Degenerate Bending Vibration Research Articles

Reaction-path dynamics with harmonic vibration frequencies in curvilinear internal coordinates: H+trans-N2H2→N2H+H 2

This paper presents a general method for treating doubly degenerate bending vibrations of bonds with 180 deg bond angles in curvilinear coordinates along a reaction path. The new treatment improves the generalized normal mode frequencies needed for rate constant calculations with variational transition state theory and for multidimensional semiclassical tunneling calculations. We apply this method to calculate harmonic vibrational frequencies and rate constants for the reaction H+trans-N2H2→N2H+H2. The new results are compared to earlier calculations employing rectilinear Cartesian coordinates in order to evaluate the sensitivity of the calculations to the coordinate system chosen.

Molecular symmetries and vibrations in high-resolution inner-shell spectroscopy

Fragment ion yields in the 90° and 0° directions are measured in the C 1s→Rydberg excitation region of CO 2 and CH 4. In CO 2 the dipole-forbidden C 1sσ g→3sσ g Rydberg transition is the strongest of all the Rydberg transitions. The ion yields in the 90° direction are dominant, indicating that the bending vibration is predominantly coupled with the 3sσ g Rydberg state and the intensity-lending dipole-allowed state is a very strong π ∗ resonance nearly located. On the other hand, in the 4sσ g Rydberg state the vibronic coupling through the antisymmetric stretching mode is clearly observed in the 0° direction. Even in CH 4 with a highly symmetrical geometry, the C 1s a 1→3p t 2 and 3d t 2 Rydberg transitions show anisotropic angular distributions of the fragment ions. This result indicates that the vibronic coupling with the two-fold degenerate bending vibration causes the Jahn-Teller distortion to the C 3v geometry and enhances mixing with t 2 ∗ valence state of antibonding character. Thus, in inner-shell excitations of polyatomic molecules the axial recoil mechanism fails when bending vibrations are highly excited by the Renner-Teller or Jahn-Teller effects and vibronic couplings, though it will still be valid even in polyatomic molecules if only stretching (symmetric and antisymmetric) vibrations are excited.

Five-dimensional local mode-Fermi resonance model for overtone spectra of ammonia

A five-dimensional local mode-Fermi resonance model for overtone spectra of the ammonia molecule has been constructed. The model Hamiltonian is expressed in terms of curvilinear internal valence coordinates and it includes the three stretching vibrations and the doubly degenerate bending vibration. The symmetric bending vibration associated with the inversion motion has been excluded. Thus the model is useful for energy levels with the totally symmetric bending vibration on its ground state. Vibrational energy levels have been calculated using van Vleck perturbation theory. Nonlinear least-squares method has been used to optimize potential energy parameters. Observed vibrational band origins for 14NH3, 14ND3, and 14NT3 have been employed as data. A fit with the standard deviation of 5.5 cm−1 has been obtained using one set of isotope invariant potential energy parameters. The optimised potential energy surface compare well with results of ab initio electronic structure calculations and with results of customary anharmonic force field calculations.

An ultrasonic micromotor using a bending cylindrical transducer based on PZT thin film

Ultrasonic motors have a good high-torque performance. In particular, it seems that cylinder-type ultrasonic motors are superior to disk- or ring-type ones in the sense of high-torque application. For miniaturization of the motor size, a simple structure of an ultrasonic transducer becomes effective. This paper presents an ultrasonic micromotor using a bending cylindrical transducer based on a lead zirconate titanate (PZT) thin film on the side wall of a small tube. The transducer of the ultrasonic motor consists of a short cylindrical titanium pipe, PZT thin film and electrodes. The titanium pipe is introduced as a base material on which to deposit the PZT thin film by a hydrothermal method. The thickness of the film is about 9 μm. The electrodes are divided into four parts in a circumferential direction to excite degenerate bending vibration modes with two r.f. driving electrical sources. A rotor loaded on the transducer turns in the intended direction. The maximum revolution speed is 295 rpm.

Stepping Drive of Self-Oscillation-Type Ultrasonic Motor

A stepping drive method that does not use an extra clock signal source for a self-oscillation-type ultrasonic motor is described. The motor used here is an in-phase drive-type ultrasonic motor using two degenerate bending vibration modes of a disk. The output electrical signals caused on a self-oscillation are used as a clock signal for the stepping drive. An angular displacement at every step is realized using an open-loop control system without a rotary encoder as an angular displacement sensor. In order to eliminate the deviation of angular displacement at every step, a multitooth rotor was used. As a result, stable stepping drive of an ultrasonic motor was realized.

Transient Response Characteristics of a Same-Phase Drive-Type Ultrasonic Motor

This paper deals with a same-phase drive-type ultrasonic motor, using two degenerate bending vibration modes of a disk. Characteristics of the motor are influenced considerably by the mechanisms for supporting a stator and pressing a rotor. By investigating these points experimentally, a motor with high efficiency characteristics was realized. Moreover, the driving method for improving the transient response of the motor is described.

Intramolecular vibrational redistribution of energy in the stimulated emission pumping spectrum of acetylene

Using a combination of low resolution dispersed Ã→X̃ fluorescence spectra and high resolution stimulated emission pumping, we have spectroscopically identified the first stages of vibrational energy flow in the highly vibrationally excited acetylene prepared by Ã→X̃ emission over the energy range 5 000–18 000 cm−1. A detailed study of the stimulated emission pumping (SEP) spectrum of acetylene in the EVIB=7000 cm−1 region, in which we report spectroscopic constants and rovibrational term values for 12 vibrational levels, has conclusively shown that Darling–Dennison resonance between the cis and trans degenerate bending vibrations is the first step in the redistribution of vibrational energy from the initially excited Franck–Condon bright CC stretch and trans-bend vibrational combination levels. This allows an extension of our prior dispersed fluorescence (DF) assignments which suggested the crucial role of Darling–Dennison coupling between the cis and trans bends in IVR [J. Chem. Phys. 95, 6336 (1991)]. We prove that the symmetric CH stretch vibration, previously thought to play a crucial role in the redistribution of vibrational energy, is Franck–Condon inactive. We have also shown that vibrational-l-resonance among the states with excitation of both degenerate bending modes, when combined with a Fermi resonance which couples CC stretch/trans/cis-bend excited states to the antisymmetric CH stretch, determines the subsequent flow of vibrational energy after the Darling–Dennison bending resonance. These resonances all scale with vibrational excitation in nearly the simple manner expected for the lowest order anharmonic terms in the Hamiltonian, which allows the prediction of the fastest processes at high energy from a detailed study of the high resolution spectrum at lower energy. We find some interesting rules for vibrational energy flow in the short time dynamics: (i) CC stretch excitation is necessary for stretch–bend coupling; (ii) if V2″ and V4″ are the quantum numbers of the initially excited bright state, and vb″ = v4″ + v5″ is the total bending quantum number of a state coupled to that bright state, then V4″ ≥ vb″ ≥ (V4″–2V2″); (iii) the total stretch quantum number ns″ = (v1″ + v2″ + v3″) is also conserved by the short time dynamics. These are severe and well characterized restrictions on the range of quantum numbers accessible to the initial bright state during the first stages of intramolecular vibrational redistribution of energy.

Centrifugal Distortion Analysis and Study of T 2 -Relaxation for l-Type Doublet Transitions of Nitrous Oxide ( 15N2O) by a Microwave Pulse Technique

We investigated l-type doublet transitions of 15N20 in the first excited state of the degenerate bending vibration v2 with 14 < J < 34. From analysis of the J-dependence of the line center frequencies, the doubling constant q(0) was obtained together with the first and second order centrifugal distortion constants q(1) and q(2) respectively. For the lines in the J-band (4 to 8.2 GHz) and K-band (18 to 26.5 GHz) we have also investigated the pressure broadening due to self-collisions with use of the transient emission technique. The experimental results for the pressure broadening parameter Γp are compared with predictions from binary collision theory, based on the modified Murphy-Boggs perturbative treatment.

Van der Waals stretching and bending force constants from the rotational spectrum of argon… 1,3,5-trioxane

The rotational spectrum of the argon… 1,3,5-trioxane van der Waals molecule has been observed by using pulsed-nozzle, Fourier-transform, microwave spectroscopy. The ground vibrational state rotational constant of this symmetric-top, semirigidrotor molecule leads to R = 363 pm for the distance of the argon atom from the centre of mass of 1,3,5-trioxane along the C3 axis. The quadratic force constant and wavenumber for the vibration corresponding to the stretching of R have been obtained from the centrifugal distortion constant DJ as kR = 1.96 Nm−1 and ωR = 35 cm−1. The combination of the centrifugal distortion constants DJK + 2DJ leads to the analogous quantities kα = 8.52 × 10−21 J and ωα = 14 cm−1 for the degenerate bending vibration corresponding to the orientation of R with respect to the C3 axis of the 1,3,5-trioxane molecule.

Same phase drive-type ultrasonic motors using two degenerate bending vibration modes of a disk

Same-phase drive-type ultrasonic motors, using two degenerate bending vibration modes of a disk, are presented. The distinctive feature of the motor is in using the standing wave modes. The motor is not driven by two input signals with different phases, but by input signals with the same phase. Therefore, only one amplifier is sufficient to drive the motor. The experimental results have proved that the motor can yield stable operational characteristics at low speed and high torque.

Characteristics and a New Control Method of a Same-Phase Drive-Type Ultrasonic Motor

This paper deals with a same-phase drive-type ultrasonic motor, using two degenerate bending vibration modes of a disk. Characteristics of the motor driven at low input power are shown. Signal waves picked up from a rotor are also shown. It is found that these signals are closely related to revolution states of the motor. Moreover, a new control method for the motor is proposed and tried.

Crystallinity and diagenesis of sedimentary apatites

The crystallinity of sedimentary apatites was determined by Fourier transform infrared spectroscopy (FT-IR) using the splitting of a triply degenerate antisymmetric bending vibration of orthophosphate. The crystallinity indices of Recent marine apatites are low (3.0–3.6) while those of onland ancient apatites are high (4.5–7.8), indicating post-depositional recrystallization. The infrared spectra reveal that recrystallization is associated with a decrease in carbonate content substituting for PO 4 3− and an increase in fluoride order within the apatite structure. The relationship between the crystallinity index and PO 4 3− δ 18O suggests alteration of the primary isotopic composition by exchange reactions between PO 4 3− oxygens and surrounding waters. The Monterey samples have a large range of crystallinity index that reflects a set of complex and highly variable diagenetic conditions. This demonstrates the use of FT-IR criteria for differentiating between pristine and altered apatites and, as a consequence, for relating geochemical markers to formation or diagenetic environments. It is suggested that only those samples that have low crystallinity indices (C. I. < 3.8) should be considered as pristine apatite. Spectra of fish remains indicate that differences in rare earth element (REE) patterns correspond to variations in crystallinity, carbonate content and F order in the apatite lattice. The fact that crystallinity is not correlated with geologic age suggests that environmental factors, such as accumulation rate and pore water chemistry, govern the recrystallization process. In general, Sr content decreases and δ 18Op exhibits high variability with increasing crystallinity.

Centrifugal Distortion Analysis and Pressure Broadening Studies for l-Type Doublet Transitions of Cyanoacetylene-15N in the Microwave Range

With the help of Fourier transform spectrometers in the range from 8 GHz to 26.5 GHz. l-type doublet transitions of HCCC15N in the first excited state of the degenerate bending vibration ν7, with 36 ≤ J ≤ 65, have been investigated. The l-dependence of the resonance frequencies was analy­sed to yield the doubling constant q(0) together with the correction terms q(1) and q(2) due to first and second order contributions from centrifugal distortion. For the lines in X- and Ku-band (8 GHz to 18 GHz) the self-broadening linewidth parameters Γp were determined from the pressure dependence of coherence decay rates 1/T2 of the observed transient emission signals, following pulsed microwave excitation. For the lines with J = 36 and 41, foreign gas broadening in mixtures of HCCC15N with H,. D, and He has also been studied. The experimental results are compared with theoretical predictions, based on a perturbative treatment of binary collisions.

Theoretical development of a Gaussian potential function in the description of the radial portion of isotropic bending vibrations

AbstractAnalysis of a Gaussian potential function suitable for modeling degenerate bending vibrations in weakly bound molecular complexes is presented. Approximate eigenvalues and eigenvectors are obtained by application of perturbation theory. Comparison to the “exact” eigenvalues obtained via a numerical solution shows that the first‐ and higher‐order perturbation corrections are consistent with variational principles.

ChemInform Abstract: VIBRATIONS AND FORCE CONSTANTS OF THE HEXAGONAL LITHIUM IODATE CRYSTAL

Force constants of the α‐LiIO3 crystal are calculated based on the thirteen k=0 infrared and Raman active vibrations. Setting up a generalized valence force field for the IO3 group and both valence and central forces for the external interactions has allowed us to obtain good agreement between experimental and calculated frequencies. The introduction of translational and librational coordinates related to the normal coordinate analysis leads to a precise assignment of the frequencies and shows that the degenerate bending vibrations of the IO3 groups are strongly coupled with the translational vibrations of the lithium atoms.

Vibrations and force constants of the hexagonal lithium iodate crystal

Force constants of the α-LiIO3 crystal are calculated based on the thirteen k=0 infrared and Raman active vibrations. Setting up a generalized valence force field for the IO3 group and both valence and central forces for the external interactions has allowed us to obtain good agreement between experimental and calculated frequencies. The introduction of translational and librational coordinates related to the normal coordinate analysis leads to a precise assignment of the frequencies and shows that the degenerate bending vibrations of the IO3 groups are strongly coupled with the translational vibrations of the lithium atoms.

Rotational Energies of Linear Polyatomic Molecules in Vibrationally Degenerate Levels of Electronic 2Σ and 3Σ States

Formulas are developed to describe the rotational energy of a linear polyatomic molecule in a 2Σ or 3Σ electronic state, where one or more quanta of a degenerate bending vibration are excited. In 2Σ states the spin doubling and l-type doubling are independent, provided that the rotational constant B is large compared with the spin–rotation interaction constant γ. In 3Σ states the normal triplet splitting patterns (e.g. Schlapp's formulas) are considerably altered by the presence of vibrational angular momentum at low rotational quantum number N, especially when the spin–spin interaction parameter λ is sizeable; however, with increasing rotation, the normal spin and l-type doubling patterns are approached, as the vibrational angular momentum is progressively uncoupled from the molecular axis.

Dynamics of the Quasi-Linear Molecule

Calculations of energy levels, eigenfunctions, dipole transition moments, and other significant properties have been made for a phenomenological model of a two-dimensional harmonic oscillator with a superposed barrier at the minimum of the harmonic potential. A high-speed electronic digital computer was employed. The method of calculation does not involve perturbation theory and converges rapidly for all barrier heights. The problem concerns the behavior of the degenerate bending vibration of a linear triatomic molecule, for example, when a potential barrier is introduced at the linear configuration. In the limit of a high barrier, the motion is that of a ``bent'' molecule with rotational motion superposed on the bending vibration about the minimum of potential energy. Results for moderate to low barriers, and those for anharmonic vibration in a well with no barrier, show that the rigid classification of molecules as ``linear'' or ``bent'' is not possible in some cases and that the intermediate case of the ``quasi-linear'' molecule must be considered. The dynamical behavior of such anharmonic motion and its interaction with other vibrations have been investigated, and the primary identifying characteristics of the quasi-linear molecule delineated. The analytical method of solution used has also been applied successfully to the one-dimensional barrier problem.

Ultrasonic Relaxation and the Vibrational Specific Heat of Carbon Disulphide

Previous work has shown that the absorption of ultrasonic waves in liquid carbon disulphide is governed by a relaxation mechanism. The measurements reported from this work were made below the frequency of 70 Mc/s, which is near the centre of the dispersion range at 25°C. Combining these results with others reported by Rapuano in the frequency range 75Mc/s to 195Mc/s, led to the conclusion that the observed behaviour was associated with the time of transfer of energy to the degenerate bending vibration of the carbon disulphide molecule. Quantitative analysis of the results, however, was not regarded as satisfactory.

Ultrasonic absorption in carbon disulphide.

IN a report1 which has just come to our notice, R. A. Rapuano describes results obtained for ultrasonic absorption in carbon disulphide in the frequency range 75–195 Mc./s., which are complementary to initial measurements made by us in the range 30–75 Mc./s. It is shown in the following that the combined results are not only consistent among themselves, but are also compatible with calculations based on the assumption that there is a relaxation of the transfer of energy to the degenerate bending vibration of the carbon disulphide molecule (fundamental frequency2, ν1 = 397 cm.−1 (Table 1)). Measurements to be made in the near future on the temperature-dependence of the ultrasonic absorption over the whole frequency-range covering the dispersion will afford a direct check for this assumption.