Perturbation method for solving the inverse vibrational problem in dependent coordinates

Solution of the inverse vibrational problem (IVP) when the dependent coordinates are excluded leads to a linear combination of the molecular force constants, of very limited usefulness for a series of related compounds. In this work we consider the question of separating these combinations during the solution of the IVP in a system of dependent coordinates. Such a solution is obtained by introducing a perturbation into the matrix of kinematic coefficients with the help of a certain self-consistent matrix. We obtain intrinsic force constants for tetrahedral hydrides (methane, silane, and germane) which reproduce experimental frequency spectra well.Three Hundredth Anniversary of the Reunion of the Ukraine with Russia State University, DnepropetrovskTranslated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1987.     

SNO results and neutrino magnetic moment solution to the solar neutrino problem

We have analysed the solar neutrino data obtained from chlorine, gallium and Super-Kamiokande (SK) experiments (1258 days) and also the new results that came from Sudbury Neutrino Observatory (SNO) charge current (CC) and elastic scattering (ES) experiments considering that the solar neutrino deficit is due to the interaction of neutrino transition magnetic moment with the solar magnetic field. We have also analysed the moments of the spectrum of scattered electrons at SK. Another new feature in the analysis is that for the global analysis, we have replaced the spectrum by its centroid.     

Neutrino magnetic moment solution for the solar neutrino problem and the SNO experiment

The motivations for the magnetic moment solution to the solar neutrino problem are briefly reviewed and the expected values for a number of observables to be measured by the SNO experiment are calculated assuming three different solar magnetic field profiles. The observables examined are the charged current event rate, the ratio of the neutral current to the charged current event rates and the charged current electron spectrum as well as their first and second moments. The dependence of results on the hep neutrino flux is also analysed and a comparison is made with the corresponding oscillation results.     

Determination of the dipole moment function of an ozone molecule on the basis of vibrational transition probabilities

Analytical relationships are obtained that connect the vibrational transition moments to molecular and electrooptical parameters. On the basis of experimental data on vibrational band intensities, coefficients of the expansions of the dipole moment function of O₃ are determined by using the above-mentioned expressions.     

静电系统受力和力矩计算

具有终端的静设备系统,是一种把电能转移为机械能的换能器。根据能量守恒和转换定律,导出该静电系统受力和力矩的两种计算方法及应用实例。     

A numerical solution of the layer-to-layer transition problem as a waveguide diffraction problem

Application of net-point methods to the solution of the layer-to-layer transition problem leads to the necessity to restrict the domain and formulate artificial boundary conditions. In the present work the introduction of an artificial coaxial for reducing the original problem to a waveguide diffraction problem is applied. The test results of the finite-element program that we developed, which demonstrate the high accuracy of the method, are considered. The investigated dependence of the solution on the artificial boundary location shows the rapid convergence of the method.     

Algorithm for solving the anharmonic vibratiqnal-rotational problem using curvilinear vibrational coordinates and the momentum representation for rotational wave functions

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 48, No. 1, pp. 103–110, January, 1988.     

Adaptation and performance of the Cartesian coordinates fast multipole method for nanomagnetic simulations

An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT.     

High order vibrational matrix elements for diatomic molecules; dipole moment function and transition moments of CO

The fifth and sixth-order contributions to the vibrational matrix elements are obtained for the transitions v→v'(v'?v+4) using an eight power internuclear Dunham potential and a quartic power series expansion of the dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and the transition moments R_v^v' (with v=5, 10, 20) deduced from a calculation including succesively third, fourth, fifth and sixth-order perturbation theory are compared. The validity of these results is discussed.Using a quintic dipole moment function, general expressions for the vibrational matrix elements corresponding to the transitions v→v'(v'? v+5) are also presented and the influence of these contributions on the calculation of the dipole moment coefficients as well as the hot band transition moments of CO is shown.     

An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: The use of redundant primitive coordinates

A modified effective scaling frequency factor (ESFF) method that takes advantage of the potential energy distribution (PED) coefficients calculated in the basis of redundant primitive internal coordinates is presented. This approach is simpler and more flexible than that based on the natural internal coordinates. The sets of optimal scaling factors for routine 9- and 11-parameter ESFF calculations based on B3LYP/6-311G∗∗ force fields are derived from Baker’s training set of 30 molecules (660 frequencies). The calculated root-mean-square (RMS) deviations for all frequencies are 11.42 and 11.44 cm⁻¹ for 9- and 11-parameter scaling, respectively. They are somewhat lower than in the case of ordinary ESFF calculations. The new sets of factors seem to be particularly well suited for scaling of frequencies in the middle region of the vibrational spectra (1000-2500 cm⁻¹) - the RMS values in this range are 8.37 for 9-, and 9.56 cm⁻¹ for 11-parameter scaling. These values are to be compared with 9.20 and 10.29 cm⁻¹, respectively, calculated within the natural coordinates based ESFF formalism.     

The effect of bending vibrations on the dipole moment of a linear polyatomic molecule: A theoretical treatment of the vibrational changes and transition moments

The vibrational effect on the dipole moment of a linear molecule is theoretically considered from the aspects of the dipole moment changes with the excitation of bending vibrations and the transition moments for the overtone, combination, and difference bands associated with bending modes. Such dipole moment changes and transition moments consist of two components, one depending on the first dipole moment derivatives with respect to bond lengths and the other depending on the second dipole moment derivatives with respect to bond angles. We show that the first component normally contributes little, and propose an approximation in which only the second component is retained. This approximation is practically important because the second component can be calculated without the anharmonic force constants. We derive formulas for the dipole moment changes and transition moments to facilitate a simultaneous analysis of different isotopic species. We introduce the concept of the equivalent mode, by which we may readily understand the correlation between the dipole moment change for a bending mode and the transition moment for a vibrational band.     

Modification of hyperspherical coordinates in the classical three-particle problem

A new version of the hyperspherical coordinates in the classical three-particle problem is considered, that leads to a modification of the Delves coordinates. A type of the kinetic and potential energy is obtained for the system. The problem is reduced in these coordinates for different cases of the classical motion. From geometrical reasonings a formula is chosen for the reduced mass of the three-body system. The triangle of masses and the relevant basic quantities and relations are introduced.