Frequencies Of Bending Vibrations Research Articles

Resonant two-photon ionization spectra of fluorotoluene–argon complexes

Abstract The S 1 ← S 0 transitions of three jet-cooled fluorotoluene–argon complexes are studied by the resonant two-photon ionization technique coupled with time-of-flight mass spectrometry. Detailed spectral analysis assisted by model calculations has allowed us to determine the stretching vibrational frequencies and two bending vibrational frequencies of the complexes. The results show that, the relative positions of the substituents (i.e., F and CH 3 ) have very little influence on the stretching vibrations of the complexes but strongly affect their bending vibrations. In addition, the Ar atom is found to influence the internal rotation of the methyl group in the complexes.

Conversion of acoustic bending vibration frequency in a freely suspended ferroelectric liquid-crystal film

A nonlinear acoustic effect was observed experimentally in a freely suspended ferroelectric liquid-crystal film. The effect consisted of a change in the frequency of the film bending vibrations under the action of a varying electric field. The up-and down-conversion efficiencies were found to be 50 and 30%, respectively.

709 軸荷重を有する平行連結棒の固有振動数計算と軸荷重推定のための一手法

709 軸荷重を有する平行連結棒の固有振動数計算と軸荷重推定のための一手法

X̃3Σ − and Ã3Π electronic states of linear disilaketenylidene (SiSiO): analysis of the Renner effect in the Ã3Π state. Comparison with the analogous multiple bonded systems SiCO, CSiO, and CCO

Ab initio electronic structure theory has been employed to investigate systematically the X̃ 3Σ − and à 3Π electronic states of linear disilaketenylidene (SiSiO). The ground state displays a SiSi double bond while the excited à 3Π state may be assigned a SiSi bond order of 5/2. The ground ( X̃ 3Σ −) state of SiSiO possesses a real degenerate bending vibrational frequency, while the first excited triplet ( à 3Π) state is subject to the Renner–Teller interaction, resulting in two distinct real vibrational frequencies along the bending coordinate. The total energies and physical properties including equilibrium geometries, dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities of the two lowest-lying triplet states were predicted using the SCF, CISD, CCSD, and CCSD(T) levels of theory with a wide range of basis sets. The à 3Π state was also studied using the equation-of-motion CCSD (EOM-CCSD) technique in order to avoid a possible variational collapse to the lower-lying state. With the cc-pVTZ EOM-CCSD method, the Renner parameter and average harmonic bending vibrational frequency for the à 3Π state were determined to be ε=−0.078 and ω 2=219 cm −1, respectively. With our most reliable method, cc-pVQZ CCSD(T), the X̃– à splitting ( T e value) of SiSiO was predicted to be 55.7 kcal mol −1 (2.41 eV, 19 500 cm −1) and the splitting including zero-point vibrational energy correction ( T 0 value) to be 56.1 kcal mol −1 (2.43 eV, 19 600 cm −1). The bond energy for SiSiO was determined to be D e=26.1 ( D 0=25.2) kcal mol −1 indicating considerable thermodynamic stability for the ground state of SiSiO against the dissociation reaction SiSiO ( X̃ 3Σ −)→Si ( 3 P g)+SiO ( X̃ 1Σ +).

Resonance Raman spectroscopic study of nitrophorin 1, a nitric oxide-binding heme protein from Rhodnius prolixus, and its nitrosyl and cyano adducts.

The resonance Raman (RR) spectra of nitrophorin 1 (NP1) from the saliva of the blood-sucking insect Rhodnius prolixus, in the absence and presence of nitric oxide (NO) and in the presence of cyanide (CN(-)), have been studied. The NP1 displayed RR spectra characteristic of six-coordinate high-spin (6cHS) ferric heme at room temperature and six-coordinate low-spin heme (6cLS) at low temperature (77 K). NO and CN(-) each bind to Fe(III), both ligands forming 6cLS complexes with NP1. The Fe(III)-NO stretching and bending vibrational frequencies of nitrosyl NP1 were identified at 591 and 578 cm(-1), respectively, on the basis of 15NO isotope shifts. These frequencies are typical of Fe-NO ferric heme proteins, indicating that the NP1 nitrosyl adduct has typical bond strength. Thus, the small NO release rate displayed by NP1 must be due to other protein interactions. Room and cryogenic temperature (77 K) RR spectroscopy and 13C, 15N, and 13C15N isotope substitutions have been used to determine vibrational mode frequencies associated with the Fe(III)-CN(-) bond for the cyano adducts at 454, 443, 397, and 357 cm(-1). The results were analyzed by normal mode calculations to support the assignment of the modes and to assess the NO and CN(-) binding geometries. The observed isotope shifts for the cyano NP1 are smaller than expected and reveal vibrational coupling of Fe(III)-CN(-) modes with heme modes. We also find that the observed frequencies are consistent with the presence of a nearly linear Fe(III)CN(-) linkage (173 degrees ) coexisting with a population with a bent structure (155 degrees ).

Influence of Cr3+ions on the structure and certain physical properties of PbO-As2O3glasses

PbO-As2O3 glasses containing different concentrations of Cr2O3 (ranging from 0 to 0.4 mol% ) were prepared. The differential thermal analysis, IR and optical absorption spectral studies of these glasses were carried out; from these studies, the variations in the values of glass transition and crystallization temperatures, optical band gap and the shifting of symmetrical bending vibrational frequency band were observed with increase in concentration of Cr2O3. Magnetic susceptibilities for these glasses were also determined and Cr3+ ion concentration was estimated. In addition, detailed studies on dielectric properties viz., dielectric constant e, loss tan δ, ac conductivity and dielectric breakdown strength were investigated. Using the results of these studies, the structural modifications taking place in the glass network were discussed in the light of Cr3+ ion concentration.

Wing instability of a full composite aircraft

Aeroelasticity as a phenomenon is the main source of instability for aircraft. For this reason, considering this phenomenon in design of aircraft structures is essential. From various types of instabilities, self-excitation vibration of wing or coupled bending–torsional vibration of wing and aileron called flutter is a very important phenomenon. To apply for certification for the full composite aircraft studied in this research, based on Joint Aviation Requirement (JAR-23), it must be shown that the wing of the aircraft is free from flutter. The natural frequency of bending and torsional vibration of the wing as well as that of rotation of aileron and bending of the wing must be different. To reach to these goals, a finite element software (Nisa) and an experimental modal analysis technique are used. A convergency analysis is used to verify the size, number and type of element used in the finite element modeling. Also, the results obtained from finite element analysis are compared with the results obtained from closed form solution. Torsional stiffness of the wing and the distribution of mass along the wing are calculated. In the next step, natural frequencies of bending and torsional vibration of the wing as well as that of the rotation of the aileron are calculated. Finally, based on JAR-23 standard and the results obtained from analysis it is concluded that the aircraft, in the range of design speed, is free from flutter.

The X̃ 2Π and à 2Σ+ electronic states of the HCSi radical: Characterization of the Renner–Teller effect in the ground state

The electronic structures of the ground and lowest lying excited state of the silicon methylidyne radical (HCSi) have been investigated at the self-consistent field, configuration interaction with single and double excitations, coupled cluster with single and double excitations (CCSD), and CCSD including a perturbative expansion for connected triples CCSD(T) levels of theory with a wide range of basis sets. The total energies and physical properties including equilibrium geometries, dipole moments, harmonic vibrational frequencies, and Renner–Teller splitting are reported. At our highest level of theory [CCSD(T)/cc-pVQZ], the ground electronic state (X̃ 2Π) has a linear geometry with re(CH)=1.0781 Å and re(CSi)=1.6956 Å. This is in good agreement with the experimental values of r0(CH)=1.0677 Å and r0(CSi)=1.6925 Å, respectively. In the à 2Σ+ state, HCSi is also found to have a linear geometry with re(CH)=1.0737 Å and re(CSi)=1.6130 Å at the [CCSD(T)/cc-pVQZ] level, confirming experimental values of r0(CH)=1.0625 Å, r0(CSi)=1.6118 Å, and the observation of C–Si triple bond character. With the same method, the X̃ 2Π and à 2Σ+ state C–H stretching vibrational frequencies are predicted to be 3271 and 3319 cm−1, respectively, for which experimental values are not available. The classical X̃–à splitting (Te value) was determined to be 32.6 kcal/mol (1.41 eV, 11 730 cm−1) and quantum mechanical splitting (T0 value) to be 33.5 kcal/mol (1.45 eV, 11726 cm−1), which are in excellent agreement with the experimental T0 value of 11 766.721 cm−1 (33.64 kcal/mol, 1.459 eV). The linear excited à 2Σ+ state of the molecule has a real degenerate bending vibrational frequency, whereas the ground state (X̃ 2Π) is subject to the Renner–Teller effect and presents two distinct real vibrational frequencies. The Renner parameter (ε) and average harmonic bending frequency (ω2) of the X̃ 2Π state are predicted to be ε=−0.114 and ω2=518 cm−1 at the CCSD(T)/cc-pVQZ level of theory. The electronic structure analysis of the ground state showed that the HCSi radical is an A-type Renner–Teller molecule.

Microprobing of the Dynamic Properties of Transparent Weak Ferromagnets Based on the Domain Boundary

Quantitative dependences of the velocity of a moving domain boundary and sizes of magnetic inhomogeneities in rare-earth orthoferrites are determined experimentally in real time. The results obtained agree satisfactorily with the parameters calculated for the physical model of parametric resonant deceleration of the domain boundary on wall (Winter) magnons. The lower threshold frequency of bending vibrations of the domain wall is of the order of 108 Hz.

DETERMINATION OF ELASTIC CONSTANTS OF MATERIALS ON SPECIMENS IN THE SHAPE OF SQUARE PLATES

The results of investigation of the natural vibration frequency spectrum for square plates have been stated. Calculation formulae have been derived and methods for measurements of elastic constants of materials by the results of measurements of bending vibration frequencies for square plates have been developed. The methods include measurements of natural frequencies of two bending vibration modes: with two nodal planes (the lowest vibration mode) and with one nodal circumference, Recommendations on the choice of apparatus for measurements have been given and engineering formulae for calculations have been offered. The results of measurements according to developed methods have been presented for a number of known and new ceramic materials.

Isotopic shift and broadening of Si–D bending vibration on Si(111)

Surface infrared spectroscopy was carried out on unreconstructed H:Si(111)1×1 and D:Si(111)1×1 and the spectra obtained were compared precisely. Two narrow absorption peaks of Si–H bond-stretching and bond-bending were clearly observed on H:Si(111), while on D:Si(111) a narrow peak for the Si–D stretching was observed. But the corresponding bending peak split into two and these widths were from three to four times larger than that of Si–H. The splitting of the bending vibration is direct evidence of the coupling of the vibration of the surface layer composed of D and Si with the second layer of Si. Isotope exchange from H to D leads to the decrease in bending vibration frequencies down to those of the substrate. The broadening suggests the interaction of the deuterized surface layer with the rest of the substrate.

Determination of conformational energy differences of propynlidyne isomers using the effective valence shell Hamiltonian method

We have applied the highly correlated ab initio effective valence shell Hamiltonian (Hv) method to determine the energy difference between the cyclic and linear isomers of propynlidyne (C3H). Calculations are also described for the vertical excitation energies, ionization potentials, electron affinities, dipole moments, oscillator strengths, and some harmonic vibrational frequencies, which are all determined using the third order Hv method. Computations at both the experimental and theoretically optimized geometries are used to illustrate the geometrical dependence of the computed properties. The Hv optimized geometry is obtained using a two-configurational reference function describing the two dominant resonance structures. Our third-order vertical excitation energy to the lowest excited state in the cyclic isomer, dipole moments, and ground state isomer conformational energy difference are all in good agreement with experiment and with other highly correlated many-body calculations. The computations for higher excited states and for ionization potentials, electron affinities, and oscillator strengths represent the first reports of these quantities. An explanation is provided for persistent theoretical difficulties in computing b1 bending vibrational frequencies of the cyclic isomer.

The silaketenylidene (SiCO) molecule: Characterization of the X̃ 3Σ− and à 3Π states

The ground (X̃ 3Σ−) and first excited triplet (à 3Π) electronic states of carbonylsilene or silaketenylidene, SiCO, have been investigated systematically using ab initio electronic structure theory. The total energies and physical properties including equilibrium geometries, dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities were predicted using self-consistent-field (SCF), configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), equation-of-motion (EOM) CCSD, CCSD with perturbative triple excitations [CCSD(T)] methods with a wide range of basis sets. The linear X̃ 3Σ− ground state of SiCO has a real degenerate bending vibrational frequency, whereas the à 3Π state of SiCO is subject to the Renner–Teller effect and presents two distinct real vibrational frequencies along the bending coordinate. The bending vibrational frequency of the à 3Π state was evaluated via the EOM-CCSD technique. At the highest level of theory with the largest basis set, cc-pVQZ CCSD(T), the adiabatic X̃–à splitting without the zero-point vibrational energy (ZPVE) correction (Te value) was determined to be 68.5 kcal/mol (2.97 eV, 23 900 cm−1) and the adiabatic splitting with the ZPVE energy correction (T0 value) to be 69.0 kcal/mol (2.99 eV, 24 100 cm−1), which are in excellent agreement with the experimental T0 value of 68.78 kcal/mol (2.983 eV, 24 056 cm−1). The theoretical ground state harmonic Si–C stretching frequency ω3=564 cm−1 is much less than the experimental estimate of 800 cm−1.

IR spectroscopic investigation of structural hydroxyl groups in W−Si heteropolycompound supported on Al2O3

Structural hydroxyl and deuteroxyl groups within the K4[SiW12O40]/Al2O3 and K6[SiW11PdO39]/Al2O3 systems were studied by diffuse-reflectance FTIR spectroscopy in a spectral range of fundamental stretching vibrations, first overtones, and combination bands of stretching and bending vibrations. For hydroxyl groups, the region of combination vibrations is the most informative. The calculated frequencies of bending vibrations of hydroxyl groups (865 and 730 cm−1) are characteristic of acidic OH groups.

Efficiency of the method of spectral vibrodiagnostics for fatigue damage of structural elements. Part 3. Analytical and numerical determination of natural frequencies of longitudinal and bending vibrations of beams with transverse cracks. Solution

Based on the concepts of linear fracture mechanics, we derive analytical expressions for the determinational of natural frequencies of longitudinal and bending vibrations of beams which are rectangular in cross section, are fixed in different ways, have variable ratios of the section height to the beam length, and have transverse cracks of various types. The results of the analytical solution are compared with those obtained by the finite-element method as well as with experimental data obtained by the authors and other scientists. The analytical solution under consideration is shown to be quite simple and provide a fairly good accuracy of the results obtained. Using a cantilever beam with one or two symmetrical edge cracks or a central through crack as an example, we consider the possible dependence of the relative change in natural frequencies of vibration on the relative crack length, crack location, and the vibration mode of a beam. We discuss the possible methods of evaluating the crack size and location from the results of experimental determination of the change in natural vibration frequencies of a cracked beam.

On determination of the natural frequency of transverse and longitudinal vibrations of a cracked beam. Part 2. Experimental and calculation results

The results of experimental investigation of the relationship between the natural frequency of the first mode bending and longitudinal vibrations of titanium alloy and alloyed steel cantilever beams and the crack parameters (crack depth and location) are presented together with the data on calculation of the relative change of the vibration frequency of cracked beams, which are obtained by the proposed analytical approaches. Based on a comparative analysis, we choose fairly simple and sufficiently accurate formulas for calculating the frequencies of bending and longitudinal vibrations of a cantilever beam with an open or closing crack.

DYNAMICS OF TRUSSES: NUMERICAL AND EXPERIMENTAL RESULTS

Complicated wave convesion phenomena in a flexible truss with pinned joints and diagonals were detected in very narrow frequency bands close to the natural frequencies for bending vibrations of individual beam members. Replacement of pinned with clamped joints and removal of the diagonals simplified greatly the topological structure of the exponential decay and phase curves in the frequency domain, in spite of the increase in the number of families of characteristic waves from four to six

A new interpretation of abnormal shift of water molecules' bending vibration frequencies in kieserite family monohydrates

The Mn(II), Fe(II), Co(II), Ni(II), Zn(II) sulphate monohydrates, which are isomorphous to MgSO 4·H 2O, belong to the socolled kieserite family. A similar type of structure form CuSO 4·H 2O. Infrared spectra of these salts revealed characteristic spectral effects: (a) shifting of the δ HOH band in the range 1480–1520 cm −1, (b) appearance of low intensity bands at about 1720–1865 cm −1, and (c) in the spectrum of CuSO 4·H 2O, splitting of both bands into two components. The observed spectral effects can be assigned to coupled bending vibration of water molecules which form chains of MO wMO′ wM type in the crystal lattice.

Dependence of the third-order coefficients in Landau free energies for bcc→fcc structural transition on hydrogen concentration in zirconium hydrides

Young’s modulus E and the modulus of rigidity G of zirconium hydrides ZrHx(0.9⩽x⩽1.65) at 941 and 1001 K have been obtained as a function of hydrogen concentration c by measuring resonance frequencies for bending and torsion vibrations of a polycrystalline wire. As c increases, observed E and G increase in the bcc β phase, slightly increase linearly in the β+δ phase, and then decrease in the fcc δ phase. On the basis of a phenomenological free energy in terms of strain components taking account of space group symmetry, two types of Landau expansion of the free energies for the β phase in terms of the strain components which play an important role in the structural phase transition between the β and the δ phases are examined. The observed E and G are assumed to be the same as the second-order coefficients of the free energy for the Bain distortions, which occur at the structural phase transition. The dependence of the third-order coefficients on c permits the expanded free energies to describe the fact that the β phase is more stable than the δ phase at low c.

Effects of wave function modifications on calculated CH vibrational frequencies and infrared intensities of the dihaloethylenes

Factorial design and principal component models are analyzed to determine how calculated CH stretching and bending vibrational frequencies and infrared intensities depend on characteristics of the molecular orbital wave functions of cis- and trans- difluoro- and dichloroethylene. All the calculated CH stretching frequencies can be described by the same factorial model indicating that their values depend on the wave function modifications in the same way. Application of Møller-Plesset MP2 perturbation treatment lowers these frequencies by 146 cm −1 whereas the effect of adding more valence orbitals provokes only a 42 cm −1 decrease. A polarization orbital-electron correlation interaction effect is also important. Considering the results for the sixteen wave functions of the factorial design all the observed CH stretching frequencies are in best agreement with the MP2 6–311 + + G results. The calculated CH stretching intensities all follow separate factorial models indicating different dependencies on the wave function characteristics. Diffuse, polarization and electron correlation effects as well as several binary interaction effects are important. In contrast to the results for the CH frequencies, best agreements between observed and calculated intensities occur for different wave functions. The calculated in-plane bending frequency values of the difluoro- and dichloroethylenes show somewhat different behavior with wave function modifications and appear to follow separate models. Wave function modifications involving valence, diffuse and polarization orbitals and the use of MP2 treatment result in significant changes in teh calculated frequencies. The calculated in-plane bending intensities all follow separate models and all the wave function factors studied here are important. Factorial designs for the out-of-plane CH bending frequencies and intensities as functions of the wave function model are also described. The calculated CH stretching frequencies can be adequately described by a single principal component. Bidimensional principal component graphs are sufficiently accurate for quantitative comparison of the results of trial wave functions with the observed results of the vibrational bending frequencies. The calculated intensity values follow more complex principal component models than do the frequencies, reflecting the greater difficulties involved in their theoretical determination.