Normal coordinate calculations of benzenoid hydrocarbons: Theoretical models of simplified valence force fields

Two types of theoretical models of simplified valence force fields for benzenoid hydrocarbons are proposed, and normal coordinate calculations are performed for benzene, naphthalene and anthracene on these models. The molecular orbital theory on force constants presented by Coulson and Longuet-Higgins is found to be of great significance in determining aromatic force fields. An alternative method of classifying CC stretching cross terms on the basis of topological considerations also gives unexpectedly successful results. A systematic choice of potential functions not only dramatically improves the least-squares fit of the calculated frequencies to the known experimental results but also considerably increases the transferability of the potential parameters.     

Determination of accurate semiexperimental equilibrium structure of proline using efficient transformations of anharmonic force fields among the series of isotopologues

The complete semiexperimental (SE) equilibrium structure of proline (45 degrees of freedom) is determined using the mixed estimation method. The cubic force fields for the parent and eight isotopologues of proline molecule are evaluated at the MP2-FC/cc-pVTZ level in Cartesian coordinates. The accuracy of the SE structure is verified by optimising the structure with the CCSD(T) model and a basis set of quadruple-ζ quality. A significantly more accurate equilibrium structure of proline is obtained when compared to the previous one. It is shown that the employed technique is efficient for the determination of SE equilibrium structures of rather large molecules. A simple transformation of anharmonic force fields between normal coordinate and Cartesian coordinate representations is proposed. The suggested technique allows efficient evaluation of the rotation–vibration interaction constants for a number of isotopologues, once the cubic force field of any species is found either in normal or Cartesian coordinates.     

Application of the Theoretical Methods of Experimental Design to a Solution of Problems in Moleculer Spectroscopy

Theoretical methods of experimental design are used to establish the dependences of the vibrational frequencies of a molecule on the bond lengths and force constants. On the example of the benzene molecule, the effect of each parameter on the examined spectral characteristics is vividly demonstrated for a wide range of variation of the examined parameter, which obviates the necessity for a conventional solution of the spectral problem of estimating the vibrational frequencies of the related molecules with the use of computer programs.     

Normal coordinate analyses for trimethylantimony(V) dihalides: A comparison of three force fields

Approximate normal coordinate analyses have been carried out for the series (CH₃)₃SbX₂ (X = F, Cl, Br, and I) assuming a molecular symmetry of D_3h and that the methyl groups behave as single atoms. Sets of seven force constants have been evaluated for each molecule using each of the following force fields: general valence, modified Urey-Bradley, and orbital valence. The fundamental vibrational frequencies have been evaluated using these force constants and have been compared with the experimentally observed values published previously. The orbital valence force constants generally led to better agreement between calculated and observed frequencies. Trends in the force constant values are discussed briefly.     

Perturbation analysis of a stationary nonequilibrium flow generated by an external force

The stationary flow of a gas in a slab under the action of a constant external force parallel to the walls is analyzed in the context of the Bhatnagar-Gross-Krook model kinetic equation. The force produces spatial gradients along the coordinate normal to the walls. By performing a perturbation expansion in powers of the force, we obtain the hydrodynamic fields up to fifth order in the force. Then the velocity distribution function and all its moments are evaluated to third order. The expansion coefficients are polynomials in the space variable of a degree increasing linearly with the expansion order. Although the series expansion is only asymptotic, it shows how the state of the system is modified by a variation of the external force beyond the linear regime.     

Presentation of Molecular Force Fields in Terms of Dimensionless Coordinates

It is suggested that force fields calculated for polyatomic molecules may be presented in dimensionless coordinates, ξ (=R/R_e, where R is internal coordinate and Re is the equilibrium value of corresponding bond distance or angle). Stretching force constants when presented in dimensionless coordinates show interesting trends. It is found that whereas the force constants in terms of internal coordinates, F_ii vary widely for bonds with different atoms in the series Z-H (Z:C, Si, Ge), Y-H (Y:N, P, As, Sb, O, S), X-H (X:F, Cl, Br, I), X-C etc, the corresponding force constants in dimensionless coordinates, Φ_ii are same within the limits of experimental errors. It is felt that such force constants may have better prospects of transferability between related molecules and may be helpful in making the normal coordinate analysis easier to some extent.     

The Degenerate Vibrations of BCl3, BBr3 and BI3 with Application of Keating Coordinates

The experimental works of vibrational spectroscopy and normal coordinate analyses for BCl₃, BBr₃ and BI₃ are reviewed extensively. Harmonic force fields of the E' species are produced using isotopic frequencies and Coriolis constants as additional data, respectively. The usefulness of Keating coordinates versus valence coordinates as basis of force field approximations is discussed. The conclusions are not unequivocal, but they go in favour of the Keating coordinates when the reliability of the different computations is taken into account. Boron trichloride is treated specifically in some detail. Final force fields are proposed for the title molecules with the aid of the mass influence on Coriolis constants.     

A reduced dimensionality model of torsional vibrations in star molecules

The torsional vibrations of star molecules are studied with a reduced dimensionality model. In this model, the molecule is described by two equivalent sets of lumped inertial cylinders and vibrational frequencies are predicted by solution of the coupled equations of motion. Force constants are determined by including them as free parameters in the model and fitting the computed frequencies to their analogs as determined using full normal coordinate analysis at the HFSCF level of theory. Best agreement between the methods occurs when torsional force constants are included for the first two layers of the molecule. This reveals that non-bonded torsional interactions are important in the vibrational dynamics of these systems. Further insight is afforded by an analysis of why simple harmonic oscillator models are sufficient for modeling some related systems but fail to reproduce the trend in global mode frequencies for saturated aliphatic star molecules. The analysis reveals that the origin of this failure lies in backbone flexibility in these branched polymeric systems.     

Reflection and transmission of phonons at a planar interface between two dissimilar solids

Two semi-infinite dissimilar crystals with, however, the same crystal structure and lattice parameter are in contact at a planar interface. Using a simple force constant model, restricted to near-neighbour interaction reflection and transmission coefficients for sound waves propagating along one solid are calculated. At low frequencies the reflection and transmission coefficients are determined solely by the force constants and the atomic masses in the two media. At high frequencies the transmission coefficient becomes small if the force constant at the interface between the two media is weak. Information of the local force constant in the interface region can be gained at least in principle, by measuring the reflection and transmission coefficients at high frequencies.     

Ab initio study of the force constants of inorganic molecules ONF and NF3

The force constants of ONF and NF₃ have been determined from Hartree-Fock ab initio wavefunctions by the force method. Three different Gaussian basis sets, ranging from 7s3p augmented with functions on the bonds to 5s2p, were used for ONF. Only the smallest basis was applied to NF₃. The results show remarkable agreement with experiment, especially for the coupling constants. The NF stretching force constant is greatly overestimated in calculations with the 5s2p basis. The calculated force field makes it possible to exclude sets of force constants which are unphysical but compatible with the experimental data. The results show that even calculations with 5s2p basis sets can contribute to the determination of force fields.The experimental value of the $\text{ON}\text{β}$ coupling constant in ONF ranges between 0.27 and 0.54 mdyn; our calculations corroborate the higher value. An estimation of the calculated molecular geometries is given.     

用光学方法研究玻璃微珠电流变液颗粒间的相互作用

运用一套适合研究颗粒间相互作用的双光镊系统,通过对粒聚集时间的测量,得出颗粒聚集时间和电场的平方成反比。这是第一次用电流变液颗粒在动态情况下直接验证电偶极子对间的相互作用。发展了一套使用高速CCD摄像机进行扩散波谱（DWS）测量的方法,首次实时测量具有颗粒结构的非各态历经体系的自相关函数,以研究电流变液机理,得到了玻璃微珠电流变液的结构响应时间和力和响应时间;测量了不同电场下体系相关函数的特征衰减时间随时间的变化。在不同电场下测量扩散系数可以反映出相互作用力与电场的平方成正比。     

A Vibrational Force Field For 1-Alkynes and Nitriles

Abstract

Normal coordinate calculations were made for 1-butyne, propionitrile, and the two conformers each of 1-pentyne and butyronitrile, using a thirty-one parameter modified valence force field. Only the triple bond stretching force constant was assumed to be different in the two families of compounds. Twenty force constants were refined to fit 117 frequencies of the six molecules, with the average error being 5.1 cm^?1, or 0.65%.     

A solution of the motion of a charged particle in magnetic mirror systems

The paper solves the motion of a charged particle in an axially symmetrical, magnetostatic field, which forms magnetic mirror systems. The solution is based on the Hamiltonian for the motion of a charged particle in such a field. The whole problem is solved in orthogonal curvilinear coordinates, the coordinate curves being formed by the lines of force and the curves perpendicular to them. By applying the perturbation method of multi-periodical systems to the Hamiltonian in these coordinates, a Hamiltonian is obtained for the motion of the guiding centre which contains only the coordinate of motion along the lines of force, the others being cyclic. Thus, in addition to the energy two other first integrals of the equations of motion are obtained (since the impulses corresponding to the cyclic coordinates are constant), from which the conditions for confinement of motion in a magnetic field are immediately obtained. Since the Hamiltonian obtained in this way contains only one coordinate, the whole problem is solved by two quadratures, which define the dependence of the time and azimuthal angle on the line-of-force coordinate, while the other quantities are constant.In conclusion, the author thanks Dr. M. Seidl for valuable remarks and discussion on this work.     

Harmonic Force Fields from Scaled SCF Calculations: Program ASYM40

We report an extended version of our normal coordinate program ASYM40, which may be used to transform Cartesian force constants from ab initio calculations to a force field in nonredundant internal (symmetry) coordinates. When experimental data are available, scale factors for the theoretical force field may then be optimized by least-squares refinement. The alternative of refining an empirical force field to fit a wide variety of data, as with the previous version ASYM20, has been retained. We compare the results of least-squares refinement of the full harmonic force field with least-squares refinement of only the scale factors for an SCF calculated force field and conclude that the latter approach may be useful for large molecules where more sophisticated calculations are impractical. The refinement of scale factors for a theoretical force field is also useful when there are only limited spectroscopic data. The program will accept ab initio calculated force fields from any program that presents Cartesian force constants as output. The program is available through Quantum Chemistry Program Exchange. Copyright 2000 Academic Press.     

弹性压扭直杆的Greenhill公式对精确模型的推广

将圆截面Kirchhoff弹性压扭直杆的Greenhill公式推广到精确模型.基于平面截面假定,在弯扭的基础上增加了拉压和剪切变形,将弹性杆的位形表达为截面的弧坐标历程.由弹性杆精确模型的平衡微分方程,得到了两端受力螺旋作用时对应于直线平衡状态的特解,导出了线性化扰动方程及其通解,再根据两端为铰支时的边界条件以及积分常数存在非零解的条件导出弹性直杆精确模型的Greenhill公式.结果表明,由力螺旋表示的稳定域为一对称的封闭区域,拉压和剪切对稳定性的影响取决于拉压柔度与剪切柔度之差、抗弯刚度和杆长这三个因素.     

Yukawa-type potential besides newtonian potential in Poincaré gauge theory of gravitation

It is shown that the spin gauge fields with non-zero mass mediate the Yukawa-type interactions besides the short-range spin-spin interactions in the Poincaré gauge theory of gravitation. The interaction range of spin gauge fields is determined from the coupling constants. The coupling constant in front of the R(W) term is bounded by the requirement of a non-oscillating solution.     

Lattice dynamical study of Sr2B′UO6 (B′=Ni, Co) double perovskites

A short range force constant model has been used within the normal coordinate analysis framework for the first time to investigate the lattice dynamics of Sr₂B′UO₆ (B′=Ni, Co) double perovskites having space group P2_1/n. The zone centre phonons have been calculated with ten stretching force constants and eight bending force constants in the nickel compound and ten stretching and nine bending force constants in cobalt compound. The theoretically obtained values of Raman and infrared wave numbers exhibit a satisfactory agreement with the experimental values. A complete assignment of these frequencies to specific modes has also been made.     

The anharmonic force fields of PH3, PHF2, PF3, PH5, and H3PO

The cubic and quartic force fields of the title compounds are determined from ab initio SCF calculations using 6-31G^** and TZP/TZ2P basis sets. The computed geometries, vibration-rotation interaction constants, l-doubling constants, anharmonicity constants, and vibrational wavenumbers are compared with the available experimental data, especially for PH₃ and PF₃. Many experimentally unknown spectroscopic constants are predicted. A scaling procedure based on calculated harmonic and anharmonic force fields is proposed for predicting the vibrational wavenumbers of unknown molecules such as PH₅.     

Scattering of electromagnetic radiation by a two-layer nonconfocal spheroid that is small compared to the wavelength

We have considered the electrostatic problem for a two-layer nonconfocal spheroid. The approach is based on surface integral equations that are similar to equations in terms of the extended boundary condition method for wave problems. Electrostatic fields are related to scalar potentials, which are represented as expansions in terms of eigenfunctions of the Laplace equation in two spheroidal coordinate systems, while unknown expansion coefficients are determined from infinite systems of linear algebraic equations. The constructed rigorous solution to the problem coincides with the known solution in a particular case of a confocal two-layer spheroid. In addition, for the nonconfocal two-layer spheroid, we have constructed an explicit approximated solution assuming that the field in the particle core is constant. This solution coincides with the rigorous solution if the scatterer shells are confocal. The formula found for the polarizability of the two-layer nonconfocal spheroid has a very simple form compared to the previously proposed cumbersome algorithm (B. Posselt et al., Measur. Sci. Technol. 13, 256 (2002)) and is more efficient numerically.     

Low-resolution microwave spectroscopy: A new band type

The effects of relaxing two constraints on an earlier force field for benzene and fluorobenzenes have been explored. If the CC/CC ortho, meta, and para interaction constants are allowed to vary independently, they take the values 62, ?34, and 48 N m^?1, respectively. The interesting features of the earlier field are retained with the possible exception that the dependence of the CC stretching constant is less clearly dependent on fluoro substitution on the bond. An attempt to use more reasonable geometries than the regular hexagonal geometry assumed hitherto produced no improvement in the fit and did not alter the field significantly.