Centrosymmetric Systems Research Articles

Transition metal derivatives of a chelating nitronyl nitroxide ligand. Nickel(II) and manganese(II) complexes

Complexes of the nitroxideligand 2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxy 3-oxide (NIT2-py) with NiCl 2 (1, C 26 H 36 Cl 6 N 6 NiO 4 ) and MnCl 2 (2, C 26 H 36 Cl 6 MnN 6 O 4 ) have been structurally and magnetically characterized. Both complexes are centrosymmetric three-spin systems in which the nitroxyl group is coordinated to the metal ion. Metal-nitroxide interactions of -110 cm -1 for 1 and -80 cm -1 for 2 (H=-2JS i ,S j ) are observed

The intensity of two-photon vibronic transitions for Gd3+ in Cs2NaGdCl6

The two-photon odd-parity vibronic transitions in centrosymmetric systems have been described by a simple model based on the third-order mechanisms. The use of symmetry-adaptation techniques and Racah-Wigner calculus has led to the expression for transition intensity, including magnetic and vibronic components as well as the polarization factor. This expression has been used for calculations of intensity strengths of two-photon vibronic transitions between the ground state ((8S72/) mod and one of the excited J multiplets >>(6P52/)) of the Gd3+ ion in surroundings of octahedral symmetry.

Many-photon effects in inelastic light scattering

The usual approach to second harmonic generation (SHG) is based on low-order pertubation theory and neglects the changes in the electronic states that are induced by the exciting beam. To see whathappens in this approximation fails we propose a new formalism, based on the method of excitation amplitudes, to set up a theory of the SHG response and other inelastic light scattering phenomena. We develop the quantum theory in the dipole approximation and show that the inclusion of electron-photon coupling to all others leads to new features. Strong exciting fields produce a nonnegligible SHG response in highly polarisable centro-symmetric systems, and the emitted spectrum shows a dynamical Stark effect.

A cellular ligand-field model forl-lspectral intensities

The model for d-d or f-f intensities of ligand-field transitions in acentric chromophores was presented in part I. Here, that model is extended to include centrosymmetric systems in which intensity is deemed to arise from parity mixing induced during ungerade molecular vibrations. The same cellular structure is maintained for the parametrization scheme, although time-averaged t variables for each vibrational mode subsume local electronic properties and ligand displacements within each vibrational normal mode. The L t λ parameters of the ‘static’ model are replaced in the dynamic regime by L t α λ where α = x or y for local bending displacements normal to the metal-ligand (z) vector and α = z for pure stretching displacements. The physical and bonding significance of static- and dynamic-type parameters are described and compared.

Optical properties and symmetry restrictions in the incommensurate phase of

The birefringence, optical activity, and rotation of the optical indicatrix have been measured in the normal and incommensurate phases of tetramethylammonium tetrachlorozincate [N(${\mathrm{CH}}_{3}$${)}_{4}$${]}_{2}$${\mathrm{ZnCl}}_{4}$ along the direction of the modulation wave vector. The measurements have been carried out on two different samples using a high-accuracy universal polarimeter. In contrast to previous observations a null value for the gyration in the whole incommensurate range has been found. In addition, up to the experimental error, no rotation of the indicatrix has been detected. The present work is therefore a confirmation of the view that the symmetric restrictions for tensors describing macroscopic properties of an incommensurate structure are those imposed by the point group associated to its superspace group. In this context, some remarks are made in relation to the different theoretical approaches that, contrary to this idea, permit the existence of gyration effects in centrosymmetric incommensurate systems.

A proposal of new organic third-order nonlinear optical compounds. Centrosymmetric systems with large negative third-order hyperpolarizabilities

An approximate formula for virtual excitation processes (three-type approximate formula) describing the third-order hyper-polarizability (γ) is rewritten by the use of polarizabilities of the ground and excited states (α 0, α n ), and a criterion for a classification of γ for organic compounds is drawn from the formula. We suggest that there exist new organic nonlinear optical systems with negative γ values. The new systems have centrosymmetric structures which exhibit large ground state polarizabilities. As new model compounds, some alternant and condensed-ring conjugated centrosymmetric systems are investigated using the coupled-Hartree—Fock (CHF) and Møller—Plesset second-order perturbation (MP2) methods combined with the semi-empirical INDO approximation. Comparisons of γ values calculated by the INDO and ab initio methods are carried out. The MP2 results suggest that the ion radical states of the condensed-ring systems such as C 60 n− possess large negative γ values.

A centrosymmetric chaos

Symmetry plays an important part in the research of the dynamical behavior of nonlinear system. It is proved in this paper that, for a class of centrosymmetric systems with parametric excitation, chaos behaves in centrosymmetric manner, which implies that chaos need not to be an unsymmetric dynamical state.

Small angle X-ray analysis of alternate-layer Langmuir—Blodgett films

Abstract Using small-angle X-ray diffraction, we demonstrate in this Letter that alternate-layer Langmuir-Blodgett films of tricosanoic acid/1-docosylamine and docosanoic acid/1-docosylamine retain their ‘as-deposited’ structure. Both of these non-centrosymmetrical bilayer structures exhibit a smaller tilting of their hydrocarbon tails than that observed for the corresponding centrosymmetric monocomponent systems. The electron-density profiles obtained for the alternate-layer systems reveal that the points of contact for the ends of the hydrocarbon chains are shifted from the centre of the unit cell and that the density maxima, corresponding to the positions of the polar head groups, possess an asymmetrical shape.

On the vibrational transition selection rules for the centrosymmetric hydrogen-bonded dimeric systems

This paper attempts to give a theoretical interpretation of the anomalies observed in the spectra of the hydrogen-bonded centrosymmetric dimers. The analyzed effects were observed in the numerous recently published dimeric spectra and ascribed to a deviation from the dipole selection rules for the centrosymmetric dimers; they depend on activation of the forbidden transition in IR to the A g excited state of the proton stretching vibrations in the hydrogen bonds. A vibronic model of interactions in the hydrogen bonds was assumed, which allowed one to derive a purely electronic matrix Hamiltonian of a dimer. It described mixing between the dimeric vibrational states, belonging to different irreducible representations of the C i group. In our model two kinds of interactions, i.e., the vibronic coupling in the Herzberg-Teller approximation and proton vibration anharmonicity, played an essential role in the coupling mechanism and determined the shape of the Hamiltonian. The analysis of some Hamiltonian properties allowed one to conclude that in some cases the vibrational transition to the A g state may be allowed for the dimers as a result of a modified Herzberg-Teller mechanism, originally established for the molecular electronic spectra to explain the vibrational spectral phenomena. The deviation from the selection rule is connected with a dynamic asymmetry of the electron charge distribution and with a dynamic asymmetry of the protonic positions in the A g excited state of the proton vibrations. The model also predicts diminution of the forbidden transition intensity after replacing the H-atoms by the D-atoms in the dimeric hydrogen bonds.

Effective polarizability of two interacting adsorbed atoms

The expression for the polarizability of a pair of centrosymmetric systems adsorbed on a dielectric or on a metallic surface is given. When the distance atom-surface becomes important our results can be also applied to the case of interactions between two colliding systems. Numerical estimations of each process are presented in the case of rare gas atoms adsorbed on a palladium surface.

The electronic structure of an atom in the vicinity of a solid body: Application to the physisorption on metal surface

A unified treatment of the modification of the electronic charge density for an atom placed in the vicinity of a solid body is presented. The nonlocality effects inside the two partners is introduced through the generalized susceptibility theory. Applications to the physisorption is proposed by treating the solid body as a nonlocal electron gas limited by a planar surface. When the extended system reduces to a single atom one recovers various results previously proposed for couples of centrosymmetric systems.

Model calculations of the micrometer to millimeter intrinsic absorption for simple ceramics

A systematic study has been made of the strength of the intrinsic absorption, or loss, for millimeter to micrometer electromagnetic radiation propagating in simple ceramic materials. This study employed a number of model diatomic systems whose simplicity enabled the basic two-phonon decay process, responsible for this intrinsic loss, to be computed with precision, even at the lowest frequencies, on a dedicated microcomputer. It was found that, at least at low frequencies, the loss was a relatively structureless universal function of the atomic mass ratio, in general agreement with earlier results for real alkali halides. In particular, it was found that, if one atomic mass was markedly increased, the low-frequency damping dropped dramatically and a "window" appeared in the loss function. This behavior and its origins are discussed and illustrated by predictions of the absolute values of the intrinsic low-frequency losses for MgO and SrO at room temperature. The values for MgO are almost an order of magnitude larger, and in reasonable accord with values measured for typical ceramics, when estimated extrinsic losses are subtracted. The present studies also provide a natural explanation of the general observation that the loss at the fundamental lattice resonance frequency is, at least in centrosymmetric systems, dominated by three-phonon decay.

Static dipole moment of two coupled systems

We present the expression for the dipole moment of a pair of nonidentical systems in terms of the frequency dependent polarizabilities and hyperpolarizabilities. Our calculations are quite general and include the two particular cases of the near-zone (London) and of the far-zone (Casimir) limits. We first consider the case oftwo disssimilar centrosymmetric systems and then, the more particular one of two spherical ones.

Very-long-range static dipole moment of two coupled systems

The expression for the very-long-range dipole moment of a pair of non-identical centrosymmetric systems (varying as R −8) is obtained. Our expression is given in terms of polarisabilities and hyperpolarisabilities of the two systems and is compared with two previous results.

Parallel solution to certain banded, symmetric and centro-symmetric systems by using the quadrant interlocking factorisation method

In this paper the authors extend the matrix quadrant factorisation techniques which are so applicable for parallel computers to include banded symmetric and centrosymmetric linear systems with a corresponding improvement in computational efficiency.

Elementary derivation of long-range moments of two coupled centrosymmetric systems

The expression for the long-range dipole moment of a pair of non-identical centrosymmetric systems (varying as R −7) in terms of frequency-dependent polarizabilities and hyperpolarizabilities is recovered more simply than hitherto. An expression in terms of frequency-dependent quantities for the quadrupole moment of an identical pair (∞ R −6) is given for the first time.

Kinetic models of aconitase action

An analytic solution is provided for the open and closed tricyclic or centrosymmetric systems. The open or closed linear system follows from either model by setting a pair of reaction rate constants equal to zero. The application of these models to rate constants for aconitase action is discussed.

The calculation of structure factors for centrosymmetric monoclinic systems with anisotropic atomic vibration

The calculation of structure factors for centrosymmetric monoclinic systems with anisotropic atomic vibration