Degenerate Bending Vibration Research Articles

Vibrational excitation of N2O by an electron impact and the role of the Renner-Teller effect in the process

Cross sections and rate coefficients for vibrational excitation and de-excitation of the ${\mathrm{N}}_{2}\mathrm{O}$ molecule by a low-energy electron for transitions between the lowest vibrational levels are computed using a first-principles approach. The present theoretical approach employs the normal-mode approximation for the description of target vibrational states, the vibrational frame transformation to compute amplitudes of vibrational transitions, and the $R$-matrix method to compute ab initio electronic bound and continuum states. It was found that the nonadiabatic Renner-Teller effect, which couples partial waves of the incident electron with degenerate bending vibrations of ${\mathrm{N}}_{2}\mathrm{O}$, is responsible for the excitation of the bending mode. Theoretical results obtained agree reasonably well with available experimental data at low energies. Thermally averaged rate coefficients are computed for temperatures in the 10--10 000 K range.

Spectroscopy and Dynamics of Jet-Cooled Polyynes in a Slit Supersonic Discharge: Sub-Doppler Infrared Studies of Diacetylene HCCCCH.

Fundamental, bending (ν6, ν7, ν8, ν9), and CC-stretch (ν2, ν3) hot band spectra in the antisymmetric CH stretch (ν4) region near 3330 cm(-1) have been observed and analyzed for jet cooled diacetylene (HC≡C-C≡CH) under sub-Doppler conditions. Diacetylene is generated in situ in the throat of a pulsed supersonic slit expansion by discharge dissociation of acetylene to form ethynyl (C≡CH) + H, followed by radical attack (HC≡CH + C≡C-H) to form HC≡C-C≡CH + H. The combination of (i) sub-Doppler line widths and (ii) absence of spectral congestion permits rotational structure and Coriolis interactions in the ν4 CH stretch fundamental to be observed and analyzed with improved precision. Of particular dynamical interest, the spectra reveal diacteylene formation in highly excited internal vibrational states. Specifically, multiple Π ← Π and Δ ← Δ hot bands built on the ν4 CH stretch fundamental are observed, due to doubly degenerate bending vibrations [cis C≡C-H bend (ν6), trans C-C≡C bend (ν7), trans C≡C-H bend (ν8) and cis C-C≡C bend (ν9)], as well as a heretofore unobserved Σ ← Σ band assigned to excitation of ν2 or 2ν3 CC stretch. Boltzmann analysis yields populations consistent with universally cold rotations (Trot ≈ 15 ± 5 K) and yet superthermal vibrations (Tvib ≈ 85-430 K), the latter of which is quite anomalous for the high collision densities in a slit jet expansion. In order to elucidate the physical mechanism for this excess vibrational excitation, high level ab initio CCSD(T) calculations have been pursued with explicitly correlated basis sets (VnZ-f12; n = 2,3) and extrapolated to the complete basis set (CBS) limit using MOLPRO quantum chemistry software. The results suggest that the extensive hot band structure observed arises from (i) highly exothermic CCH + HCCH addition to yield a strongly bent HCCHCCH radical intermediate (ΔH = -62.6 kcal/mol), followed by (ii) rapid fragmentation over a submerged transition state barrier (ΔH = -18.9 kcal/mol) to form vibrationally hot diacetylene + H products (ΔH = -25.6 kcal/mol), and consistent with crossed molecular beam studies by Kaiser et al. [Phys. Chem. Chem. Phys. 2002, 4, 2950.] Finally, RRKM fragmentation rates for this complex are calculated, which exceed collision frequencies in the slit jet expansion and suggest near unity quantum efficiency for diacetylene formation.

Simplified Cartesian basis model for intrapolyad emission intensities in the bent-to-linear electronic transition of acetylene.

The acetylene emission spectrum from the trans-bent electronically excited à state to the linear ground electronic X̃ state has attracted considerable attention because it grants Franck–Condon access to local bending vibrational levels of the X̃ state with large-amplitude motion along the acetylene ⇌ vinylidene isomerization coordinate. For emission from the ground vibrational level of the à state, there is a simplifying set of Franck–Condon propensity rules that gives rise to only one zero-order bright state per conserved vibrational polyad of the X̃ state. Unfortunately, when the upper level involves excitation in the highly admixed ungerade bending modes, ν4′ and ν6′, the simplifying Franck–Condon propensity rule breaks down--as long as the usual polar basis (with v and l quantum numbers) is used to describe the degenerate bending vibrations of the X̃ state--and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. In this article, we show that, when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with vx and vy quantum numbers), the propensity for only one zero-order bright state (in the Cartesian basis) is restored, and the intrapolyad intensities are simple to model, as long as corrections are made for anharmonic interactions. As a result of trans ⇌ cis isomerization in the à state, intrapolyad emission patterns from overtones of ν4′ and ν6′ evolve as quanta of trans bend (ν3′) are added, so the emission intensities are not only relevant to the ground-state acetylene ⇌ vinylidene isomerization, they are also a direct reporter of isomerization in the electronically excited state.

Vibrational Spectroscopic Characterization of the Arsenate Mineral Barahonaite: Implications for the Molecular Structure

ABSTRACT The mineral barahonaite is in all probability a member of the smolianinovite group. The mineral is an arsenate mineral formed as a secondary mineral in the oxidized zone of sulphide deposits. We have studied the barahonaite mineral using a combination of Raman and infrared spectroscopy. The mineral is characterized by a series of Raman bands at 863 cm−1 with low wavenumber shoulders at 802 and 828 cm−1. These bands are assigned to the arsenate and hydrogen arsenate stretching vibrations. The infrared spectrum shows a broad spectral profile. Two Raman bands at 506 and 529 cm−1 are assigned to the triply degenerate arsenate bending vibration (F 2, ν4), and the Raman bands at 325, 360, and 399 cm−1 are attributed to the arsenate ν2 bending vibration. Raman and infrared bands in the 2500–3800 cm−1 spectral range are assigned to water and hydroxyl stretching vibrations. The application of Raman spectroscopy to study the structure of barahonaite is better than infrared spectroscopy, probably because of the much higher spatial resolution.

Geometrical effect on the issue of asymmetric C 1s photoelectron angular distributions detected in coincidence with the fragment ion pairs of CO+–O+ for CO2 molecules

We have measured C 1s photoelectron angular distributions (PADs) in coincidence with the CO+–O+ fragment ion pairs of CO2 molecules at the photoelectron energies of 85, 120 and 150 eV. The observed left–right asymmetric PADs have been well reproduced by our theoretical model taking into account the two degenerate zero-point bending vibrations. This leads to a conclusive result on the interpretation of such PADs; although it has been believed so far that they are the molecular frame, in fact they are the recoil frame.

Raman spectroscopy of the arsenate minerals maxwellite and in comparison with tilasite

Maxwellite NaFe3+(AsO4)F is an arsenate mineral containing fluoride and forms a continuous series with tilasite CaMg(AsO4)F. Both maxwellite and tilasite form a continuous series with durangite NaAl3+(AsO4)F. We have used the combination of scanning electron microscopy with EDS and vibrational spectroscopy to chemically analyse the mineral maxwellite and make an assessment of the molecular structure. Chemical analysis shows that maxwellite is composed of Fe, Na and Ca with minor amounts of Mn and Al. Raman bands for tilasite at 851 and 831cm−1 are assigned to the Raman active ν1 symmetric stretching vibration (A1) and the Raman active triply degenerate ν3 antisymmetric stretching vibration (F2). The Raman band of maxwellite at 871cm−1 is assigned to the ν1 symmetric stretching vibration and the Raman band at 812cm−1 is assigned to the ν3 antisymmetric stretching vibration. The intense Raman band of tilasite at 467cm−1 is assigned to the Raman active triply degenerate ν4 bending vibration (F2). Raman band at 331cm−1 for tilasite is assigned to the Raman active doubly degenerate ν2 symmetric bending vibration (E). Both Raman and infrared spectroscopy do not identify any bands in the hydroxyl stretching region as is expected.

A theoretical systematic study of a series of isocyanopolyynes

Several isocyanopolyynes, HCnNC (n=0, 2,…,16), are analyzed in this theoretical work. We performed calculations at MP2/cc-pVTZ (n=0–16), CCSD/cc-pVDZ (n=0–12) and CCSD/cc-pVTZ (n=0–6) levels. The dipole moments from the best treatment, CCSD/cc-pVTZ, are in much closer agreement with those obtained in CCSD/cc-pVDZ calculations (deviations up to 0.05 Debye) than with the results from MP2/cc-pVTZ (discrepancies that can reach 0.55 Debye). Moreover, the CCSD/cc-pVTZ level yields values in excellent accordance with experimental dipole moments for HNC and HC2NC. Hence, this allows concluding that the correct treatment of electron correlation is more important than increments in basis sets for this electric property in isocyanopolyynes and CCSD/cc-pVDZ values are indicated as the best estimates available for large isocyanopolyynes. The findings from infrared intensities of fundamental vibrational bands are also similar (mean deviations of 3.1kmmol−1 for CCSD/cc-pVDZ and 12.6kmmol−1 for MP2/cc-pVTZ with respect to CCSD/cc-pVTZ results). Thus, we decided to use the charge – charge flux – dipole flux (CCFDF) model from multipoles given by the Quantum Theory of Atoms in Molecules (QTAIM), which were obtained at the CCSD/cc-pVDZ level, to investigate the variations in infrared intensities of some selected modes along these systems. The intensity of the band associated with CH stretching shows an increase with the size of these molecules (from 96 to 146kmmol−1 between n=4 and 12) that is readily explained by variations in the charge flux contribution to this mode, in a similar way as found before for cyanopolyynes. Furthermore, the degenerate CH bending vibrations present almost constant intensities in these isocyanopolyynes (around 37–38kmmol−1 from n=4 up to n=12) and this pattern is supported by CCFDF/QTAIM contributions. The band mostly assigned to stretching of the NC triple bond, which can also be described as asymmetric stretching mode of all pairs of adjacent triple bonds, shows an increase of intensity up to n=6 and is associated to values around 96–102kmmol−1 in the remaining larger members. Another important mode detected is a symmetric stretching of NC and CC triple bonds belonging to the isonitrile end (between 66 and 101kmmol−1 when n=6–12) for which the charge contribution is nearly constant and dynamic contributions change in a more complicated way. The most intense fundamental band in each isocyanopolyyne from n=4 to 12 is assigned to vibrations of triple bonds in both ends of these systems (from 129 to 164kmmol−1) and an alternating behavior according with even or odd numbers of CC triple bonds is observed for these values and also for respective CCFDF/QTAIM contributions. Finally, this work also brings values derived from regressions that are indicated as the best estimates of rotational constants and dipole moments to be used for detection of large isocyanopolyynes in the interstellar medium.

The infrared fundamental intensities of some cyanopolyynes

Some cyanopolyynes, HCnN (n=1, 3, …, 17), are investigated by means of calculations at the MP2/cc-pVTZ and CCSD/cc-pVDZ levels. Although the MP2/cc-pVTZ results for geometries and molecular dipole moments are encouraging, the CCSD/cc-pVDZ level was superior for the study of infrared fundamental intensities. The main bands are also analyzed with a charge–charge flux–dipole flux (CCFDF) partition model based on quantities given by the Quantum Theory of Atoms in Molecules (QTAIM). The intensity of vibrations corresponding to the stretching of CH bonds (3471–3473cm−1) increases in line with the number of carbon atoms (from 61 to 146kmmol−1 between HCN and HC13N). This increase is due to the charge flux contribution while the other contributions remain roughly unaltered except for HCN. Moreover, the hydrogen atom loses an almost constant amount of electronic charge during the CH bond enlargement and a small fraction of this charge spreads to atoms farther and farther away from hydrogen as the molecule size increases. The band associated with the doubly degenerate CH bending vibrations (643–732cm−1) presents approximately the same intensity in all the studied cyanopolyynes (from 67 to 76kmmol−1). The CCFDF/QTAIM contributions are also nearly the same for these bending modes in HC5N and larger systems. The intensity of the mode mostly identified as CN stretching (around 2378–2399cm−1 except for HCN) increases from HCN up to HC7N (from 0.3 to 83kmmol−1) and nearly stabilizes around 80–90kmmol−1 for larger systems. The CCFDF/QTAIM contributions for this mode also change significantly up to HC7N and remain almost constant in larger systems. We also observed the appearing of a very relevant band between 2283 and 2342cm−1. This mode is mainly associated with the symmetric stretching of CC triple bonds near the molecule center and exhibits large charge fluxes while the other contributions are almost negligible in the largest cyanopolyynes. The two vibrational bands associated with the smallest frequencies are also studied and extrapolation equations are suggested to predict their positions in larger cyanopolyynes.

Rotational and rovibrational spectroscopy of the v 8 = 1 and 2 vibrational states of CH3NC

The lowest frequency vibration–rotation band ν 8, corresponding to the degenerate CNC bending vibration of methyl isocyanide (CH3NC) with band center at 267.3 cm−1, was studied by FTIR spectroscopy between 215 and 320 cm−1 and rotational spectroscopy in the range from 201 to 383 GHz in order to describe the vibration–rotation dynamics with the inclusion of all important anharmonic and vibration–rotation interactions. Assignments extended to higher-K rotational states in both vibration–rotation and rotational spectra reveal a resonance crossing with the v 8 = 2 overtone level due to a local anharmonic Fermi resonance. The simultaneous analysis of both types of data provides a fully quantitative reproduction of the experimental data as well as a preliminary characterization of the v 8 = 2 level. The parallel component of the overtone band with band center at 524.6 cm−1 was assigned for the first time from spectra in the region from 480 to 585 cm−1 together with the hot bands in the region of the fundamental band.

Raman spectroscopic study of the uranyl mineral pseudojohannite Cu6.5[(UO2)4O4(SO4)2]2(OH)5·25H2O

AbstractRaman spectra of pseudojohannite were studied and related to the structure of the mineral. Observed bands were assigned to the stretching and bending vibrations of (UO2)2+ and (SO4)2− units and of water molecules. The published formula of pseudojohannite is Cu6.5(UO2)8[O8](OH)5[(SO4)4]·25H2O. Raman bands at 805 and 810 cm−1 are assigned to (UO2)2+ stretching modes. The Raman bands at 1017 and 1100 cm−1 are assigned to the (SO4)2− symmetric and antisymmetric stretching vibrations. The three Raman bands at 423, 465 and 496 cm−1 are assigned to the (SO4)2−ν2 bending modes. The bands at 210 and 279 cm−1 are assigned to the doubly degenerate ν2 bending vibration of the (UO2)2+ units. UO bond lengths in uranyl and OH···O hydrogen bond lengths were calculated from the Raman and infrared spectra. Copyright © 2009 John Wiley & Sons, Ltd.

Acetylene, 12C2H2: new CRDS data and global vibration-rotation analysis up to 8600 cm−1

The absorption spectrum of 12C2H2 has been recorded using cavity ringdown spectroscopy and analyzed in the ranges 6000 − 6356 cm−1 and 6667−7015 cm−1. Fourteen new bands have been identified and additional J-lines were assigned in 10 already known bands. These new data, together with the published vibration–rotation absorption lines of 12C2H2 accessing vibrational states up to 8600 cm−1 have been gathered in a database. The resulting set includes 12137 transitions involving 186 different k = l 4 + l 5 sub-states, with l i the angular momentum quantum number associated to the i degenerate bending vibration. These lines have been fitted simultaneously to spectroscopic parameters through J-dependent Hamiltonian matrices exploiting the vibrational polyad or cluster block-diagonalization, in terms of the pseudo-quantum numbers Nr = 5v 1 + 3v 2 + 5v 3 +v 4 +v 5 and Ns = v 1 + v 2 + v 3, also accounting for k and e/f parities and u/g symmetry. Modes 1 and 2 correspond to the symmetric CH and CC stretchings, mode 3 to the antisymmetric CH stretch, and modes 4 and 5 to the trans- and cis-degenerate bendings, respectively. The fit was successfully achieved, with a dimensionless standard deviation of 0.92, leading to the determination of 266 effective vibration-rotation parameters.

Towards Toroidal Hydrogen Bonds

Abstract We present hydrogen bonds with toroidal densities of the protons, called toroidal hydrogen bonds, in systems with cylindrical symmetry e.g. triatomic molecules AHB or ions AHB+ or AHB–. These may be prepared by excitation of the degenerate bending vibrations and related pseudorotation such that the hydrogen atom (or the corresponding proton) is no longer located on the symmetry axis between atoms A and B, but – classically speaking – it rotates around that axis. Quantum mechanically, the toroidal hydrogen bond is represented by an excited nuclear eigenstate with nuclear wavefunction and corresponding nuclear density which have toroidal shapes around the central nodal line which conincides with the AB symmetry axis. The properties of these bonds are analyzed, including the pseudorotational angular momentum. Toroidal hydrogen bonds may be excited by means of circularly polarized infrared (IR) laser pulses. The results are demonstrated exemplarily for the oriented model system FHF–, by means of combined quantum chemistry calculations of the potential energy and dipole surfaces (adapted from L. González, G. Pérez-Hernández, J. González-Vázquez, (2008), submitted), calculations of the vibrational and pseudorotational states in the frame of Watson’s isomorphic Hamiltonian for linear molecules (J. K. G. Watson, Mol. Phys. 19 (1970) 465), and quantum dynamics simulations of the laser driven nuclear dynamics, analogous to recent applications to CdH2 (I. Barth, J. Manz, P. Sebald, Chem. Phys. 346 (2008) 89).

The bending vibrational levels of the acetylene cation: A case study of the Renner-Teller effect in a molecule with two degenerate bending vibrations

Forty three vibronic levels of C2H2+, X 2Pi u, with upsilon4 = 0-6, upsilon5 = 0-3, and K = 0-4, lying at energies of 0-3520 cm(-1) above the zero-point level, have been recorded at rotational resolution. These levels were observed by double resonance, using 1+1' two-color pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. The intermediate states were single rovibrational levels chosen from the A1Au, 4nu3 (K = 1-2), 5nu3 (K = 1), nu2+4nu3 (K = 0), and 47,206 cm(-1) (K = 1) levels of C2H2. Seven of the trans-bending levels of C2H2+ (upsilon4 = 0-3, K = 0-2) had been reported previously by Pratt et al. [J. Chem. Phys. 99, 6233 (1993)]; our results for these levels agree well with theirs. A full analysis has been carried out, including the Renner-Teller effect and the vibrational anharmonicity for both the trans- and cis-bending vibrations. The rotational structure of the lowest 16 vibronic levels (consisting of the complete set of levels with upsilon4 + upsilon5 < or = 2, except for the unobserved upper (2Pi u component of the 2nu4 overtone) could be fitted by least squares using 16 parameters to give an rms deviation of 0.21 cm(-1). The vibronic coupling parameter epsilon5 (about whose magnitude there has been controversy) was determined to be -0.0273(7). For the higher vibronic levels, an additional parameter, r45, was needed to allow for the Darling-Dennison resonance between the two bending manifolds. Almost all the observed levels of the upsilon4 + upsilon5 = 3 and 4 polyads (about half of the predicted number) could then be assigned. In a final fit to 39 vibronic levels with upsilon4 + upsilon5 < or = 5, an rms deviation of 0.34 cm(-1) was obtained using 20 parameters. An interesting finding is that Hund's spin-coupling cases (a) and (b) both occur in the Sigmau components of the nu4 + 2nu5 combination level. The ionization potential of C2H2 (from the lowest rotational level of the ground state to the lowest rotational level of the cation) is found to be 91,953.77 +/- 0.09 cm(-1) (3sigma).

Inversion vibration of PH3+(X̃A2″2) studied by zero kinetic energy photoelectron spectroscopy

We report the first rotationally resolved spectroscopic studies on PH3+(X2A2") using zero kinetic energy photoelectron spectroscopy and coherent VUV radiation. The spectra about 8000 cm(-1) above the ground vibrational state of PH3+(X2A2") have been recorded. We observed the vibrational energy level splittings of PH3+(X2A2") due to the tunneling effect in the inversion (symmetric bending) vibration (nu2+). The energy splitting for the first inversion vibrational state (0+/0-) is 5.8 cm(-1). The inversion vibrational energy levels, rotational constants, and adiabatic ionization energies (IEs) for nu2+ = 0-16 have been determined. The bond angles between the neighboring P-H bonds and the P-H bond lengths are also obtained using the experimentally determined rotational constants. With the increasing of the inversion vibrational excitations (nu2+), the bond lengths (P-H) increase a little and the bond angles (H-P-H) decrease a lot. The inversion vibrational energy levels have also been calculated by using one dimensional potential model and the results are in good agreement with the experimental data for the first several vibrational levels. In addition to inversion vibration, we also observed firstly the other two vibrational modes: the symmetric P-H stretching vibration (nu1+) and the degenerate bending vibration (nu4+). The fundamental frequencies for nu1+ and nu4+ are 2461.6 (+/-2) and 1043.9 (+/-2) cm(-1), respectively. The first IE for PH3 was determined as 79670.9 (+/-1) cm(-1).

Isotopomer fractionation in the UV photolysis of N2O: Comparison of theory and experiment

In the photodissociation of N2O, absorption cross sections differ with isotopic substitution, leading to a wavelength‐dependent fractionation of the various isotopomers. Several models ranging from shifts by zero‐point energy differences to propagation of wave packets on the excited electronic state potential energy surface have been proposed to explain the observed fractionations. We present time‐independent fractionation calculations for the isotopomers 447, 448, 456, 546, and 556. Besides largely agreeing with the experimental data, these calculations have the advantage of not being computationally intensive, as well as satisfying the physical facts that the asymmetric stretch and the doubly degenerate bending vibration are the principal Franck‐Condon active modes in the photodissociation. The latter is reflected in the actual dissociation and in the high rotational excitation and lack of vibrational excitation of the N2 product. The calculations are based on a multidimensional reflection principle using an ab initio potential energy surface. The theory for the absorption cross section and isotopomer fractionation accompanying photodissociation is described. The absolute value of the theoretically calculated absorption cross section is very close (90%) to the experimentally observed value. The present computations also provide data for the slope of a three‐isotope plot of the fractionation of 447/446 relative to 448/446, using the fractionations at different wavelengths. The resulting slope is compared with a perturbation theoretical expression for direct photodissociation given elsewhere.

Raman spectroscopic study of molten SmCl3–ACl systems (A=Li, Na, K)

Abstract Raman spectra of molten SmCl 3 –ACl systems (A=Li, Na, K) were measured at different compositions and temperatures. The spectra showed polarized peaks centered at about 256 cm −1 in the whole range of concentration and depolarized peaks at about 120 cm −1 in the low concentration range of SmCl 3 . These Raman shifts were identified as the totally symmetric stretching vibration υ 1 and the degenerate bending vibration υ 5 of octahedral SmCl 6 3− complex anion, respectively. Peak splitting of the isotropic component was recognized clearly in the reduced Raman spectra of mixtures. Clustering of complex anions is thought to occur in the melts. However, the clustering might be restrained when the SmCl 3 concentration became relatively low by adding LiCl, NaCl or KCl. The υ 5 peak was the strongest at the SmCl 3 concentration of 25 mol% in the SmCl 3 –KCl system among the three systems. The temperature effect on the Raman shift, reflecting the structural change, was negligibly small between 823 K and 1023 K.

Ab initio investigation of the Renner–Teller effect in the ground electronic state of HCCD+

Results of an ab initio treatment of the Renner–Teller effect in the ground electronic state of HCCD+ are presented. The model Hamiltonian employed involves four nuclear degrees of freedom correlating at linear geometry with two degenerate bending vibrations. Computations of vibronic energy levels and wave functions are carried out by means of a variational approach. The results of calculations are compared with those for symmetric isotopic species HCCH+ and DCCD+.

Density Functional Study on the Structures and Energies of the Ti2C3 Cluster

The structures and energies of the binary dititanium tricarbide Ti2C3 in the lowest singlet, triplet, and quintet states have been investigated by density functional theory using the hybrid B3LYP functionals. Geometries and frequencies for a number of isomeric structures are presented at the B3LYP level. A pentagonal structure with a C2 unit at the base and a carbon at the apex, Xs, is found to be the global Ti2C3 minimum. Cyclic structures V−VIII derived from the 2-fold addition of titanium to the most stable “fan” and “kite” isomers of TiC3 are characterized as higher energy local minima. Linear structures I−IV with all probable relative positioning of the two titanium atoms have been identified as higher order saddle points with respect to the degenerate bending vibration, except for the cumulene-like valence structure I. Cyclic structures are energetically favored over the linear structures. A comparison with the penta-atomic group IVA silicon−carbon clusters is given, where appropriate.

High resolution spectroscopy of Ar-CH4 and Kr-CH4 in the 7 μ region (j = 1 ← 0 transition)

Abstract Diode laser spectra of the rare gas - spherical top van der Waals complexes Ar-CH4 and Kr-CH4 were measured in the wavelength region near 1310 cm-1 and assigned. The most prominent lines of both complexes exhibit three dense but well resolved RP0, QR0, and RQ0 branches, correlated to the R(0) transition of the triply degenerate bending vibration v4 of methane, CH4. A model Hamiltonian based on Coriolis coupled states was applied for the assignment, analysis and fitting of the spectra to within the experimental accuracy of ≈ 15 MHz. The rotational B constants of the upper and lower states determined from the three allowed branches appeared to be strongly correlated. The precision in the determination of the rotational B constants of the two complexes was substantially increased by additional recording of several weak transitions in the nearly forbidden QP0 and RR0 branches, which were fitted together with the allowed transitions. The separation between the rare gas atom and the methane molecule in the ground vibrational state was determined to be 3.999 Å and 4.094 Å for Ar-CH4 and Kr-CH4, respectively. The measured small values of the splitting between the K=0 and the K = ±1 levels in the vibrationally excited state (0.39 cm-1 and 0.67 cm-1 for Ar-CH4 and Kr-CH4, respectively), which characterizes the anisotropy of the intermolecular potential, indicated that Kr-CH4 and Ar-CH4 together with Ne-SiH4 represent examples close to the free rotor limit, where the spherical top CH4 is almost free to rotate within the complex. In comparison, the previously analyzed Ar-SiH4 van der Waals molecule is closer to the hindered rotor limit.

Effect of Pressing Force Applied to a Rotor on Disk-Type Ultrasonic Motor Driven by Self-Oscillation

In this paper the relationship between the pressing force applied to a rotor and the rotation characteristic of an ultrasonic motor driven by self-oscillation are discussed. The motor used here is an in-phase drive-type ultrasonic motor using two degenerate bending vibration modes of a disk. The picking-up electrical signal caused by self-oscillation is positively fed back into the piezoelectric ceramics for driving through an operational amplifier and a step-up transformer. The pressing force applied to a rotor was measured using a force gauge coupled to the shaft of the ultrasonic motor. As a result, it was confirmed that the selection of the picking-up position for the feedback signal is important for a stable starting and running of the disk-type ultrasonic motor driven by self-oscillation.