Vibratory Conveying by Harmonic Longitudinal and Polyharmonic Normal Vibrations of Inclined Conveying Track

Vibratory conveying of a material point by harmonic longitudinal and polyharmonic normal vibrations of an inclined conveying surface is considered. The dependence of dimensionless conveying velocity – a ratio of velocity to the product of frequency and amplitude of longitudinal vibration – on several dimensionless parameters is investigated in the moving modes without hopping. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and phase difference angle between the longitudinal and normal vibrations, which are called optimal. Their values are dependent on two dimensionless parameters: the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. In a condition of the intensive longitudinal vibration, when its amplitude significantly greater than amplitudes of normal vibration, dimensionless velocity is almost independent of the intensive vibration parameter and it depends only on inclination angle parameter, i.e. on inclination angle and frictional coefficient. The optimal values of harmonics' amplitudes of polyharmonic normal vibration are determined in dependence of inclination angle parameter with the number of harmonics from 2 to 7. The graphs of considered dependencies are presented and the most important values of parameters are presented in the table. Conclusions are made to determine the optimal vibration parameters and the problems of further research are indicated. The considered vibrations can be used in different vibratory conveying devices with electromagnetic drives.

DFT Study of Molecular and Electronic Structure of Y, La and Lu Complexes with Porphyrazine and Tetrakis(1,2,5-thiadiazole)porphyrazine

Electronic and geometric structures of Y, La and Lu complexes with porphyrazine (Pz) and tetrakis(1,2,5-thiadiazole)porphyrazine (TTDPz) were investigated by density functional theory (DFT) calculations and compared. The nature of the bonds between metal atoms and nitrogen atoms has been described using the analysis of the electron density distribution in the frame of Bader’s quantum theory of atoms in molecule (QTAIM). Simulation and interpretation of electronic spectra were performed with use of time-dependent density functional theory (TDDFT) calculations. Description of calculated IR spectra was carried out based on the analysis of the distribution of the potential energy of normal vibrations by natural vibrational coordinates.

Theoretical research of the force field of (difluoroamino)trinitromethane in the coordinates Хδ0

Actual problem of modern chemists-researchers is studying the properties of molecules of compounds. The latest achievements in the field of computer engineering and quantum chemistry make it possible to research various physicochemical parameters of studying compounds using theoretical calculations. Calculation methods can greatly simplify the task, as they are safer and more economical than experiment. It is noted that methane derivatives are also currently of interest for research in connection with their widespread use. This paper is devoted to the study of the force fields of molecule of (difluoro-amino)trinitromethane using quantum chemical calculations. The Becke-Lee-Yang-Parr method of density functional theory (DFT) B3LYP with a hybrid potential of 6-311++G(3df, 3pd) was chosen as the main approximation for the work performed, since when using it, the best quality of the result is noted. Also, in the present work, as an alternative to chemical (natural) coordinates, new coordinates Xδ0 were chosen, which allows one to take into account torsional vibrations. The calculations presented in this work were performed using the Gaussian and GaussView programs, designed to calculate a large number of properties and characteristics of chemical reactions. In this paper, using the proposed approach, the geometry of the molecule of (difluoroamino)tri-notromethane has been optimized, the geometric parameters of these compound were considered, in particular, the valence angles, dihedral angles, and long bonds were calculated, corresponding to the minimum energy of this molecule. For the first time, generalized force coefficients for F2NC(NO2)3 were calculated, and the "stiffness" of the chemical compounds of the molecule under study was evaluated. The frequencies of normal vibrations (wave numbers) for the studied compound in the harmonic approximation were calculated and analyzed. A comparison of the obtained wave numbers with experimental data is given. The results obtained indicate a satisfactory agreement between theory and experiment. A general view of the vibrational spectrum of (difluoroamino)trinotromethane obtained as a result of quantum chemical calculations is presented. The conclusion is drawn about the possibilities of applying the B3LYP 6-311++G(3df, 3pd) approach for calculating the frequencies of normal vibrations and force coefficients.

Изотопные эффекты в спектрах комплексов с водородными связями. Ангармонические расчеты изотопологов комплекса [F(HF)-=SUB=-2-=/SUB=-]-=SUP=---=/SUP=-

The frequencies and intensities of IR absorption bands of symmetric and asymmetric H-bonded complexes [FL1FL2F]- (L1, L2 = K-meson Ka, proton H, deuton D, and triton T) are calculated. The equilibrium configuration and potential energy and dipole moment surfaces of isotopologues [FL1FL2F]- were calculated by the MP2/6-311++G(3df,3pd) method with the basis set superposition error taken into account. The calculations of spectral parameters with allowance for anharmonic interactions of all vibrations were carried out using the second-order vibrational perturbation theory. Variation of Li and L2 masses in wide regions allowed significant changes in the forms of normal vibrations and values of anharmonic interaction constants upon isotopic substitution to be obtained. The trends in the changes of spectral parameters were determined upon transition from one symmetric isotopologue to another and upon transition from symmetric to asymmetric isotopologues. The D-F stretching band frequency predicted for [FHFDF]- is in good agreement with the experimental value. The assignment of this band was improved.

Optimization of vibratory conveying upward by inclined track with polyharmonic normal vibrations

The paper is devoted to the research of vibratory conveying of piece goods along an inclined track, performing harmonic longitudinal and polyharmonic normal vibrations. It is considered the conditions of reaching maximum conveying velocity at specified values of frequency and amplitude of longitudinal vibrations – the conditions of maximum dimensionless conveying velocity, depending on several dimensionless parameters in the moving modes without hopping. These dimensionless parameters are the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient, the intensive vibration coefficient – a ratio of the longitudinal amplitude of vibration to the amplitude of the first harmonic of normal vibration and frictional coefficient. Maximal conveying velocity is achieved at the certain values of normal vibration amplitudes and values of phase difference angles between longitudinal and normal vibrations, which are called optimal, and their values are dependent on these two dimensionless parameters, while maximum normal vibration acceleration should be equal to the gravitational acceleration. The research was made by approximate harmonic balance method and by numerical step-by-step integration method, which allows performing calculations with any given accuracy. The results obtained by the two methods are compared. To determine the maximal and optimal values of elevation angles, there are calculated the maximal value of the inclination angle parameter at which the value of dimensionless velocity is equal to zero, and the value of the inclination angle parameter at which a particle moves to a specified height in the minimum time. The optimal values of amplitudes of harmonics of polyharmonic normal vibration are determined in dependence on the inclination angle parameter with the number of harmonics from four to seven. The graphs of these dependencies are presented and the most important values of dimensionless parameters are presented in the table.

Спектральная диагностика динамики образования гомосопряженного комплекса [HCN.H.NCH]-=SUP=-+-=/SUP=-

A quantum-mechanical analysis of the manifestations of the NHN hydrogen bond in the vibrational spectra of the [HCN.H.NCH] + linear complex along the proton transfer reaction profile is given, and the laws governing the diagnostic parameters — potential descriptors of the dynamics of this process — are established. The surface of the potential energy and harmonic frequencies of normal vibrations along the profile of the proton transfer reaction path in the system studied are calculated. It has been shown that when the [HCNH] + and NCH fragments come closer together, a noticeable distortion of the forms of their skeletal vibrations occurs, up to complete mixing into the symmetric and antisymmetric forms. The frequency of the longitudinal vibration of the central proton ν (NH) varies along the reaction path from ~ 3600 to ~ 500 cm-1. In the region of intersection of the terms ν (NH) and ν (CN) an abrupt nature of frequency change is detected.