Torsional Dependence Research Articles

Azo-group dihedral angle torsion dependence on temperature: A theorerical–experimental study

Quantum chemical calculations were carried out to explain the observed shifts in the absorption spectrum of different azo-aromatic compounds due to changes in the dihedral angle of the azo-group. Our results reveal that the π−π∗ transition presents a hypsochromic shift and an oscillator strength drop upon increase of the dihedral angle. Nevertheless, the n−π∗ transition exhibits the opposite behavior. This effect is attributed to the reduction in the π−electron conjugation length of the molecule. Experimentally, we performed temperature dependence measurements of the linear absorption spectrum. Both the theoretical and experimental results demonstrate that small energy changes are mirrored in the electronic transitions of conjugated linear molecules.

Symmetry and Fourier analysis of the ab initio-determined torsional variation of structural and Hessian-related quantities for application to vibration–torsion–rotation interactions in CH 3OH

The aim of the present paper is to investigate the use of quantum chemistry calculations to obtain the torsional dependence of various structural and vibrational-force-field-related quantities that could help in estimating the vibration–torsion–rotation interaction terms needed to treat perturbations observed in the spectra of methanol-like molecules. We begin by using the Gaussian suite of programs to determine the steepest-descent path from a stationary point at the top of the internal rotation potential barrier in methanol to the equilibrium structure at the bottom of the barrier. This procedure requires determining the gradient ∇ V of the potential (as calculated in mass-weighted Cartesian coordinates) along the internal rotation path. In addition, we use the Gaussian suite to calculate the Hessian ∇∇ V along this path and to generate from these second derivatives the 3 N − 7 small-amplitude vibrational frequencies and the 3 N Cartesian vibrational displacements for each of these vibrations. We then symmetrize the internal coordinates used in presenting the structures, gradients, Hessians and vibrational displacements along the path to take into account the periodic variation of the behavior of the three methyl hydrogen atoms H i as they pass in turn through the C s -plane of the HOC frame. The symmetrized linear combinations of the CH i stretches, of the OCH i bends, and of the HOCH i dihedral angles of the methyl group depend on the internal rotation angle γ and they are determined by considering coordinate transformations from the G 6 permutation-inversion group appropriate for internally rotating methanol. This symmetrization procedure permits us to explore the feasibility of expressing the structures, gradients, Hessians, and vibrational displacement vectors along the internal rotation path as short Fourier series in γ, which is one of the main goals of this paper. In summary, we find that the symmetrized structures, gradients, and Hessians, as well as nine of the 11 projected vibrational frequencies and the vibrational displacement vectors for the three vibrations occurring primarily in the HOC frame can be expressed by short Fourier series expansions to their precision in the Gaussian output, and that these series involve only sin 3 nγ or only cos 3 nγ terms, as required by G 6 symmetry considerations. A preliminary discussion is given of why short Fourier expansions fail for the projected frequencies of the two methyl asymmetric stretches, and for the vibrational displacement vectors of the methyl group vibrational modes. Looking more closely at the symmetrized and projected 3 N × 3 N Hessian, we find algebraically that only elements in the (3 N − 7) × (3 N − 7) small-amplitude-vibrational block of the Hessian are useful for spectroscopic problems. Non-zero elements in the rest of the 3 N × 3 N symmetrized and projected Hessian cannot be converted into quantities needed for perturbation studies.

Analysis of One‐Bond Se‐Se Nuclear Couplings in Diselenides and 1,2‐Diselenoles on the Basis of Molecular Orbital Theory: Torsional Angular Dependence, Electron Density Influence, and Origin in 1J(Se, Se)

Nuclear couplings for the Se-Se bonds, 1 J(Se, Se), are analyzed on the basis of the molecular orbital (MO) theory. The values are calculated by employing the triple ζ basis sets of the Slater type at the DFT level. 1 J(Se, Se) are calculated modeled by MeSeSeMe (1a), which shows the typical torsional angular dependence on ϕ(CMeSeSeCMe). The dependence explains well the observed 1 J obsd (Se, Se) of small values (≤ 64 Hz) for RSeSeR′ (1) (simple derivatives of 1a) and large values (330–380 Hz) observed for 4-substituted naphto[1,8-c, d]-1,2-diselenoles (2) which correspond to symperiplanar diselenides. 1 J (Se, Se: 2) becomes larger as the electron density on Se increases. The paramagnetic spin-orbit terms contribute predominantly. The contributions are evaluated separately from each MO (ψ i) and each ψ i → ψ a transition, where ψ i and ψ a are occupied and unoccupied MO's, respectively. The separate evaluation enables us to recognize and visualize the origin and the mechanism of the couplings.

Torsional Angular Dependence of 1J(Se,Se) and Fermi Contact Control of 4J(Se,Se): Analysis of nJ(Se,Se) (n=1–4) Based on Molecular Orbital Theory

(n)J(Se,Se) (n=1-4) nuclear couplings between Se atoms were analyzed by using molecular orbital (MO) theory as the first step to investigating the nature of bonded and nonbonded (n)J(Se,Se) interactions between Se atoms. The values were calculated by employing Slater-type triple xi basis sets at the DFT level, which were applied to structures optimized with the Gaussian 03 program. The contribution from each occupied MO (psi(i)) and psi(i)-->psi(a) (psi(a)=unoccupied MO) transition was evaluated separately. 1J(Se,Se) was calculated for the MeSeSeMe model compound, which showed a typical dependence on the torsion angle (phi(C(Me)SeSeC(Me))). This dependence explains the small values (< or =64 Hz) of 1Jobsd(Se,Se) observed for RSeSeR' and large values (330-380 Hz) of 1Jobsd(Se,Se) observed for 4-substituted naphtho[1,8-c,d]-1,2-diselenoles, which correspond to synperiplanar diselenides. The HOMO-->LUMO and HOMO-1-->LUMO transitions contribute the most to 1J(Se,Se) at phi=0 and 180 degrees to give large values of 1J(Se,Se), whereas various transitions contribute and cancel each other out at phi=90 degrees to give small values of 1J(Se,Se). Large 4Jobsd(Se,Se) values were also observed in the nonbonded Se...Se, Se...Se=O, and O=Se...Se=O interactions at naphthalene 1,8-positions. The Fermi contact (FC) term contributes significantly to 4J(Se,Se), whereas the paramagnetic spin-orbit (PSO) term contributes significantly to 1J(Se,Se). 2J(Se,Se) and 3J(Se,Se) were analyzed in a similar manner and a torsional angular dependence was confirmed for 3J(Se,Se). Depending on the structure, the main contribution to (n)J(Se,Se) (n=2, 3) is from the FC term, with a lesser contribution from the PSO term. Analysis of each transition enabled us to identify and clearly visualize the origin and mechanism of the couplings.

Modeling of torsion stress giant magnetoimpedance in amorphous wires with negative magnetostriction

A model describing the influence of torsion stress on the giant magnetoimpedance (GMI) in amorphous wires with negative magnetostriction is proposed. The wire impedance is found by means of the solution of Maxwell equations together with the Landau−Lifshitz equation, assuming a simplified spatial distribution of the magnetoelastic anisotropy induced by the torsion stress. The impedance is analyzed as a function of the external magnetic field, torsion stress and frequency. It is shown that the magnetoimpedance ratio torsion dependence has an asymmetric shape, with a sharp peak at some value of the torsion stress. The calculated field and stress dependences of the impedance are in qualitative agreement with results of the experimental study of the torsion stress GMI in Co-based amorphous wires.

Rotational and translational optokinetic nystagmus have different kinematics

We studied the dependence of ocular torsion on eye position during horizontal optokinetic nystagmus (OKN) elicited by random-dot translational motion (tOKN) and prolonged rotation in the light (rOKN). For slow and quick phases, we fit the eye-velocity axis to vertical eye position to determine the tilt angle slope (TAS). The TAS for tOKN was 0.48 for both slow and quick phases, close to what is found during translational motion of the head. The TAS for rOKN was less for both slow (0.11) and quick phases (0.26), close to what is found during rotational motion of the head. Our findings are consistent with the notion that translational and rotational optic flow are processed differently by the brain and that they produce different 3-D eye movement commands that are comparable to the different commands generated in response to vestibular signals when the head is actually translating or rotating.

Investigation of torsional barriers and nonlinear optical (NLO) properties of phenyltriazines

In this study, electronic and nonlinear optical properties of six phenyltriazine isomers were calculated. The calculated properties are electronic energy, HOMO–LUMO energies, static polarizability α, anisotropy of polarizability Δ α, and first static hyperpolarizability β at equilibrium geometry and their torsional dependence. The torsional barriers and potential energy curves were calculated at HF/6-31++G(d,p) and B3LYP/6-31++G(d,p) methods. The number of ortho hydrogen atoms mainly determines the torsional barriers of these molecules, while the meta hydrogen atoms have a small influence on the equilibrium torsional angles and barriers. Nonlinear optical properties (NLO)-dihedral angle θ correlations of phenyltriazine isomers were calculated at the B3LYP/6-31++(d,p) level. Polarizabilities of phenyltriazines decrease with shifting the nitrogen atoms to the para position. On the contrary, hyperpolarizabilities of phenyltriazines increase with shifting the nitrogen atoms to the ortho position.

A theoretical study of the linear, nonlinear optical properties and conformational analysis of 3-phenylthiophene and its fluoro derivatives with torsional dependence

In this study, we have investigated the energies, dipole moments, HOMO–LUMO energy differences and polarizability values of 3-phenylthiophene and its fluoro-substitued derivatives as a function of the torsional angle. For each molecule, geometrical parameters have obtained using ab initio [Hartree–Fock (HF) and second-order Møller–Plesset (MP2)] and Density Functional Theory (DFT) with the 6-31++G ∗∗ and 6-311++G ∗∗ basis sets. The calculated physical quantities, such as electronic energy, dipole moment ( μ), HOMO–LUMO energy differences (Δ E), polarizability ( α) and hyperpolarizability ( β) values are at the ground state geometry. The effect of the position of fluorine substituent on structural parameters, on dipole moments and on torsional potentials have been examined. The frontier molecular orbital calculations clearly show that there is an inverse relationship between HOMO–LUMO energy differences and their polarizabilities. We have also calculated λ max values from the HOMO–LUMO energy differences. Finally we have discussed the trends in the calculated torsional potentials, barrier heights, and energy differences between conformers and correlated them with selected structural parameters.

Torsional dependence of the reactivity of diphenylamine-type antioxidants

The dependence of energy, geometry and electronic structure of dihenylamine Ph 2NH, its aminyl radical Ph 2N , cation radical Ph 2NH + and nitroxide radical Ph 2NO on the phenyl ring torsion have been investigated using B3LYP treatment. Stable structures of these systems are non-planar. The most significant changes are related to the nitrogen spin density as well as lengths, strengths and π character of C–N bonds. The reactivity of the cation and aminyl radical exhibits the highest sensitivity on the C–N bond torsion as deduced from nitrogen spin density and C–N bonds non-equivalence.

Torsional stress impedance effect in Fe 71 Cr 7 Si 9 B 13 amorphous wire

The magnetoimpedance effect has been measured in as-received and current annealed Fe71Cr7Si9B13 amorphous wires under torsional stress varied up to 1.2 rad/cm. It was found that the torsional stress dependence of impedance of as-received amorphous wire has a non-monotonous shape with first an increase of the impedance and then a decrease. On the other hand, the impedance of current annealed wire directly starts to decrease with increasing torsional stress. The current annealing of wire results in a large variation in the magnitude of torsional stress impedance effect, (ΔZ/Z)ξ(%), up to 150%. Also, a simple mathematical model based on the magnetic moment rotation to explain torsional stress versus impedance data was developed and the results were partly discussed on the basis of this model. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear giant magnetoimpedance and the asymmetric circumferential magnetizationprocess in soft magnetic wires

The magnetoimpedance effect and its nonlinear terms are analysed for a(Co0.94Fe0.06)72.5Si12.5B15 amorphous wire. In order to enhance the nonlinear contribution the sample was previouslysubjected to current annealing (Joule heating) to induce a circumferential anisotropy. Theeffect of the application of a torsional strain on the nonlinear magnetoimpedance isanalysed in terms of the torsional dependence of the magnetic permeability, evaluatedthrough experimental circumferential hysteresis loops. The results obtained clearly confirmthe direct correlation between the asymmetric circumferential magnetization process andthe occurrence of nonlinear second-harmonic terms in the magnetoimpedance voltage.

Maxwell’s field coupled nonminimally to quadratic torsion: Axion and birefringence

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^\alpha$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}

The effect of torsion stress on the circumferential permeability of CoFeBSi amorphous wires

In this paper, a domain model and the complex inductance formalism are employed to study the effect of torsion stress on the low-frequency magnetoimpedance (MI) response of CoFeBSi amorphous wires (125 /spl mu/m in diameter). In particular, the torsional dependence of the calculated circumferential permeability /spl mu//sub /spl phi// is found to be very sensitive to the wire's scalar permeability /spl mu//sub dc/ which, in turn, depends inversely on the wire's induced anisotropy K/sub i/. Calculated /spl mu//sub /spl phi// exhibited a marked increase for increased /spl mu//sub dc/ and a decrease for reduced /spl mu//sub dc/. Experimental spectroscopic plots of /spl mu//sub /spl phi// under various torsion stresses (counter- and clockwise-oriented) which resulted in various helically induced anisotropies K/sub h/ are consistent with an enhancement/counterbalancing effect of K/sub i/ through the addition/subtraction of K/sub h/ to K/sub i/.

Torsional selection rules, Raman tensors, and cross sections for degenerate modes of C2H6

We analyze the peculiarities induced by the torsional motion on the Raman spectra of the degenerate vibrational bands of ethane. Selection rules for the Raman transitions between the torsionally split energy levels are derived first in terms of symmetry arguments. Then, their associated intensities are calculated with a model for the torsional dependence of the molecular polarizability. New experimental spectra of the Raman degenerate bands of C2H6, some recorded in jet expansions, are also included and analyzed to show the current state of the problem.

Torsional stress dependence of reactance and resistance in Fe-rich amorphous wires at low frequencies

Amorphous ferromagnetic wire with a highly positive saturation magnetostriction coefficient, made of Fe 73.5Si 13.5B 9Nb 3Cu 1, was simultaneously submitted to both, an AC current passing through it and a torsional stress, in order to induce a helical magnetic anisotropy in the wire that modifies its domain structure and therefore the magnetic response of the sample. The aim of this work is to study the reactive, resistive and impedance behaviour in this Fe-rich wire, submitted to different applied torsional stresses, and for several values of the AC current amplitude through the wire (5–20 mA rms), in the low frequency range, f<MHz. The experimental results are explained on the basis of the core-shell model.

Torsional dependence of second-harmonic amplitude of giant magnetoimpedance in FeCoSiB amorphous wire

The effect of torsional stresses in the magnetoimpedance response of a (Co/sub 0.94/Fe/sub 0.06/)/sub 72.5/Si/sub 12.5/B/sub 15/ amorphous wire is analyzed. In particular, the occurrence of a second-harmonic contribution of the magnetoimpedance voltage is analyzed and compared with the first-harmonic amplitude (impedance). The evolution of both harmonic components are correlated to the estimated permeability contributions obtained through the analysis of the estimated rotational hysteresis loops. The highest torsional dependence of the second-harmonic contribution can be used in the development of new magnetoelastic sensors.

Structure dependence of optical properties of bridged bis-thienyls. I. Simple five-membered aromatic bridges

The torsional dependence of the heat of formation (ΔHf), averaged electronic polarisabilities (〈α〉) and second-order hyperpolarisabilities (〈γ〉), lowest singlet–singlet and singlet–triplet transition energies of neutral analogues of α-terthiophenes (compound T1) like 2,5-di(2′-thienyl)-furane (compound F1), 2,5-di(2′-thienyl)-pyrrole (compound P1), 2,5-di(2′-thienyl)-[1,3,4]oxadiazole (compound F2), 2,5-di(2′-thienyl)-[1,3,4]thiadiazole (compound T2) and 2,5-di(2′-thienyl)-[1,3,4]triazole (compound P2) has been studied by semi-empirical AM1 and ZINDO/S methods. The molecules P1 and F1 are more planar than T1. Replacing carbon atoms (CH groups) in β-positions of the central ring in T1, P1 and F1 by nitrogens slightly forces the structure to planarity what is connected with higher effectiveness from the charge transfer point of view. On the other hand, the small decrease in the wavelengths of electron spectra as well as electro-optical properties is expected with this central ring modification. The shape of 〈α〉 and 〈γ〉 torsion dependence is of nearly squared-sine type with minimum at perpendicular conformations.

On the Relation Between Conformational Changes and Optical Properties in Oligothiophenes, 2. Linear and Nonlinear Optical Properties

The dependence of microscopic electronic non-resonant polarizabilities (a) and second-order hyper-polarizabilities (y) of short oligothiophenes on the mutual torsional ring orientation was investigated by employing the time-dependent Hartree-Fock method within the AM1 approximation. The a and y quantities exhibit the uniform shape of the torsional dependence regardless of the mutual ring's orientations for all the systems under study (minima occur for perpendicular geometries and maxima are indicated for planar structures). The frequency dependence of y hyperpolarizability below the first resonance frequency is fairly well evaluated in the form of a simple power series. The trends of AM1 results agree with the current theoretical treatments as well as experimental data/

A note on the torsion dependence of D-brane RR couplings

The dependence on the torsion H= db of the Wess–Zumino couplings of D-branes that are trivially embedded in space–time is studied. We show that even in this simple set-up some torsion components can be turned on, with a non-trivial effect on the RR couplings. In the special cases in which either the tangent or the normal bundle are trivial, the torsion dependence amounts to substitute the standard curvature with its generalization in the presence of torsion, in the usual couplings involving the roof genus Â.

Target-space anomalies and elliptic indices in heterotic orbifolds

We present a complete string theory analysis of all mixed gauge, gravitational and target-space anomalies potentially arising in the simplest heterotic Z_N orbifold models, with N odd and standard embedding. These anomalies turn out to be encoded in an elliptic index, which can be easily computed; they are found to cancel through a universal GS mechanism induced by the dilaton multiplet. The target-space symmetry is then shown to have a nice geometric interpretation in terms of torsion, and the target-space dependence of the four-dimensional GS couplings can be alternatively rederived from the implicit torsion dependence of the standard ten-dimensional GS couplings. The result is universal and consists essentially of a Bianchi identity for the NSNS B field depending on all the curvatures, and in particular on the target-space curvature.