Nuclear magnetic relaxation by quadrupole interactions in non-spherical molecules

The nuclear magnetic relaxation times associated with quadrupole interactions are investigated by an analytical method for molecules that may be linear or symmetric rotators, or may be totally asymmetric. The molecules are subject to random thermal couples, and it is supposed that the consequent rotational motion is Brownian. The results are in agreement with those obtained otherwise by Hubbard for the special case of spherical molecules.     

Radial motion of a solid spherical body in a magnetic field

The object of the present paper is to investigate the radial motion of a solid spherical body, assumed to be homogeneous, isotropic and elastic, in presence of a magnetic field in the azimuthal direction. The body is assumed to be in a state of initial stress which is hydrostatic in nature. This theory of radial motion of a solid spherical body in a magnetic field has been utilised to find the small radial motion of a solid Earth assumed to be homogeneous isotropic elastic sphere in presence of a magnetic field in the azimuthal direction. Considering the effect of gravity and the initial stress produced by slow process of creep due to extra masses over the surface of the Earth, the fundamental equations of motion are derived which are non-linear in character and are solved. The times of a desired radial displacement are calculated in presence of a magnetic field only and in presence of the same magnetic field, initial stress and gravitational field, which are compared and exhibited numerically.     

Nonadiabatic theory of diamagnetic susceptibility of molecules

A nonadiabatic theory of diamagnetic susceptibility of molecules is presented in which the electrons and nuclei are considered to be a united system of charged particles whose motion is simultaneously per-turbed by a magnetic field. It is found that on separating out the translational motion of the molecule as a whole, there is certain freedom in choosing the phase of the wave function. Its optimum choice corresponds to the gauge of the vector potential with which two contributions opposite in sign to the magnetic susceptibility—the first order diamagnetism and the second order paramagnetism—have minimum magnitudes. Expressions for non-adiabatic calculations of the diamagnetic susceptibility of atoms and molecules are derived. The diamagnetic contributions to the energy of the hydrogen, helium, and lithium atoms, the hydrogen molecule, the π^?μ^?π⁺μ⁺ and p ^? K ^? p ⁺ K ⁺ mesomolecules, and the positronium molecule e ^? e ^? e ⁺ e ⁺ are calculated. The nonadiabatic contribution of the nuclear motion to the diamagnetic susceptibility amounts to 0.01–0.1% for ordinary atoms and molecules, is increased by several hundred times on passing to mesomolecules, and reaches 50% for the positronium molecule.     

Mössbauer relaxation spectra of the spherical superparamagnetic particles with zero energy of anisotropy

Superoperator equations of Fokker-Planck type, describing the common dynamics of the hyperfine field and the nuclear spin are derived under the conditions of diffusional motion of the magnetic moment of the particles. The solution of this equation in the case of particles with zero energy of magnetic anisotropy is considered. Mössbauer spectra of⁵⁷Fe nuclei are calculated over a large range of the diffusion coefficient.     

Nuclear spin-spin coupling constants prediction based on XGBoost and LightGBM algorithms

Nuclear magnetic resonance (NMR) is a robust method for the analysis of molecular complex structures, and the measurement of the nuclear spin–spin coupling constant is the key. In this paper, based on the 3D coordinates of the atoms in the molecule, the spin–spin coupling constants of atom-pairs are directly predicted using Extreme Gradient Boosting (XGBoost) and Light Gradient Boosting Machine (LightGBM). The calculated result of DFT method is taken as the target value. Experiment shows that LightGBM (R²: 0.93) overall performance is better than XGBoost. In some molecules, the predicted fit (R²) of the coupling constant between atoms even reached 1.00. This research avoids complex quantum mechanics and can assist in NMR to gain insight into the structure and dynamics of molecules, thereby enriching the data information analysis method of nuclear magnetic interaction.     

<Superscript>23</Superscript>Na and <Superscript>27</Superscript>Al NMR Study of Structure and Dynamics in Mordenite

Temperature dependencies of ²⁷Al and ²³Na nuclear magnetic resonance spectra and spin–lattice relaxations in mordenite have been studied in static and magic angle spinning regimes. Our data show that the spin–lattice relaxations of the ²³Na and ²⁷Al nuclei are mainly governed by interaction of nuclear quadrupole moments with electric field gradients of the crystal, modulated by translational motion of water molecules in the mordenite channels. At temperatures below 200 K, the dipolar interaction of nuclear spins with paramagnetic impurities becomes an important relaxation mechanism of the ²³Na and ²⁷Al nuclei.     

Calculations of intermolecular interactions and their influences on structure and13C,1H magnetic shielding constants of solute molecules

On the basis of an improved method of molecular mechanics the spatial structures of molecular clusters modelling the solvate shell of methane in acetone and benzene, 2,9,10-trimethyl-1,3-dithia-5,6-benzocycloheptene in carbon disulfide have been calculated. The nuclear magnetic shielding constants for these structures are calculated by quantum chemical methods in the approach of the density functional theory of the B3LYP/6-31(d,p) level with the usage of gauge-invariant atomic orbitals. It is shown that the increase of the number of the solvent molecules results in better agreement of the calculated and experimental values of¹H and¹³C chemical shifts.     

Magnetic shielding and spin-rotation interaction in ground state alkali molecules

Precision measurements of nuclear magnetic dipole moments in alkali molecules are performed using atom-molecule exchange optical pumping. A comparison with measurements on alkali atoms gives the magnetic shielding differences between atoms and molecules and an approximate value for the spin-rotation interaction constant of the alkali molecules. It is reported on experiments on³⁹K₂ and⁸⁷Rb₂.     

Ab initio NMR parameters of BrCH3 and ICH3 with relativistic and vibrational corrections

This study is focused on two effects identified when NMR parameters are calculated based on first principles. These effects are 1. vibrational correction of properties when using ab initio optimized equilibrium geometry; 2. relativistic effects and limits of using the Flygare equation. These effects have been investigated and determined for nuclear spin-rotation constants and nuclear magnetic shieldings for the CH₃Br and CH₃I molecules. The most significant result is the difference between chemical shieldings determined based on the ab initio relativistic four-component Dirac-Coulomb Hamiltonian and chemical shieldings calculated using experimental values and the Flygare equation. This difference is approximately 320 ppm and 1290 ppm for ⁷⁹Br and ¹²⁷I in the CH₃X molecule, respectively.     

Control of the nuclear spin of the <Superscript>129</Superscript>Xe and <Superscript>131</Superscript>Xe isotopes in the spin-exchange interaction with <Superscript>87</Superscript>Rb atoms

Nuclear spin dynamics of the ¹²⁹Xe and ¹³¹Xe isotopes in an external magnetic field B ₀ is considered. Nuclear spin is pumped by the laser through ⁸⁷Rb, which transfers the electron spin to the ¹²⁹Xe and ¹³¹Xe nuclei in the spin-exchange interaction. The nuclear spin dynamics is controlled with a transverse magnetic field that causes nuclear magnetic resonance in both ¹²⁹Xe and ¹³¹Xe isotopes. Numerical calculations are performed to find conditions at which the transverse component of the nuclear spin in the established motion is of maximum and the slope angle relative to the vector of the constant magnetic field B ₀ is 45°. This regime is taken to be optimal for simulation of practical applications. It is also found that the pump of the nuclear spin of xenon is strongly attenuated when the rubidium polarization vector is turned to the plane perpendicular to the external magnetic field vector B ₀.     

Nuclear vibrations and rotations of like nucleons in the same shell in even-even nuclei

The vibrational and rotational motions in even nuclei are considered. A microscopic study of these motions leads to a relation between the vibrational motion in spherical nuclei and the rotational motion in deformed nuclei. Nuclei with like nucleons in the same shell are considered. The quadrupole two-body interactions are used in the large singlej-shell of even nuclei. The energies and transition operators of nuclei in the nuclear rotational region are calculated using this microscopic method. Quadrupole moments are also calculated. These calculations are compared with the rotational model of the aligned coupling scheme. The present calculations are in good agreement with previous calculations.     

Analytical approach to the study of molecular rotation in liquids

The rotational thermal motion of molecules is investigated by the combined use of the stochastic rotation operator, the Euler-Langevin equations of Brownian motion and the Krylov-Bogoliubov method of solving nonlinear differential equations. The results are applied to dielectric relaxation by orientational polarization and to nuclear magnetic relaxation by a variety of mechanisms.     

Nuclear magnetic spin-rotational relaxation times for symmetric molecules

It is shown that the problem of calculating times related to nuclear magnetic spin-rotational interactions may be solved for the symmetric rotator model of a molecule by employing the method already proposed in a general manner for asymmetric molecules that undergo rotational thermal motion. Expressions are derived for the spin-rotational correlation time and for the contributions arising from spin-rotational interactions to the longitudinal and transverse relaxation times.     

The role of Fermi motion and quark exchange as a nuclear medium effect in the nuclear structure function of 3He, 3H nuclei and their EMC effects

To extract the nuclear structure function of light nuclei like ³He and ³H, the convolution of proton and neutron structure functions in the conventional approach could not explain the modification of nuclear structure functions of these nuclei because of some nuclear medium effects. There are some models that have some success to explain the modification of nuclear structure functions in limited x range. So in this investigation the quark exchange model is considered to extract the nuclear medium effect of this phenomenon (quark exchange effect) for nuclear structure functions of ³He and ³H nuclei. The Fermi motion part of the nuclear structure functions for these nuclei is extracted by taking the GRV’s neutron and proton structure functions in the conventional approach. So the nuclear structure functions and the EMC ratios of ³He and ³H nuclei are calculated by considering both Fermi motion and the nuclear medium effect of quark exchange. Finally the extracted results are compared with available data.     

Theory of nuclear magnetic spin-rotational relaxation for asymmetric molecules

A stochastic differential equation study of nuclear magnetic relaxation by spin-rotational interactions was successfully completed for spherical, symmetric rotator and linear molecules. This theory has now been extended to asymmetric rotator molecules by first establishing the conditions under which such an extension is mathematically feasible and then investigating the consequences of accepting these conditions.     

<Superscript>27</Superscript>Al NMR Study of the Structure and Dynamics of Natrolite

The temperature dependences of nuclear magnetic resonance and magic angle spinning nuclear magnetic resonance spectra of ²⁷Al nuclei in natrolite (Na₂Al₂Si₃O₁₀· 2H₂O) have been studied. The influence of water molecules and sodium ions mobility on the shape of the ²⁷Al NMR spectrum and framework dynamics have been discussed The temperature dependences of the spin–lattice relaxation times T₁ of ²⁷Al nuclei in natrolite have also been studied. It has been shown that the spin–lattice relaxation of the ²⁷Al is governed by the electric quadrupole interaction with the crystal electric field gradients modulated by translational motion of H₂O molecules in the natrolite pores. The dipolar interactions with paramagnetic impurities become significant as a relaxation mechanism of the ²⁷Al nuclei only at low temperatures (<270 K).     

季铵盐型双子表面活性剂16-4-16聚集状态的NMR研究

核磁共振弛豫，自扩散以及2D NOESY谱研究结果表明：双子表面活性剂16-4-16溶液在形成胶束的过程中，联结基团及其邻近的碳氢链质子形成胶束的壳层，而距离离子头较远的疏水质子位于胶束的内部. 与对应的单链的表面活性剂CTAB相比，其分子运动更受限制. 2D NOESY谱显示联接基团及临近的碳氢链的质子间有较强的交叉峰，表明形成胶束时，分子在联结基团附近堆积的较为紧密. 由2D NOESY谱计算得到的质子间距与HYPERCHEM模拟值有偏差，表明这些强交叉峰是分子间相互作用的结果，并且对应质子对在双子表面活性剂16-4-16分子中位于邻近的区域. 因此我们推测，双子表面活性剂16-4-16分子在球形胶束中形成特殊的排列方式.     

Vibration-rotation effects on the polarizabilities of CH4 and CD4 calculated from an ab initio polarizability surface

A polarizability surface has been calculated for the methane molecule using a Hartree-Fock wavefunction. Coefficients of the surface are given to second order in terms of both symmetry coordinates and internal coordinates. The polarizability is sensitive to bond stretching and angle bending. The effects of nuclear motion on the polarizabilitles of ¹²CH₄ and ¹²CD₄ have been calculated from the coefficients of the surface. Some of the second order coefficients are found to be significant in contributing to the nuclear motion corrections. The ν₃ mode is the dominant contributor to the corrections. The temperature dependences of the mean molecular polarizabilities of ¹²CH₄ and ¹²CD₄ are also calculated. The results suggest that modern methods of measurement could distinguish between the isotopomers CH_4-n D _n (n=0–4) thereby enabling an experimental surface to be obtained.     

Nuclear deformations in the pairing-plus-quadrupole model (III). Static nuclear shapes in the rare-earth region

The potential energy of deformation (β, γ), is calculated with the pairing-plus-quadrupole model for nuclei with N=82–126, Z=50–82. There is a sudden onset of deformation in the N=86–90 region, and the static nuclear shape, the lowest minimum of the potential function, changes from spherical to prolate. The disappearance of deformation in the Z=74–80 region is more gradual, and the static shape changes from prolate to asymmetric to oblate to spherical. The energy of zero-point motion is calculated, and it is concluded that all the stable deformed shapes of the region are prolate. Proton and neutron energy gaps, intrinsic quadrupole moments, moments of inertia and gyromagnetic ratios of the doubly even nuclei of the rare-earth region are calculated and compared with the experimental data.     

Nuclear spin-lattice relaxation in the triply rotating frame and ultraslow molecular motions in solids

A method for measuring nuclear magnetic spin-lattice relaxation in solids in the effective field H_e3 acting in the triply rotating frame (TRF) is described. The method advances the previously described techniques whereby nuclear magnetic resonance and relaxation in the rotating (RF) and doubly rotating frames (DRF) are measured directly. In the present work, the RF and DRF are employed for suppressing the secular part of nuclear dipole-dipole (DD) interactions in the first two orders. As a result, the higher-order DD interactions (four- and five-particle ones) were separated, and their contribution to the nuclear spin-lattice relaxation in the TRF was studied experimentally. The experiments were carried out on protons in polycrystalline benzene. With the introduced technique, an overall spin-lattice relaxation decay in the TRF was recorded continuously during a single radio-frequency pulse with a length not exceeding 1 s. The contribution of multiproton nonsecular DD interactions to the proton spin-lattice relaxation in the TRF was observed selectively as a pronounced local minimum in the temperature dependence of the relaxation timeT _1ϱϱϱ. This contribution corresponds to ultraslow motion of benzene molecules with a rate about γH_e3 ≈ 2π · (10¹-10³) s^-1 and is determined quantitatively by specific correlation functions corresponding to the multiparticle nonsecular DD interactions of protons. The prospects of using this method for studying ultraslow atomic and molecular dynamics in solids are discussed.