Two-, three-, and four-bond N–F spin–spin coupling constants in fluoroazines

Ab initio EOM-CCSD calculations have been performed to investigate 2-, 3- and 4-bond ¹⁵N–¹⁹F coupling constants in mono-, di-, and trifluoroazines. ²J(N–F) values are negative and are dominated by the Fermi-contact (FC) term. Absolute values of ²J(N–F) tend to decrease as the number of N atoms in the ring increases, and may also be influenced by the number and positions of C–F bonds. ³J(N–F) values are positive with three exceptions, are usually dominated by the FC term, and also tend to decrease as the number of N atoms increases. The three molecules which have negative values of ³J(N–F) have dominant negative paramagnetic-spin orbit (PSO) terms, and are structurally similar insofar as they have an intervening C–F bond between the N and the coupled F. ⁴J(N–F) values are negative because the PSO, FC, and spin-dipole (SD) terms are negative, with only one exception. Four molecules have significantly greater values of ⁴J(N–F). These are structurally similar with the coupled N bonded to two other N atoms. The computed EOM-CCSD ⁿJ(N–F) coupling constants are in good agreement with the few experimental values that are available.     

Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, J_slow (ω), and fast, J_fast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the ¹⁵N-H?···?N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the ¹³C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D _∥/D _⊥?≈?5 at room temperature and for a fast or slow internal motion.     

NMR spin–spin coupling constants in microhydrated ortho-aminobenzoic acid

The influence of the hydrogen-bond formation on the NMR spin–spin coupling constants, including the Fermi contact, the diamagnetic spin–orbit, the paramagnetic spin–orbit and the spin dipole term, has been investigated for the ortho-aminobenzoic acid microhydrated with up to three water molecules. The one-bond and two-bond spin–spin coupling constants for several intra-molecular and across-the-hydrogen-bond atomic pairs are calculated employing high-level density functional theory in combination with the B3LYP functional with two different types of extended basis sets for each level of microhydration. The spin–spin coupling constants, in general, vary inversely with the hydrogen bond length. The Fermi contact term is found to be the dominant contributor to the total value of spin–spin coupling constant followed by the paramagnetic spin–orbit term. The variations of Fermi contact term and atomic charge distribution with size of microhydration follow quite similar trend. The effect of explicit solvation provided by microhydration has also been compared briefly with that of bulk implicit solvation obtained through polarised continuum model and mixed microhydration/continuum approach.     

Density-functional calculations of the nuclear magnetic shielding and indirect nuclear spin–spin coupling constants of three isomers of C20

The parameters of the nuclear magnetic resonance (NMR) spectrum – shielding constants and indirect spin–spin coupling constants – of three isomers of C₂₀ are studied using density-functional theory. The performance of different exchange–correlation functionals is analysed by optimising the geometry for the ring, bowl and cage isomers, followed by a computation of the NMR constants at the optimised structure. The results are analysed and rationalised by performing comparisons of the three isomers with one another and with related systems such as polyynes (for the ring), o-benzyne (for the bowl) and C₆₀ (for the cage). The shielding and spin–spin parameters calculated using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional are sufficiently reliable to assist in future experimental NMR studies of C₂₀ and, in particular, the identification of its isomers.     

Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.     

Prediction of the 1H NMR spectra of epoxy-fused cyclopentane derivatives by calculations of chemical shifts and spin–spin coupling constants

¹H NMR spectra of epoxy-fused cyclopentane derivatives have been computationally investigated with density functional calculations in order to unravel the shielding effect of the epoxy ring on the ¹H NMR chemical shifts of N-substituted epoxy-fused cyclopentane-3, 5-diol derivatives. Both ¹H NMR chemical shifts and spin–spin coupling constants have been calculated with the WP04/cc-pVTZ level of theory in solution. The WP04/cc-pVTZ// B3LYP/6-31+G(d) methodology has been found to reproduce the best experimental results on epoxy-fused cyclopentane derivatives. This study is expected to lead experimentalists in their endeavour to characterize epoxy-fused cyclic systems with ease.     

Interplays ofμSR,susceptibility and neutron studies on dilute-alloy spin glasses

Static spin polarization of Fe moments in a spin glassAuFe, determined by zero-fieldSR, is compared to an ac-susceptibility measurement below the cusp temperatureT _g, and a rather uniform amplitude of the static polarization is pointed out for frozen spins. Completely random orientation of frozen spins is revealed by neutron scattering in a dilute 1%CuMn, and an importance of comparing results of these different methods is demonstrated.     

Stationary states and rotational properties of spin–orbit-coupled Bose–Einstein condensates held under a toroidal trap

We consider a pseudospin-1/2 Bose–Einstein condensate with Rashba spin–orbit coupling in a two-dimensional toroidal trap. By solving the damped Gross–Pitaevskii equations for this system, we show that the system exhibits a rich variety of stationary states, such as vehicle wheel and flower-petal stripe patterns. These stationary states are stable against perturbation with thermal energy and can survive for a long time. In the presence of rotation, our results show that the rotating systems have exotic vortex configurations. These phenomenon originates from the interplay among spin–orbit coupling, trap geometry, and rotation.     

Molecular properties in the Tamm–Dancoff approximation: indirect nuclear spin–spin coupling constants

The Tamm–Dancoff approximation (TDA) can be applied to the computation of excitation energies using time-dependent Hartree–Fock (TD-HF) and time-dependent density-functional theory (TD-DFT). In addition to simplifying the resulting response equations, the TDA has been shown to significantly improve the calculation of triplet excitation energies in these theories, largely overcoming issues associated with triplet instabilities of the underlying reference wave functions. Here, we examine the application of the TDA to the calculation of another response property involving triplet perturbations, namely the indirect nuclear spin–spin coupling constant. Particular attention is paid to the accuracy of the triplet spin–dipole and Fermi-contact components. The application of the TDA in HF calculations leads to vastly improved results. For DFT calculations, the TDA delivers improved stability with respect to geometrical variations but does not deliver higher accuracy close to equilibrium geometries. These observations are rationalised in terms of the ground- and excited-state potential energy surfaces and, in particular, the severity of the triplet instabilities associated with each method. A notable feature of the DFT results within the TDA is their similarity across a wide range of different functionals. The uniformity of the TDA results suggests that some conventional evaluations may exploit error cancellations between approximations in the functional forms and those arising from triplet instabilities. The importance of an accurate treatment of correlation for evaluating spin–spin coupling constants is highlighted by this comparison.     

Spin–spin coupling constants in linear substituted HCN clusters

The indirect nuclear spin–spin coupling constants of homogeneous hydrogen-bonded HCN clusters are compared with those of inhomogeneous HCN clusters where one of the terminal HCN molecules is substituted by its isomer HNC and by LiCN. Both the intra- and intermolecular (across the hydrogen bond) coupling constants are calculated for the linear form of the clusters containing up to three molecular monomers using different hybrid DFT functionals. The geometry of the monomers and clusters is optimised at the B3LYP/6-311++G(d,p) level. The effect of substitution by the ionic compound LiCN on the coupling constants of HCN is found to be more pronounced than that by HNC. The Ramsey parameters that form the total spin–spin coupling constants are also analysed individually. Among the four Ramsey parameters, the Fermi Contact term is found to be the dominant contributor to the total coupling constants in most cases. The presence of LiCN in the cluster tends to decrease the intramolecular Fermi Contact values, while HNC increases the same in all dimers and trimers. The contributions of localised molecular orbitals have been analysed for the HCN–HNC cluster to obtain some additional insight about the SSCC transmission mechanism along the coupling pathway.     

Ground-states and rotational properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate in a concentrically coupled toroidal trap

We investigate the ground states of an antiferromagnetic spin-1 Bose–Einstein condensate with spin–orbit coupling in a concentrically coupled toroidal trap. A new necklace-type state with double-ring structure is created in the system due to the spin–orbit coupling. The petal number of the necklace state is increased with enhancing the strength of the spin–orbit coupling. When the rotation is introduced, the condensate can be dragged into the outer trough of the trap by increasing the rotation frequency, which makes it possible to realize the exotic ground state combined by the necklace state at the inner trough and the persistent flow at the outer one. Once the two troughs of the toroidal trap are populated by the persistent flow at the specific effective interactions between atoms, the hidden vortices may occur in the central region of the trap and at the barrier between the two troughs. In addition, the visible vortex with the laminar structure can be generated under the more effective atomic interaction.     

A review of current research on spin currents and spin–orbit torques

Spintronics is a new discipline focusing on the research and application of electronic spin properties. After the discovery of the giant magnetoresistance effect in 1988, spintronics has had a huge impact on scientific progress and related applications in the development of information technology. In recent decades, the main motivation in spintronics has been efficiently controlling local magnetization using electron flow or voltage rather than controlling the electron flow using magnetization. Using spin–orbit coupling in a material can convert a charge current into a pure spin current(a flow of spin momenta without a charge flow) and generate a spin–orbit torque on the adjacent ferromagnets. The ability of spintronic devices to utilize spin-orbit torques to manipulate the magnetization has resulted in large-scale developments such as magnetic random-access memories and has boosted the spintronic research area. Here in, we review the theoretical and experimental results that have established this subfield of spintronics. We introduce the concept of a pure spin current and spin-orbit torques within the experimental framework, and we review transport-, magnetization-dynamics-, and opticalbased measurements and link then to both phenomenological and microscopic theories of the effect. The focus is on the related progress reported from Chinese universities and institutes, and we specifically highlight the contributions made by Chinese researchers.     

Nuclear field theory treatment of K ≠ 0 rotational bands

The properties of the lowest members of K ≠ 0 rotational bands are described as anharmonic vibrational bands. The anharmonicity is calculated by the nuclear field theory (particle-vibration coupling) method. It is shown to be important not to truncate the diagrammatic expansion at a fixed number of vertices. Instead, the way in which the diagrams depend on the number of degrees of freedom participating is used to guide the truncation.     

Thermoelectric transport and spin density of graphene nanoribbons with Rashba spin–orbit interaction

In the present paper, we have theoretically investigated thermoelectric transport properties of armchair and zigzag graphene nanoribbons with Rashba spin–orbit interaction, as well as dephasing scattering processes by applying the nonequilibrium Green function method. Behaviors of electronic and thermal currents, as well as thermoelectric coefficients are studied. It is found that both electronic and thermal currents decrease, and thermoelectric properties been suppressed, with increasing strength of Rashba spin–orbit interaction. We have also studied spin split and spin density induced by Rashba spin–orbit interaction in the graphene nanoribbons.     

g factor of hydrogenlike ²⁸Si¹³⁺

We determined the experimental value of the g factor of the electron bound in hydrogenlike 2?Si13? by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)2 and (Zα)? and represents a stringent test of bound-state quantum electrodynamics calculations.     

Kramers–Kronig analysis of the optical constants of magnetite,pyrite, and chalcopyrite in the microwave range

The optical constants of a series of ore minerals (pyrite, magnetite, and chalcopyrite) have been analyzed in the microwave range using the Kramers–Kronig method. The spectral dependences of the reflectance of these minerals in a wide frequency range (from deep UV to microwave) have been plotted based on numerous experimental data from different sources. These dependences made it possible to calculate the optical constants of the minerals under study in a frequency range of 12–145 GHz and compare them with the results of the theoretical and laboratory studies published in different sources.     

Characteristics of persistent spin current components in a quasi-periodic Fibonacci ring with spin–orbit interactions: Prediction of spin–orbit coupling and on-site energy

In the present work we investigate the behavior of all three components of persistent spin current in a quasi-periodic Fibonacci ring subjected to Rashba and Dresselhaus spin–orbit interactions. Analogous to persistent charge current in a conducting ring where electrons gain a Berry phase in presence of magnetic flux, spin Berry phase is associated during the motion of electrons in presence of a spin–orbit field which is responsible for the generation of spin current. The interplay between two spin–orbit fields along with quasi-periodic Fibonacci sequence on persistent spin current is described elaborately, and from our analysis, we can estimate the strength of any one of two spin–orbit couplings together with on-site energy, provided the other is known.     

Determination of the thickness and optical constants of amorphous Ge–Se–Bi thin films

The effect of varying bismuth concentration on the optical constants of amorphous Ge₂₀Se_{80? x} Bi _x (where x = 0, 3, 6, 9 and 12 at%) thin films prepared by thermal evaporation has been investigated. The transmission spectra T(λ) of the films at normal incidence were obtained in the spectral region from 400 to 2500 nm. An analysis proposed by Swanepoel [J. Phys. E: Sci. Instrum. 16 (1983) p.1214], based on the use of the maxima and minima of the interference fringes, was applied to derive the real and imaginary parts of the complex index of refraction and also the film thickness. Increasing bismuth content was found to affect the refractive index and extinction coefficient of the Ge₂₀Se_{80? x} Bi _x films. Optical absorption measurements show that the fundamental absorption edge is a function of composition. With increasing bismuth content, the refractive index increases while the optical band gap decreases.