impedance tube. The key factors affecting the transmission loss are analyzed. The theoretical calculation results of the transmission loss of the side outlet muffler are in good agreement with the experimental results.

Determination of accurate rest frequencies and hyperfine structure parameters of cyanobutadiyne, HC5N

Very accurate transition frequencies of HC5N were determined between 5.3 and 21.4 GHz with a Fourier transform microwave spectrometer. The molecules were generated by passing a mixture of HC3N and C2H2 highly diluted in neon through a discharge valve followed by supersonic expansion into the Fabry-Perot cavity of the spectrometer. The accuracies of the data permitted us to improve the experimental 14N nuclear quadrupole coupling parameter considerably and the first experimental determination of the 14N nuclear spin-rotation parameter. The transition frequencies are also well suited to determine in astronomical observations the local speed of rest velocities in molecular clouds with high fidelity. The same setup was used to study HC7N, albeit with modest improvement of the experimental 14N nuclear quadrupole coupling parameter. Quantum chemical calculations were carried out to determine 14N nuclear quadrupole and spin-rotation coupling parameters of HC5N, HC7N, and related molecules. These calculations included evaluation of vibrational and relativistic corrections to the non-relativistic equilibrium quadrupole coupling parameters; their considerations improved the agreement between calculated and experimental values substantially.

Self-Assembly of DNA and RNA Building Blocks Explored by Nitrogen-14 NMR Crystallography: Structure and Dynamics.

The isotopic enrichment of nucleic acids with nitrogen-15 is often carried out by solid-phase synthesis of oligonucleotides using phosphoramidite precursors that are synthetically demanding and expensive. These synthetic challenges, combined with the overlap of chemical shifts, explain the lag of nitrogen-15 NMR studies of nucleic acids behind those of proteins. For the structural characterization of DNA and RNA-related systems, new NMR methods that exploit the naturally occurring 99.9 % abundant nitrogen-14 isotope are therefore highly desirable. In this study, we have investigated nitrogen-14 spectra of self-assembled quartets based on the nucleobase guanine in the solid state by means of magic-angle spinning NMR spectroscopy. The network of dipolar proton-nitrogen couplings between neighboring stacked purine units is probed by 2D spectra based on 1 H→14 N→1 H double cross-polarization. Interplane dipolar contacts are identified between the stacked G quartets. The assignment is supported by density functional theory (DFT) calculations of the anisotropic chemical shifts and quadrupolar parameters. The experimental spectra are fully consistent with internuclear distances obtained in silico. Averaging of chemical shifts due to internal motions can be interpreted by semiempirical calculations. This method can easily be extended to synthetic G quartets based on nucleobase or nucleoside analogs and potentially to oligonucleotides.

Structure and Catalytic Characterization of a Second Framework Al(IV) Site in Zeolite Catalysts Revealed by NMR at 35.2 T.

Ultrahigh field 27Al{1H} 2D correlation NMR experiments demonstrate that at least two framework Al(IV) sites with hydroxyl groups can exist in acidic zeolite catalysts in their dehydrated and catalytically active states. In addition to the known Al(IV) at the framework bridging acid site (BAS), a new site created by a second tetrahedral Al atom and its hydroxyl group protons in zeolite HZSM-5 is clearly resolved at 35.2 T field strengths, enabled by recently developed series-connected hybrid (SCH) magnet technology. Coupled with computational modeling, extensive 27Al MQMAS experiments at multiple field strengths, and 1H MAS NMR experiments, these data indicate that this second tetrahedrally coordinated Al site (denoted Al(IV)-2) experiences an increased chemical shift and unique quadrupolar parameters relative to the BAS in both dehydrated and hydrated states. These new experimental data, supported by computational and catalytic reaction work, indicate that the second site arises from partially bonded framework (SiO)4-n-Al(OH)n species that significantly increase catalyst reactivity in benzene hydride-transfer and n-hexane cracking reactions. Al(IV)-2 sites result either from framework crystallization defects or from incomplete postsynthetic hydrolysis of a framework Al, prior to the formation of extraframework Al. Populations of this second acidic proton site created by the Al(IV)-2 species are shown to be controlled via postsynthetic catalyst treatments, should be general to different catalyst structures, and significantly enhance catalyst reactivity in the cited probe reactions when they are present. The results herein communicate the highest magnetic field strength data on active zeolite catalyst structures to date and enable for the first time the detection of Al and H association on a dry HZSM-5 catalyst, i.e., under conditions representative of typical end-use processes.

Separation of quadrupolar and paramagnetic shift interactions with TOP-STMAS/MQMAS in solid-state lighting phosphors.

A new approach for processing satellite-transition magic-angle spinning (STMAS) and multiple-quantum magic-angle spinning (MQMAS) data, based on the two-dimensional one-pulse (TOP) method, which separates the second-rank quadrupolar anisotropy and paramagnetic shift interactions via a double shearing transformation, is described. This method is particularly relevant in paramagnetic systems, where substantial inhomogeneous broadening may broaden the lineshapes. Furthermore, it possesses an advantage over the conventional processing of MQMAS and STMAS spectra because it overcomes the limitation on the spectral width in the indirect dimension imposed by rotor synchronization of the sampling interval. This method was applied experimentally to the Al solid-state nuclear magnetic resonance of a series of yttrium aluminum garnets (YAGs) doped with different lanthanide ions, from which the quadrupolar parameters of paramagnetically shifted and bulk unshifted sites were extracted. These parameters were then compared with density functional theory calculations, which permitted a better understanding of the local structure of Ln substituent ions in the YAG lattice.

Quasinormal modes of generalized black holes: δ-Kerr spacetime

The nonlinear superposition of the -metric and the Kerr metric results in a -Kerr metric that represents a deformed Kerr black hole with , where q > 0 is proportional to the nonrelativistic quadrupole moment of the collapsed configuration. We study this spacetime and determine q+ such that for q, 0 < q < q+ , the outer spacetime singularity remains a null hypersurface. In this case, -Kerr spacetime represents a generalized black hole, namely, an asymptotically flat, stationary and axisymmetric vacuum solution of general relativity for which the outer singularity is a closed null hypersurface. For an approximate variant of -Kerr spacetime characterized by mass M, quadrupole parameter q and angular momentum parameter a, where the latter two parameters are treated to first and second orders of approximation, respectively, we analytically determine the quasinormal mode (QNM) frequencies in the ray approach using the light-ring method as well as in the complementary wave approach for massless scalar field perturbations in the a = 0 limit. The QNM frequencies of -Kerr spacetime turn out to be nearly the same as those of the rotating Hartle–Thorne spacetime.

Multiple phase transitions and high-field quadrupolar order in a model for β−TeVO4

Motivated by the complex behavior of the frustrated magnet $\beta$-TeVO$_4$, we study an anisotropic Heisenberg model for coupled spin-$1/2$ zigzag chains. Using cluster mean field approach to capture quantum correlations we find, upon reducing temperature in the absence of applied field, (i) a partially ordered state, (ii) a collinear antiferromagnetic phase, and (iii) an elliptical spiral state characterized by finite vector chirality. For finite fields, we find metamagnetic response close to saturation magnetization. We show via explicit calculations that the quadrupolar order parameter is finite in the metamagnetic regime. The exchange parameters reported in the ab-initio study of $\beta$-TeVO$_4$ are used in our study. We compare our results with those reported in recent experiments on $\beta$-TeVO$_4$ and highlight similarities as well as differences between experimental results and our cluster mean field calculations.

Effects of Li Confined Motion on NMR Quadrupolar Interactions: A Combined 7 Li NMR and DFT-MD Study of LiR2 (PO4 )3 (R=Ti or Zr) Phases.

Ab initio molecular dynamics (MD) simulations and NMR GIPAW (gauge including projector augmented wave) calculations have been used to analyze the coordination and mobility of Li ions in LiTi2(PO4)3 (rhombohedral), LiZr2(PO4)3 (triclinic), and LiZr2(PO4)3 (rhombohedral) phases. Significant discrepancies are observed between static calculations of 7Li quadrupolar parameters and experimental values. The dynamical origin of this disagreement is demonstrated by incorporating in the calculations thermal vibrations and local motion of atoms with MD simulations. For LiTi2(PO4)3, the quadrupolar constant associated with Li ions grows with temperature because the local symmetry of the system decreases, whereas for the Zr phases, the quadrupolar constant decreases because thermal vibrations reduce the anisotropy of the interaction. Finally, for both Zr phases, MD yields Li distributions that compare well with disorder reported from diffraction studies.

The VN2 negatively charged defect in diamond. A quantum mechanical investigation of the EPR response

The VN2− defect in diamond consists of a vacancy surrounded by two substitutional nitrogen atoms, which lower the local symmetry from Td to C2v. Calculations of the doublet ground state geometry, electronic structure, EPR parameters, and IR spectra of this defect are reported along with a preliminary investigation of the observed optical transition. For the most part our results were obtained using a uniform charge compensated supercell approach together with the B3LYP functional and all-electron Gaussian basis sets designed for the properties studied. In particular, the computed hyperfine and quadrupolar EPR parameters for the carbon and nitrogen atoms adjacent to the vacancy agree very well with the experiments (Fermi contact values are 245 MHz vs 241 for 13C, and 4.1 vs 4.0 for 15N). The accompanying spin distribution may be described as a damped spherical spin wave with little spin density on the nitrogen atoms. IR spectra show some interesting features in the range of approximately 360–1310 cm−1, which are absent in the pristine diamond. Functionals without exact exchange, such as PBE, better reproduce the observed zero phonon line.

Simplest static and stationary vacuum quadrupolar metrics

In the present paper we argue that a special case of the Bach-Weyl metric describing a static configuration of two Schwarzschild black holes gives rise, after extending its parameter space to complex values, to a very simple 2-parameter model for the gravitational field of a static deformed mass. We compare this model, which has no restrictions on the quadrupole parameter, with the well-known Zipoy-Voorhees $\delta$-metric and show in particular that the mass quadrupole moment in the latter solution cannot take arbitrary negative values. We subsequently add an arbitrary angular momentum to our static model and study some properties of the resulting 3-parameter stationary solitonic spacetime, which permits us to introduce the notion of the Fodor-Hoenselaers-Perj\'es relativistic multipole moments.

Constraints on the binary black hole nature of GW151226 and GW170608 from the measurement of spin-induced quadrupole moments

According to the "no-hair" conjecture, a Kerr black hole (BH) is completely described by its mass and spin. In particular, the spin-induced quadrupole moment of a Kerr BH with mass $m$ and dimensionless spin $\chi$ can be written as $Q=-\kappa\,m^3\chi^2$, where $\kappa_{\rm BH}=1$. Thus by measuring the spin-induced quadrupole parameter $\kappa$, we can test the binary black hole nature of compact binaries and distinguish them from binaries comprised of other exotic compact objects, as proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we present a Bayesian framework to carry out this test where we measure the symmetric combination of individual spin-induced quadrupole moment parameters fixing the anti-symmetric combination to be zero. The analysis is restricted to the inspiral part of the signal as the spin-induced deformations are not modeled in the post-inspiral regime. We perform detailed simulations to investigate the applicability of this method for compact binaries of different masses and spins and also explore various degeneracies in the parameter space which can affect this test. We then apply this method to the gravitational wave events, GW151226 and GW170608 detected during the first and second observing runs of Advanced LIGO and Advanced Virgo detectors. We find the two events to be consistent with binary black hole mergers in general relativity. By combining information from several more of such events in future, this method can be used to set constraints on the black hole nature of the population of compact binaries that are detected by the Advanced LIGO and Advanced Virgo detectors.