A systematic Monte Carlo simulation and renormalized perturbation theoretical study of the dielectric constant of the polarizable Stockmayer fluid

A systematic Monte Carlo (MC) simulation and perturbation theory (PT) study is reported for the dielectric constant of the polarizable Stockmayer fluid. Our MC simulations apply the ‘pair approximation for polarization interaction’ procedure suggested by P?edota et al. The theoretical approach is based on our newly introduced equation (Valiskó et al., 2002, Molec. Phys., 100, 559) which is a density expansion for the dielectric constant using Wertheim's renormalized PT method. The agreement between our MC and PT results is excellent for low to moderate dipole moments and polarizabilities. At stronger dipolar interactions ergodicity problems and anisotropic behaviour appear where simulation results become uncertain and the theoretical approach becomes invalid.     

液晶SmC*相自发极化的统计理论

采用格胞模型，定义在格胞中心上的极化序参量．选用双轴性并具有横向电矩的分子作用势，求得系统的自由能，得到自发极化强度的大小和螺旋变化螺距的表达式．计算了DOBAMBC和3M2CPOOB等4种典型SmC^*相液晶的自发极化强度大小和螺距随温度的变化及其受分子横向电矩的影响，结果与实验相符．表明SmC^*相的自发极化强度主要产生于分子的双轴性和横向电矩． 关键词：     

Dipole dipole interactions and Davydov splitting in crystals

The dipole dipole interaction theory of Davydov for factor group (Davydov) splitting in the vibrations of molecular groups in crystals is discussed. It is shown that, even in a particularly simple case, dipole dipole interactions alone are insufficient to explain the observed effects.     

Electric and magnetic response to the continuum for A = 7 isobars in a dicluster model

The mirror isobars ⁷Li and ⁷Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of the deuteron. Energy-weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S -factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.     

Corrections to the Casimir–Polder potential arising from electric octupole coupling

ABSTRACT

Molecular QED theory is employed to derive a generalised formula for the dispersion potential between two molecules with mixed electric multipole polarisability tensors of arbitrary order at each centre. This expression is used to readily extract the pair energy shift between an electric dipole polarisable molecule and a mixed electric dipole–octupole polarisable one, and that between two mixed electric dipole–octupole polarisable species. This is done to see whether these interaction energies give rise to higher-order corrections to the Casimir–Polder potential, as was found in the previously calculated case of the dispersion energy shift between an electric dipole polarisable molecule and an electric octupole polarisable one. Interestingly, for orientationally averaged species, both of the computed interaction energies are independent of the octupole weight-3 term, are retarded, and may be interpreted as higher-order corrections in the fine structure constant to the leading dipole–dipole dispersion potential.     

Analytical representation of half-width for molecular ro-vibrational lines in the case of dipole–dipole and dipole–quadrupole interactions

The analytical formula for half-width of molecular ro-vibrational lines is obtained for the case of dipole–dipole and dipole–quadrupole interactions. This formula depends on the variable parameters, which have to be determined by fitting to experimental half-widths or to half-widths calculated by semi-classical methods. The application of the analytical formula to the H₂O–H₂O, NH₃–NH₃, DCl–HCl and CO–H₂O systems is discussed.     

Ordering of p‐n‐alkylbenzoic acids (nBAC) having four,five, and six alkyl chain carbon atoms – a computational analysis

A computational analysis of ordering in p‐n‐alkylbenzoic acids, having 4 (4BAC), 5 (5BAC), and 6 (6BAC) alkyl chain carbon atoms, has been carried out based on quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic centre has been carried out through an all‐valance electron (CNDO/2) method. The modified Rayleigh‐Schrodinger perturbation theory along with multicentered‐multipole expansion method has been employed to evaluate long‐range intermolecular interactions while a ‘6‐exp’ potential function has been assumed for short‐range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature, nematic‐isotropic transition temperature and above transition temperature using the Maxwell‐Boltzmann formula. A comparative picture of molecular parameters like total energy, binding energy and total dipole moment has been given. A model has been developed to describe the nematogenicity of these acids in terms of their relative order with molecular parameter introduced in this article.     

Molecular ordering in a bipolar nematogenic cyanobiphenyl – a computer simulation approach

The molecular ordering of 4-(6-hydroxypropyloxy)-4′-cyanobiphenyl (H3CBP), a bipolar nematogen, has been carried out at room temperature (300 K) with respect to translatory and orientational motions. The complete neglect differential overlap (CNDO/2) method has been employed to compute the net atomic charge and atomic dipole moment at each atomic center. The modified Rayleigh–Schrodinger perturbation theory with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a 6-exp potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature using the Maxwell–Boltzmann formula. On the basis of stacking, in-plane, and terminal interactions energy calculations, all possible geometrical arrangements of the molecular pair have been considered. Further, an attempt has been made to develop a model for liquid crystallinity based on probability of dimer complexes.     

Intensities of the photoelectron spectra of weakly bound anions: A complex of an atomic anion with a diatomic molecule

A closed formula for the state-resolved photodetachment probabilities of an electron from a weakly bound complex of an atomic anion with a diatomic molecule residing in a nondegenerate electronic state is obtained. Due to the reduction of the dipole moment matrix elements in terms of molecular electronic wave functions to the matrix elements in terms of atomic wave functions, the formula allows one to calculate the relative intensities of the photoelectron spectrum taking into account rovibrational and spin-orbit interactions and using practically convenient representations of the wave functions of the bound initial state of an anionic complex and of the bound or unbound final state of a neutral system. The methods of estimation of the atomic dipole moment matrix elements, the error due to neglect of the photoelectron rescattering, and possible modifications and generalizations of the formula are discussed.     

Collective vibrational modes of isotopic mixtures of CO on Cu(111) and Cu(001)

Recent infrared absorption measurements of isotopic mixtures of CO on Cu(111) and Cu(001) are analyzed in terms of a dipole coupling theory for substitionally disordered overlayers. The variation of frequencies as well as intensities of the collective C–O stretching vibrational modes with composition are in excellent agreement with the dipole theory. The electronic and vibrational contributions to the molecular polarizability are consistent with those derived from a direct measurement of the normal mode dispersion using electron loss spectroscopy. The interaction of a vibrating dipole with its own image is discussed and it is shown that this effect should not be included explicitly in the dipole sum.     

Ordering of Mesogenic Compounds in a Dielectric Medium at the Nematic-Isotropic Transition Temperature - A Comparative Study

A comparative study of molecular ordering of trans-trans-4′-alkylbicyclohexyl-4-carbonitriles (cyclohexylcyclohexanes, CCHs) with alkyl group: propyl (CCH3); pentyl (CCH5); and heptyl (CCH7) has been carried out with respect to translational and orientational motions. The CNDO/2 method has been employed to compute the net atomic charge and atomic dipole moment at each atomic centre. Configurational energy has been computed using the Rayleigh-Schrodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium (i.e. non-interacting and non-mesogenic solvent, benzene) at the phase transition temperature using the Maxwell-Boltzmann formula. Further, the flexibility of various configurations has been studied in terms of variation of probability due to departure from the most probable configurations. It is observed that, in a dielectric medium, the probabilities are redistributed, although the order of preference remains the same. An attempt has been made to explain the nematogenic behaviour of these mesogenic compounds, and thereby develop a molecular model for the liquid-crystallinity.     

Dipole-Dipole Interaction and the Directional Motion of Brownian Motors

The electric field of the microtubule is calculated according to its dipole distribution. The conformationalchange of a molecular motor is described by the rotation ofa dipole which interacts with the microtubulc. The mricalsimulation for the particle current shows that this interaction helps to produce a directional motion along the microtubule.And tte average displacement executes step changes that resemble the experimental result for kinesin motors.     

A “Master” perturbation series for the transition amplitude in a light field

We derive a “master” perturbation series for the quantum amplitude for a given transition process induced by laser-matter interaction. The result is derived using a complete set of basis functions depending on a real parameter λ. It provides a one-parameter (λ) family of infinitely many equivalent series representations of one and the same transition amplitude defined in the minimal coupling (MC) “velocity gauge”. As a first application of the master series we put λ = 0 and 1 in the formula and immediately obtain the two well-known perturbation series, traditionally derived in the “velocity” and “length” gauges. The master formula can be used to obtain any number of equivalent perturbation series by simply choosing a real number for λ; e.g., a “hybrid perturbation” series follows from putting λ = 1/2 in the formula.     

Dipole—Dipole Interaction and the Directional Motion of Brownian

The electric field of the microtubule is calculated according to its dipole distribution.The conformational change of a molecular motor is described by the rotation of a dipole which interacts with the microtubule.The numerical simulation for the particle currend shows that this interaction helps to produce a directional motion along the microtubule.And the average displacement executes step changes that resemble the experimental result for kinesin motors.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.     

氖原子光电子角分布的理论计算

本文利用密度矩阵理论和Racah代数推导出了光电子角分布的一般计算公式, 并在多组态Dirac-Fock方法基础上发展了计算原子光电离过程中产生的光电子角分布的相对论程序, 利用该程序对氖原子2s和2p光电子角分布的偶极和非偶极参数进行了具体计算, 所得结果与已有文献具有很好的一致性. 在此基础上, 本文讨论了光子与电子相互作用多级展开中的非偶极项以及入射光的极化性质对光电子角分布的影响.     

Radial-fluctuation-induced stabilization of the ordered state in two-dimensional classical clusters

Melting of two-dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined either by a circular hard wall or by a parabolic external potential and interact through a dipole or a screened Coulomb potential. We found that, with decreasing strength of the interparticle interaction, clusters with a short-range interparticle interaction and confined by a hard wall exhibit a reentrant behavior in its orientational order.     

The validity range of the dipole approximation for a dielectric mixture

This paper investigates the validity range of the dipole approximation for a dielectric mixture with spherical inclusions through electric field analyses according to a new criterion: if the maximum perturbation on an arbitrarily selected sphere surface caused by the interactions among spheres is less than a given allowable error, the dipole approximation is considered acceptable. Based on the dipole-enhanced dipole approximation previously presented by us, a theoretical formula for calculating the validity range of the dipole approximation is derived. It shows that the validity range depends on three parameters, the dielectric mismatch, the volume fraction of inclusions, and the allowable error. The calculated results by this formula are compared with those numerically obtained by the FEM. The good agreement between them indicates the credibleness of this formula.     

Molecular Ordering of a Nematogen at Phase Transition Temperature - A Theoretical Study

Molecular ordering in 4-cyano-4'- n -propylbiphenyl ( CB3 ), a nematic liquid crystal, has been studied with the help of intermolecular interaction energy calculations. The CNDO / 2 method has been employed to compute the net atomic charge and atomic dipole moment at each atomic centre. Modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a ' 6-exp ' potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using Maxwell-Boltzmann formula. All possible geometrical arrangements between molecular pair have been considered during stacking, in-plane and terminal interactions. An attempt has been made to identify the most probable configuration at the phase transition temperature during stacking, in-plane and terminal interactions. Results obtained have been discussed in the light of experimental as well as other theoretical observations.     

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ₀(E). Numerical results are given for O¹⁶ and C¹² by evaluating σ₀(E) in a square well potential.