Dispersion energies of interaction between asymmetric molecules

A formula is derived that expresses the contribution of the electric dipole-quadrupole forces to the dispersion energy between two unexcited molecules possessing axial symmetry. The relative orientation of the symmetry axes is arbitrary and the molecules need not be identical. Our formula holds for the case that each molecule belongs to a substance whose optical dispersion curve is characterized by a pair of resonance frequencies. A few orientations of special interest are subjected to numerical analysis based on the experimental data for polarizabilities of some diatomic molecules. Thus estimates are gained of the magnitude of errors inherent in energy values computed as if spherical symmetry obtained.     

Surface raman electromagnetic enhancement factors for molecules at the surface of small isolated metal spheres: The determination of adsorbate orientation from sers relative intensities

Expressions are derived for the surface Raman electromagnetic enhancement factors and depolarization ratios for a molecule with a general polarizability tensor adsorbed at the surface of a small sphere in the dipole approximation. The constraint of some of the elements of the Raman tensor to zero for molecules with certain elements of symmetry leads to differences in the relative enhancements of modes belonging to different symmetry classes. The least enhanced modes are those whose Raman tensor components involve the two axes in the plane of the surface. The application of these results in a qualitative way to determine the orientation of pyridine at a silver electrode surface is explored, and it is concluded that the pyridine is adsorbed face-on to the electrode surface.     

Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoids of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adjacent ellipsoids is 7.5°, so the molecules are twisted. At high densities they form a cholesteric phase where their twist axes are oriented around the cholesteric axis and the symmetry axes of the ellipsoids are approximately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a temperature gradient parallel to the cholesteric axis induces a torque that rotates the director. The converse is also possible: rotation of the director can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the torque, and the cross-coupling coefficient between the director angular velocity and the heat current have been calculated by non-equilibrium molecular dynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relations from equilibrium simulations. Two ensembles have been utilized: the ordinary canonical ensemble and another ensemble where the director angular velocity is constrained to be a constant of motion. All the methods give consistent results for the twist viscosity and the thermal conductivity. The NEMD estimates of the cross-coupling coefficients agree within a relative error of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relative error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.     

Analysis of dispersion characteristics of phononic structures

A general theory for calculating the dispersion of bulk acoustic waves in 3D and 2D phononic crystals made of anisotropic materials is presented, which is based on the plane-wave expansion method. Two approaches to separating acoustic modes in the dispersion diagrams are proposed. The pattern of the acoustic field distribution is studied as depending on the wavevector direction for various types of modes. Degeneracy of acoustic modes in directions different from the axes of symmetry of the phononic crystal is demonstrated. Possibilities of the proposed method are illustrated by the application to 3D and 2D silicon-based phononic crystal structures.     

Topological singularities and phonon focusing

The focusing directions of phonon images generated by the anisotropic propagation of ballistic phonons are interpreted as singularities of the Gauss map of the energy surface. While a linear dispersion produces only folds and cusps, a nonlinear dispersion relation generically induces singular events for critical values of the frequency. These events are classified by means of catastrophe theory and the local topology on the energy surfaces is elucidated. On reflection planes or symmetry axes new types of singularities occur. The consequences of Morse singularities in the dispersion relation for the focusing directions are discussed.     

Tilt-induced ferromagnetic ordering in anisotropic molecular monolayers

It is shown that orientational ordering of anisotropic organic molecules with permanent magnetic dipoles in a tilted film should result in a macroscopic magnetisation in the plane of the film. The important requirement here is that the molecules are strongly biaxial, and the corresponding biaxial orientational order parameter in the tilted phase is sufficiently large. The molecules should also be characterised by a reduced symmetry of the magnetic core compared with existing “single molecular magnets". Possible symmetry groups of the molecular magnetic core, which allow for the existence of nonzero average magnetic moment, are discussed in detail. The tilt-induced ferromagnetic ordering of such molecules may be determined by nonmagnetic intermolecular interactions including, for example, quadrupole-quadrupole electrostatic interaction or dispersion interaction between molecules of particular symmetry. Magnetic intermolecular interactions are not important here, and as a result the induced ferromagnetic state may be stable in any temperature range where the corresponding tilted film is stable. These general conclusions, which form a theoretical foundation for the existence of novel fluid low-dimensional magnetic materials, are based on symmetry arguments and are supported by a simple mean-field molecular model. We also discuss how such induced ferromagnetic ordering may be observed in Langmuir-Blodgett films which seem to be the best candidates for preparing these magnetic materials.     

Effect of dipole forces on the structure of the liquid phases of DNA

The dipole-dipole contribution to the energy of the pair interaction between DNA molecules has been calculated and analyzed. Rigid fragments of DNA, i.e., of a length of about the persistent length, which have discrete dipole moments of base pairs, are considered. For a given distance between the centers of mass of molecules, the energy of the dipole-dipole interaction is a function of three angular variables; the angles ?₁ and ?₂ between the central dipoles of both molecules and the z axis passing through the centers of the molecules, as well as the angle ξ between long axes of the molecules, are taken as these variables. It is shown that the dipole energy has minima when the mutual orientation of the molecules satisfies one of the following conditions: (i) ?₁ = ?₂ = 0 or (ii) ?₁ = ?₂ = π. The cholesteric twist angle ξ can be both positive and negative in dependence on the type of the minimum. For realistic cholesteric dispersion parameters, the dipole energy is only slightly lower than the experimentally known binding energy of the molecules in dispersion. The results allow the assumption that the dipole forces significantly affect the structure and other properties of DNA suspensions; in particular, they can lead to nontrivial texture phenomena, biaxial correlation, and multistability.     

Nonrelativistic dispersional equations for crystals of sphalerite and diamond structure

The tenth- and eleventh-order dispersion equations obtained for sphalerite and diamond structures in previous works are reduced to algebraic form and compared. The dispersion equation for the sphalerite structure is factorized at the axes and in the planes of symmetry. At the axes and the factorization is complete; the zones of heavy and light holes are the same as in the diamond structure. At the axes gS only a zone of heavy holes is isolated, which is again no different from that obtained from the diamond structure. Factorization of the equations for both structures in the whole of the (110) plane is performed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 3–6, November, 1982.     

Cartesian Dynamics of Simple Molecules I Diatomics and Centrosymmetric Triatomics

A simple spring model for molecular vibrations is described in which Cartesian co-ordinates are used for both longitudinal and transverse displacements. The transverse restoring forces are shown to be electrostatic in origin and much weaker than the elastic longitudinal forces. The technique is applied to diatomic and centrosymmetric triatomic molecules. In the latter case, an analytical expression for the bending mode frequency is obtained which is equivalent to that derived by conventional methods using bending constants and internal co-ordinates. The model offers certain advantages when applied to the dynamics of crystals, for which Cartesian co-ordinates, aligned with the unit cell axes, are the natural choice. Reference is made to recent work on molecular and ionic crystals using extensions of this model.     

Cones of optical axes in gyrotropic crystals with scalar permittivity

A theory is constructed for the degeneracy of electromagnetic waves in gyrotropic crystals near their isotropy points (in temperature and other parameters), in which permittivity ? becomes scalar due to dispersion and optical anisotropy is entirely determined by gyrotropy. It is shown that closed lines of intersection of sheets of the refraction surface, which correspond to the cones and, in particular, planes of the optical axes, are formed for isotropic ?. The polarization characteristics of wave fields experience a jump upon a transition through such lines. The conditions for the existence and geometry of the degeneracy cones under investigation are analyzed for crystals of all symmetry classes permitting optical activity. It is shown that the degeneracy lines disappear for a small deviation of ? from isotropy, while polarization anomalies persist. Isolated (one or two) degeneracy points may retain in place of the lines in the case when the optical axes of a perturbed crystal with “switched-off” gyrotropy belong to the initial cone.     

Mode energy transformation between two connected multimode general square-law-index optical waveguides

A coherent states method is used to investigate the mode coupling coefficients in the most general buttjoint problem for two multimode general square-law-index optical waveguides, when two different waveguides with elliptical cross-sections are to be butt-jointed with axis displacement, tilt and some turning of symmetry axes with respect to each other. The explicit expressions for the mode coupling coefficients and recurrence relations for the mode overlap integrals are obtained; the sum rules for the mode coupling coefficients are formulated and a method of experimental data analysis is proposed for this general problem. The method of calculating mode coupling coefficients is proposed for the case of the butt-joint problem when the waveguide cross-sections are only partially overlapping and then it is used to investigate the influence of misalignment on mode power distribution and pulse dispersion in the second waveguide. The experimental data are compared and it is shown that the coupling coefficients obtained in square-law-index model can be used in dispersion calculations forα-profile fibres in the case when the valueα is not far from the valueα=2.     

Angular forces in the lattice dynamics of diamond crystal lattices

The lattice dynamics of the diamond lattice has been investigated using a model in which the interatomic forces include, in addition to central forces, the angular forces of the type employed by de Launay and Clark, Gazis and Wallis. The 2 models have been applied to silicon and germanium to investigate the phonon dispersion curves in the three symmetry directions of the Brillioun zone. The results are found to be qualitatively in good agreement with experiments.     

Collision-broadened line widths of tetrahedral molecules—I. Theoretical formulation

A theoretical formulation is presented within the framework of Anderson-Tsao- Curnutte theory for calculating the half-widths of spectral lines belonging to tetrahedral molecules. The importance of tetrahedral symmetry in the change distribution and in the wave functions is emphasized. Expressions for the interruption functions S₂(b) have been derived for octopole-dipole, octopole-quadrupole, octopole-octopole, octopole-hexadecapole, hexadecapole- hexadecapole, anistropic dispersion interactions as well as for an assumed overlap interaction potential. The earlier theoretical work of Tejawni and Yamamoto and Hirono is shown to be inappropriate for molecules of tetrahedral symmetry.     

The existence of pure surface modes in elastic materials with orthorhombic symmetry

A pure surface mode in a semi-infinite elastic body with a traction-free boundary is a progressive harmonic surface wave in which the displacement is everywhere co-planar with the wave and surface normals. When the elastic material has orthorhombic symmetry, with one of the 2-fold symmetry axes normal to the bounding plane, there are generally only two directions in which a pure surface mode may propagate, but additional directions appear when the transmitting material has higher symmetry. It is shown that for all the possibilities arising in this way the positive definiteness of the strain energy is a sufficient condition for the existence of a unique pure surface mode. The properties of pure modes in elastic materials belonging to the orthorhombic, tetragonal, hexagonal and cubic systems are discussed with particular reference to conditions under which the motion has the same features as a Rayleigh wave.     

Relative equilibria of D2H + and H2D+

Relative equilibria of molecules are classical trajectories corresponding to steady rotations about stationary axes during which the shape of the molecule does not change. They can be used to explain and predict features of quantum spectra at high values of the total angular momentum J in much the same way that absolute equilibria are used at low J. This paper gives a classification of the symmetry types of relative equilibria of AB₂ molecules and computes the relative equilibria bifurcation diagrams and normal mode frequencies for D₂H⁺ and H₂D⁺. These are then fed into a harmonic quantization procedure to produce a number of predictions concerning the structures of energy level clusters and their rearrangements as J increases. In particular the formation of doublet pairs is predicted for H₂D⁺ from J ≈ 26.     

Fluctuations and stability of stationary non-equilibrium systems in detailed balance

A generalized thermodynamic potential for Markoffian systems with detailed balance and far from thermal equilibrium has been derived in a previous paper. It was shown that the principle of detailed balance is equivalent to a set of conditions fulfilled by this potential (“potential conditions”). The properties of this potential allow us to extend the validity of a number of thermodynamic concepts well known for systems in or near thermal equilibrium to stationary states far from thermal equilibrium. The concept of symmetry breaking phase transitions for these systems is introduced in analogy to thermal equilibrium systems by considering the dependence of the stationary probability density of the system on a set of externally controlled parameters {λ}. A functional of the time dependent probability density of the system is defined in close analogy to the Gibb's definition of entropy. This functional has the properties of a Ljapunov functional of the governing Fokker-Planck equation showing the stability of the stationary probability density. The Langevin equations connected with the Fokker-Planck equation are considered. It is shown that, by means of the potential conditions, generalized “thermodynamic” fluxes and forces may be defined in such a way that the smoothly varying part of the Langevin equations (kinetic equations) constitutes a linear relation between fluxes and forces. The matrix of coefficients is given by the diffusion matrix of the Fokker-Planck equation. The symmetry relations which hold for this matrix due to the potential conditions then lead to the Onsager-Casimir symmetry relations extended to systems with detailed balance near stationary states far from thermal equilibrium. Finally it is shown that under certain additional assumptions the generalized thermodynamic potential may be used as a Ljapunov function of the kinetic equations.     

Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

含有五度旋转轴点群的超拉曼张量的计算

超拉曼散射涉及晶格振动, 因此它需要由动态张量来描述。根据坐标积与张量元在对称操作下的变换形式相同的原理, 通过C语言编程, 计算了属于不同不可约表示的动态张量, 并列出了含有五度旋转轴点群的三阶超拉曼张量。