Electro-optical parameters and Raman intensities of CH4, CH3D,CH2D2, CHD3 and CD4

The absolute Raman intensities and the depolarization ratios of the vibrational bands of gaseous CH₄, CH₃D, CH₂D₂, CHD₃ and CD₄ have been computed here using a compact formulation of the bond polarizability theory, in its zero and first-order approximations. The agreement with experimental values taken from the literature is very good for the first-order approximation, although the difference between both approximations is not very large for these molecules. The derivatives of the polarizability with respect to the symmetry coordinates of methane are given with signs that are physically meaningful.     

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.     

Vibrational properties of polyatomic molecules by quantum chemical methods

Force constants and dipole moment derivatives have been computed for the molecules CH₃ X(X=F, Cl, Br, I) using MO wavefunctions with pseudo-potentials for the interaction between the inner shell and valence electrons. The values obtained at the SCF approximation level from a set of gaussian valence orbitals contracted in double-zeta form and enriched with polarization functions compare well with experimental assignments of force and interaction constants, as well as integrated intensities from infrared data. The transferability of atomic force fields and polar tensors (second derivatives of total energies and first derivatives of dipole moments with respect to atomic displacements in cartesian coordinates) is discussed.     

An ab initio study of vibrational corrections to the electrical properties of ethane

SCF quartic property hypersurfaces have been computed for the energy, quadrupole moment and polarizability tensor of ethane via finite differences of analytical derivatives to obtain zeropoint vibrational corrections to the properties. Coupled with accurate electrical properties computed at a correlated r _e geometry, using a range of correlated methods, especially BD and BD(T), excellent estimates of these properties have been obtained that incorporate the effects of vibrational averaging. The effect of deuterium substitution on the properties has been investigated, including the first known theoretical prediction of the dipole moment of CH₃CD₃, and the frequency dependence of the polarizability tensor and Rayleigh depolarization ratio have been examined. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements. Although the vibrational corrections are limited to SCF theory, and basis sets not as extensive as used in some studies of this kind, nevertheless the results can be compared quantitatively with experiment, and the agreement is found to be excellent. The results underline the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, and suggest a viable approach for studies on larger molecules.     

Anion polarizability functions in alkali halide crystals

Anion polarizabilities in alkali halide crystals are analysed as a function of interionic separation R. The anion polarizability is treated as a function of the anion and cation radii, with its partial derivatives approximated by those with respect to R for fixed cation and anion, respectively. With pressure derivatives of the ionic radii deduced from the crystal compressibility, assuming transferability among crystals, the polarizability derivatives with respect to ionic radius yield pressure derivatives of the polarizability that agree with experiment to within a factor of two. These results offer a useful means of predicting the pressure dependence of dielectric data.     

Boron Trifluoride: Application of the Keating Bendings to the Degenerate Vibrations

The harmonic force field of the E' species of BF₃ is studied. The Keating force field (KFF) is defined in analogy with the familiar VFF and CFF. In this connection three different coordinate sets are introduced. All of them contain bond stretchings. In addition, the valence coordinates include ordinary (Decius') bendings, the central coordinates nonbond stretchings, and Keating coordinates the Keating's bendings.

The experimental data of vibrational frequencies and Coriolis constants are reviewed extensively, as well as previous normal coordinate analyses. The different coordinate sets are tested for their usefulness as basis of force field approximations. For this purpose two different sets of experimental data are applied. The general conclusion goes in favour of the Keating coordinates.     

The rovibrational Raman spectrum of water vapour v 1 and v 3

The OH stretching region in the Raman spectrum of water vapour has been observed and reproduced by computer simulation using rovibrational wave functions derived from the analysis of high-resolution absorption spectra. Relative intensity measurements allow the determination of the depolarization ratio and the ratio of the two non-vanishing second-order irreducible tensor components for v ₁. These quantities have been combined with the literature value for the cross section of this band to calculate the principal cartesian components of the v ₁ derived polarizability tensor. The cross section for the v ₃ vibration was also determined, and these results are considered in terms of the bond polarizability theory.     

Dipole moment of a small water cluster. The effect of size,temperature, and electric field

A molecular dynamics simulation of neutral clusters (H₂O) _{n ≤ 21} has been performed in the framework of the flexible polarized model. The formation and evolution of the dipole moment of the cluster have been investigated with a change in the size and temperature of the cluster and an external electric field. It has been shown that at low electric fields corresponding to the experiments on the deflection of clusters in the transverse inhomogeneous electrostatic field (Moro et al., 2006), the induced polarization of the cluster is determined by the orientational polarizability of the “rigid” cluster, rather than by the intracluster reorientation of the molecules. The calculated dependence of the effective polarizability of the cluster in the low field on n qualitatively reproduces the experimental results, but the calculated polarizability is numerically much higher than the experimental value by, e.g., a factor of 4 for n ≈ 20.     

Static electric dipole polarizabilities of Na clusters

The static electric dipole polarizability of Na _N clusters with even N has been calculated in a collective, axially averaged and a three-dimensional, finite-field approach for , including the ionic structure of the clusters. The validity of a collective model for the static response of small systems is demonstrated. Our density functional calculations verify the trends and fine structure seen in a recent experiment. A pseudopotential that reproduces the experimental bulk bond length and atomic energy levels leads to a substantial increase in the calculated polarizabilities, in better agreement with experiment. We relate remaining differences in the magnitude of the theoretical and experimental polarizabilities to the finite temperature present in the experiments. Received 8 November 1999     

Local-field anisotropy in cholesteric liquid crystals

The first experimental values of the Lorentz tensor components L _j for the cholesteric and smectic A phases of derivatives of cholesterol have been obtained using the dispersion of the refractive indices in the visible range. The temperature dependence of the components L _j has been determined; it is invariant with respect to the cholesteric-smectic A phase transition. The effect of the isotropization of the Lorentz and local field tensors with decreasing anisotropy of the molecular polarizability has been revealed.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

Theoretical interpretation of the vibrational spectrum of bicyclo[1.1.0]butane in terms of an ab initio anharmonic model

The anharmonic vibrational IR and Raman spectra of the bicyclo[1.1.0]butane molecule have been calculated in the range of up to 4000 cm^?1 using a numerical and analytical realization of the van Vleck second-order operator perturbation theory. Cubic and quartic force constants in normal coordinates, as well as cubic surfaces of the dipole moment and polarizability, have been found by numerical differentiation of the corresponding first and second derivatives calculated by the MP2/cc-pVTZ quantum-mechanical method. In order to increase the prediction accuracy of vibrational transitions, corresponding harmonic frequencies have been obtained by the CCSD(T)/cc-pVTZ high-precision quantum mechanical method. The anharmonic intensities of the IR and Raman spectra have been calculated using canonical transformations of the operators of the dipole moment and polarizability expanded into a Taylor series around the equilibrium configuration. The assignment of experimental vibrational bands in the IR and Raman spectra has been analyzed. It has been shown that the anharmonic calculation based on the above-described procedure of combining more exact harmonic frequencies with the anharmonic force field obtained with a more economical method makes possible the reliable interpretation of the majority of spectral bands, including Fermi and Darling-Dennison resonances.     

Calculation of the Normal Vibrations of Benzene in the First Singlet Electron-Excited State 1 B 2u

Using the CIS/6-311+G^** method, the normal vibrations of the benzene molecule in the first singlet electron-excited state ¹ B _2u have been calculated. The algorithm of calculation of the force field in dependent coordinates by the method of generalized inversion is described. A method of autoscaling in dependent natural coordinates is suggested. For six groups of natural coordinates scaling factors have been obtained, the use of which has led to agreement between the calculated and experimental frequencies of the vibrations of benzene. The frequencies of the B _1u -symmetry-type vibrations, for which there is no experimental assignment, have been calculated. The problem of selection of the force field in dependent coordinates is discussed.     

Orientational order and distribution function in nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene

The refractive indices (n _e,?n _o) and density have been measured as a function of temperature in the liquid-crystalline and liquid phases of nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene. The molecular polarizability and orientational order parameter have been computed using the Neugebauer anisotropic local field model. The distribution function f(β), and hence the higher order parameter ?P ₄?, and nematic pair-potential have been computed at different temperatures in the nematic phase.     

Relationships in Raman intensity theories,in particular the Mayants-Averbukh theory

Brief surveys are given of the Mayants-Averbukh Raman intensity theory, and of the polar tensor Raman intensity theory recently presented by Bogaard and Haines. It was found that these intensity theories in essence are equivalent. In addition, the appearances of the symmetry invariant parameter matrices F_n⁰ of the Mayants-Averbukh theory were derived and tabulated for various symmetries of bond n. These matrices, and a single bond coordinate system, can be used as a convenient alternative to the Mayants-Averbukh treatment of bonds which have some kind of symmetry with respect to the midpoint of the bond. A modification of the Mayants-Averbukh treatment is also suggested. The rotational mode equations of the Mayants-Averbukh theory have been investigated to elecudate the constraints which they impose on Raman intensity theories based on the bond polarizability model. It was found that the valenceoptical theory is in conformity with the rotational modes only if all electrooptical parameters $\text{?α}{}_{\mathrm{ii}}{}^{\mathrm{(n)}}\text{?γ}{}_{\mathrm{p}}$ are neglected, where α_ii⁽ⁿ⁾ (i = 1, 2, 3) are the diagonal components of the polarizability α⁽ⁿ⁾ of bond n, and γ_p is the pth internal angular coordinate. Furthermore, the valence-optical theory was found to be strictly applicable only for cylindrical bond symmetry, C_mv (m ≥ 4). A generalized valence-optical Raman intensity theory, allowing also for non-zero off-diagonal components α_ij⁽ⁿ⁾, was found to be incompatible with the rotational mode equations of the Mayants-Averbukh theory. However, its basic polarizability equation was useful for suggesting a unique interpretation of a set of f parameters (elements of F_n⁰) in terms of components of the anisotropic part of a symmetric bond polarizability.     

Lie derivatives and deviation equations in Riemannian spaces

The connection between Lie derivatives and the deviation equations has been investigated in Riemannian spacesV _n. On this basis the deviation equations of the geodesies have been obtained, in spaces with symmetries, as well as deviation equations of nongeodesic trajectories, through imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory.     

Shape of the clusters of a percolative system in the presence of tunneling bonds and a finite electric field

We consider a model correlated percolative system on a 2D square lattice with a finite electric field applied accross its two opposite sides. We study the shape of the clusters formed with the addition of a new kind of bond (we call them tunneling bonds) which respond only above a finite threshold voltage. As expected, the clusters do have an overall elongated shape in the-direction of the applied field. Intuitively, one expects the elongation (with the aspect ratio >1) to increased indefinitely with the field. But, in a previous study, we found the model to belong to the same universality clas in the limits of a zero and an infinite electric field. We explain this behavior by studying the change in these elongated shapes as a function of the applied voltage in finite size samples and find that actually the amount of elongation takes on a maximum value at a size (L)-dependent finite voltageV _m (L) and that asV thje overall deviation from isotropy in the field direction tends to zero (i.e., aspect ratio1) again.     

Metal–insulator transition in a quantum well under the influence of magnetic field

Ionization energies of a shallow donor in a quantum well of the Cd_1-xinMn_xinTe/Cd_1-xoutMn_xoutTe superlattice system are obtained. A variational procedure within the effective mass approximation is employed in the presence of magnetic field. Within the one-electron approximation the occurrence of Mott transition is seen when the binding energy of a donor vanishes is observed. The effects of Anderson localization and exchange and correlation in the Hubbard model are included in our model. It is found that the ionization energy (i) decreases as well width increases for a given magnetic field, (ii) decreases when well width increases, (iii) the critical concentration at which the metal–insulator transition occurs is enhanced in the external magnetic field and (iv) spin polaronic shifts not only with the increase in a magnetic field but also with the well width increases. All the calculations have been carried out with finite barriers and the results are compared with available data in the literature.     

Donor electron in a quantum well under the influence of an electric field

The ionization energies and the polarizabilities of a donor in an isolated well of a quasi two dimensional (Q2D) GaAs/Ga_1−x Al _x As heterostructure have been obtained for different well widths including electron-lattice coupling. A wave function that properly reduces to the hydrogenic function in the limiting case has been used. For fields of the order of 10⁵ V/m, the ionization energies decrease slightly with electric fields for all well widths (10 nm to 50 nm) studied. Also for a given electric field, as the well width increases, the ionization energy decreases. For fields of the order of 10⁷ V/m and for smaller well widths (<10 nm), the ionization energy generally increases with electric field. The results also show that for electric fields of this order, no donor bound state associated with the lowest subband is possible for well widths greater than 20 nm. The polarizabilities estimated using the expression for the dipole operator show that as the well width increases, the polarizability values also increase and do not show any abnormal behaviour.