HCNO as a semirigid bender: The degenerate ν4 state

The semirigid bender Hamiltonian for fulminic acid HCNO (Bunker, Landsberg, and Winnewisser, J. Mol. Spectrosc.74, 9–25 (1979)) is extended. The extended Hamiltonian describes the manifold of large amplitude vibrational states (due to the ν₅ HCN bending mode) superimposed on a high frequency vibrational state involving excited quanta of the ν₄ CNO bending mode. Such high frequency vibrational states may be degenerate when the large amplitude coordinate is zero, and the semirigid bender Hamiltonian is modified to account for the ν₄ vibrational angular momentum around the molecular axis in the linear limit, and for l-doubling effects. The extended Hamiltonian is used to fit HCN bending and rotation energy level separations for HCNO superimposed in the ν₄ fundamental level. It is found that the effective HCN bending potential in the ν₄ state is very similar to that in the high frequency vibrational ground state. The results obtained confirm the conclusion reached by Bunker, Landsberg, and Winnewisser: HCNO is linear at equilibrium.     

HCNO as a semirigid bender

The semirigid bender Hamiltonian [Bunker and Landsberg, J. Mol. Spectrosc., 67, 374–385 (1977)] is used to fit the rotation-vibration energy level separations in the fulminic acid (HCNO) molecule. The allowance made in the model for the variation of the CH and CN bond lengths with the HCN bending angle proves to be very important, and as well as achieving a good fit we are able to make a detailed investigation of the shape of the HCN bending potential function.From the results we conclude that the equilibrium structure of HCNO is linear but that excitation of the ν₁ or ν₂ stretching vibrations gives rise to an effective HCN bending potential function having its minimum at a nonlinear configuration. Even in the ground state the zeropoint vibrational contributions from ν₁ and ν₂ to the effective HCN bending potential give a small barrier (11.5 cm^?1) to linearity, and we determine that the zero-point HCN bending vibrational amplitude is ±34°.     

C3O2 as a semirigid bender: The degenerate ν5 state

The semirigid bender Hamiltonian for carbon su?ide C₃O₂ [P. R. Bunker, J. Mol. Spectrosc.80, 422–437 (1980)] is extended in a manner similar to the extension previously described for HCNO [P. Jensen, J. Mol. Spectrosc.101, 422–439 (1983)]. The extended Hamiltonian describes the manifold of large-amplitude vibrational states (due to the ν₇ CCC bending mode) superimposed on a high-frequency vibrational state involving excited quanta of the CCO bending modes ν₅ and ν₆. The extended model is used to fit CCC bending and rotation energy level separations for¹²C₃¹⁶O₂ superimposed on the ν₅ fundamental level. Due to the severely limited experimental data it is not possible to unambiguously determine the effective CCC bending potential energy function in the ν₅ state, but estimates of the potential energy parameters are obtained by determining them in two limiting cases.     

Vibrational satellites in the microwave spectrum of cyclopropylidene methanone: Extension of rigid and semirigid bender calculations to larger molecules

The microwave spectrum of cyclopropylidene methanone (CPM) at room temperature includes a large number of vibrational satellites. It has been possible to assign the spectrum of the ground state and nine additional series of satellites. Assignment to vibrational states with up to four quanta of the low-lying out-of-plane (ν₁₅) and two quanta of the in-plane (ν₂₁) bending modes was made by use of several lines of argument:

• 1.(i) relative intensities of lines of the same vibrational state for determination of the parity;
• 2.(ii) variation of A and B-C with vibrational quantum number in comparison with model calculations for in-plane and out-of-plane bending of the heavy atoms;
• 3.(iii) identification of members of the same vibrational sequence by inspection of quotients of differences of their rotational constants.

We have generalized the bender method of Bunker et al. for numerical application to larger molecules. Resulting formulae are given in the text. The rigid bender model was used to fit the changes in rotational constants of the vibrational satellites of the out-of-plane bending mode to a double minimum potential with a barrier of 38.1 ± 0.8 cm⁻¹ and minima at ±17.0 ± 0.1°. The ground state lies 5 cm⁻¹ below the barrier. The in-plane bend is almost harmonic. Its frequency of 197 cm⁻¹ was determined from an analysis of a Coriolis interaction of the v₁₅ = 3, v₂₁ = 0 state with the v₁₅ = 0, v₂₁ = 1 state. The vibrational-state dependence of the centrifugal distortion constants could be at least qualitatively reproduced in this model. The vibrational satellite shifts are equally well fitted when semirigidity is included as suggested by ab initio 4–31G MO calculations. In this case the barrier is slightly lower and the frequencies of ν₁₅ and ν₂₁ decrease by ca. 20%. On the basis of the experimental data presented here it cannot be decided whether the inclusion of semirigidity is necessary.Because the ground state out-of-plane vibrational wavefunction is practically constant over a wide range of the bending coordinate we term CPM quasisymmetric.     

Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ²T_VIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C₃ molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C₃. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.     

On the study of the vibrational energy levels of Arsine molecule

We compare two formalisms applied to the vibrational modes of the molecule of AsH₃ of C_3v molecular symmetry group. Indeed, the close stretching modes of this molecule may be considered as those of a three-dimensional oscillator whereas the bending modes may be considered either as a one-dimensional oscillator of symmetry A₁ and a two-dimensional oscillator of symmetry E or as an approximate three-dimensional oscillator. So, we have applied the U(p + 1) formalism to the both stretching and bending modes and introduced coupling terms acting on an appropriate coupled vibrational basis through a local mode formalism. We have then compared the result of our fitting with those obtained with the coupling of a local mode formalism adapted to the stretching vibrations with a normal mode formalism for the bending ones. Finally we compare our results with other methods recently proposed in the literature.     

Vibration-rotation interaction in HCNO caused by accidental resonances and enhanced by the quasilinearity of the molecule

The recent assignment of the vibrational spectrum of the quasilinear molecule HCNO revealed several near coincidences between vibrational energy levels involving the two bending modes, ν₄ (skeletal bending mode) and ν₅ (HCN-bending mode), and the lowest-lying stretching mode, ν₃ (NO stretching mode). By considering the correlation between the energy levels of a linear and a bent molecular model of HCNO, it is seen that resonance interactions which would be of third or higher order in a linear molecule Hamiltonian would be of first or second order in the Hamiltonian of a bent molecule, and thus might be significant in the quasilinear molecule HCNO. In this way we were able to identify the type of observed interaction occurring between three pairs of nearly coincident levels, (00010, 00002), (00020, 00012), and (00100, 00004). Anomalous centrifugal distortion effects had been observed and reported earlier for the pure rotational transitions arising from molecules in the 00010, 00020, and 00002 levels. Rotational transitions arising from molecules in the 00004 and 00100 vibrational states of HCNO and the 00100 state of DCNO are reported here for the first time. For two pairs of levels, (00010, 00002) and (00100, 00004), we could determine the magnitude of the coefficients of the interaction matrix elements from an analysis of the centrifugal distortion effects.     

Vibrational modes of the stibine molecule

In this paper, we use the algebraic approach to describe the vibrational modes of stibine molecule (of C_3v molecular symmetry group) up to 21 quanta. As the stibine molecule exhibits stretch-bend resonances, we build an algebraic pyramidal coupling operator between stretching modes and bending modes adapted to this molecule. The standard deviation associated to the fit of the vibrational levels is 1.75 cm⁻¹.     

Carbon suboxide: The vibrational dependence of the ν7 bending potential function

Data on the vibrational energy levels and rotational constants of carbon suboxide for the low-wavenumber bending mode ν₇ are reviewed, in the ground-state manifold, and in the ν₂-, ν₃-, ν₄-, and ν₂ + ν₄-state manifolds. Following the procedure developed by Duckett, Mills, and Robiette [J. Mol. Spectrosc.63, 249 (1976)] the data have been inverted to give the effective bending potential in ν₇ for each of these five states. Values are obtained for various other parameters in the effective vibration-rotation Hamiltonian. The potential and rotational constants in ν₂ + ν₄ are given to a close approximation by linear extrapolation from the ground state through the ν₂ and ν₄ states.     

The potential function and rotation-vibration energy levels of the methyl radical CH3

The equilibrium bond length and the shape of the complete potential energy curve for the methyl radical CH₃ are determined. This is done by fitting the experimental data [mainly from C. Yamada, E. Hirota, and K. Kawaguchi, J. Chem. Phys.75, 5256–5264 (1981)] using the nonrigid invertor Hamiltonian and a model anharmonic potential function. As a result the v₂ (out-of-plane bending) dependence of the rotational constants is explained and the v₂ dependence of the spin-rotation coupling constants is modeled. In addition, some of the vibrational energies and rotational, centrifugal distortion, and spin-rotation constants are predicted for the ¹³CH₃, ¹²CD₃, and ¹²CT₃ isotopes.     

The two-dimensional anharmonic oscillator: The CCC bending mode of C3O2

Newly observed data on the rotational constants of carbon su?ide in excited vibrational states of the low-wavenumber bending vibration ν₇ have been successfully interpreted in terms of the two-dimensional anharmonic oscillator wavefunctions associated with this vibration. By combining these results with published infrared and Raman spectra the vibrational assignment has been extended and a refined bending potential for ν₇ has been derived: this has a minimum at a bending angle of about 24° at the central C atom, with an energy maximum at the linear configuration some 23 cm^?1 above the minimum. From similar data on the combination and hot bands of ν₇ with ν₄ (1587 cm^?1) and ν₂ (786 cm^?1) the effective ν₇ bending potential has also been determined in the one-quantum excited states of ν₄ and ν₂. The effective ν₇ potential shows significant changes from the ground vibrational state; the central hump in the ν₇ potential surface is increased to about 50 cm^?1 in the v₄ = 1 state, and decreased to about 1 cm^?1 in the v₂ = 1 state. In the light of these results vibrational assignments are suggested for most of the observed bands in the infrared and Raman spectra of C₃O₂.     

The rotation-vibration spectrum and double-minimum ν12 potential function of propadienone: A semirigid bender analysis

Propadienone is an interconverting molecule having a pair of equivalent symmetry related conformers separated by an energy barrier rising well above the vibrational ground state. Microwave spectra of molecules in excited states of the large-amplitude in-plane bending mode ν₁₂, including intersystem lines, have been successfully represented using the semirigid bender model. The model reveals a double-minimum bending potential with a barrier rising 359 cm⁻¹ above the minima at C₁C₂C₃ = 142°. In the ground state the interconversion frequency is 3.7 GHz and the ν₁₂ fundamental frequency is predicted to be 160 cm⁻¹. Analysis of other vibrational satellites involving the lowest-frequency out-of-plane mode ν₈ indicates a vibrational frequency of 240 cm⁻¹. The inplane vibrational satellite and also the ground state substitution spectra are quite accurately reproduced by the model. Our generalized semirigid bender method offers a variety of approaches to fitting molecular parameters to the experimental data.     

Simultaneous Analysis of Rovibrational and Rotational Spectra of thev5= 1 andv8= 1 Vibrational Levels of Propyne

The microwave and submillimeter wave spectra of propyne between 17 and 358 GHz were measured and the rotational transitions in thev₈= 1 excited vibrational state of the CH₃rocking vibration were assigned. About 1050 wavenumbers of the ν₈vibration–rotation fundamental band and about 600 wavenumbers of the ν₅fundamental band of the[formula]stretching vibration were assigned from the infrared spectrum between 910 and 1130 cm⁻¹which was used previously (G. Graneret al., J. Mol. Spectrosc.161,80–101 (1993)) in the analysis of the combinationv₉=v₁₀= 1 and thev₁₀= 3 overtone levels (ν₉being the[formula]bending and ν₁₀the[formula]bending vibrations). The rovibrational and rotational data corresponding to the two fundamental levels were analyzed simultaneously in least-squares fits using a model which treats together all the vibrational levels in the region around 1000 cm⁻¹with their strong anharmonic and vibration–rotation resonances. The refined parameters reproduce the infrared and submillimeter wave data of thev₅= 1 level with standard deviations of 0.32 × 10⁻³cm⁻¹and 59 kHz, respectively, while for thev₈= 1 level the standard deviations were 0.41 × 10⁻³cm and 290 kHz. The refined parameters of the combination and overtone levels provide reliable predictions for future submillimeter wave studies.     

The potential function for HCNCNH isomerization

The semirigid bender model (P. R. Bunker and D. J. Howe, J. Mol. Spectrosc.83, 288–303 (1980)) has been developed to fit the observed vibrational energy levels of the ground electronic state of $\text{HCN}\text{CNH}$ and $\text{DCN}\text{CND}$ allowing for the complete bending (internal rotation) of HCN into CNH and of DCN into CND. From the fit we have been able to determine the bending potential function and the contribution to the bending potential that arises from the effect of averaging over the two stretching vibrations. The results are compared with ab initio calculations.     

Calculation of the magnetic hyperfine structure in the ground electronic state of HCCO

In this paper we analyze the spin-spin hyperfine interaction in the two components of the ground electronic state of the free π radical HCCO, A²A′[²Π] and X²A″. Electronic mean values of the Fermi contact constants of all magnetic nuclei [¹H, ¹³C₁, ¹³C₂,¹⁷O] are calculated using models that include the electron-correlation correction, primarily CCSD method in the cc-pwCVTZ basis set and B3LYP functional in the cc-pCVQZ basis set. Also, we have calculated components of the anisotropic hyperfine tensor for the ground X²A″ state. The dependence of hyperfine coupling constants (HFCCs) on the two bending coordinates is examined, and the results of HCC bending (vibrational) averaging of electronic mean values are presented for both states. It is demonstrated that electronic and subsequent vibrational averaging of the HFCCs suffices for obtaining results that are in good agreement with available experimental findings (for proton) in the X²A″ state, owing to a small geometry dependence of these quantities, and relatively distant minimum from linearity.     

Photoelectron spectra of ethylene and of the six deuterated derivatives

The photoelectron spectra of C₂H₄ and of six deuterated molecules of ethylene — C₂D₄, C₂D₃H, C₂H₃D, cis-C₂H₂D₂, trans-C₂H₂D₂ and gem-C₂H₂D₂ — have been recorded with the 584-Å resonance line of He. The adiabatic ionization potentials of the X²B_3u and the ²B_3g states of the seven isotopic components have been determined with an accuracy of about 7 meV. The ionization potentials of the other excited electronic states have been measured with a lower accuracy owing to a less well defined onset. The measured ionization potentials of C₂H₄ are 10.514 eV, 12.431 eV, 14.4₃ eV, 15.7₄ eV and 18.7 eV. The vibrational structure of the first electronic band shows that the two normal modes ν₂ (symmetric CC stretching) and ν₃ (symmetric HCH bending) are excited simultaneously. The measured vibrational frequencies show no abnormal isotopic effect if the assignment given in the literature for the ν₂ and ν₃ modes in C₂H₄⁺ are reversed and if a stronger excitation of the ν₃ symmetric bending mode in the least deuterated compounds is assumed. The vibrational modes most strongly excited in the second and third electronic bands are ν₁ (symmetric CH stretching) and ν₃, and in the fourth band ν₃.     

Excitation dependence of the bending mode temperature in pulsed TE CO2 lasers

The observation of “steps” which appear in the gain immediately after excitation in pulsed TE CO₂ discharges is reported. It is shown that the measurement of the step size relative to the peak gain serves to determine the population of the lower laser level and thereby, the initial vibrational temperature (T₁) of the bending mode. This technique is applied to a study of T₁ as a function of the discharge input energy.     

The rotational spectra of the υ8 = υ9 = 1 and υ6 = υ7 = 1 interacting vibrational states of nitric acid (HNO3)

The analysis of the rotational spectrum of HNO₃ has been extended to include the υ₈ = υ₉ = 1 state at 1205.7 cm⁻¹ and the υ₆ = υ₇ = 1 state at 1223.4 cm⁻¹. Based on 78-519 GHz data, the assignments in the 8¹9¹ vibrational state have been significantly expanded from the previously reported microwave measurements [T.M. Goyette, F.C. De Lucia, J. Mol. Spectrosc. 139 (1990) 241-243]. A new microwave analysis is also reported for the 6¹7¹ vibrational state. A simultaneous analysis takes into account the localized ΔK_a = ±2 Fermi resonances between the vibrational states, describes the torsional splitting of 3.3 and 1.4 MHz for the 8¹9¹ and 6¹7¹ states respectively, and fits to experimental accuracy over 1500 rotational transition frequencies that extend up to J = 59. Infrared energy levels [A. Perrin, J.-M. Flaud, F. Keller, A. Goldman, R. D. Blatherwick, F. J. Murcray, C. P. Rinsland, J. Mol. Spectrosc. 194 (1999) 113-123] were also included in the analysis and fit to experimental accuracy. Measurement of strongly perturbed transitions in each vibrational state provide a determination of the band origin difference of 17.733184(17) cm⁻¹. The rotational constants agree well with those predicted by vibrational-rotational constants of the fundamental modes. Furthermore, the analysis will provide a very accurate simulation of the infrared spectrum of HNO₃ in the 8.3 μm region.     

Torsion-vibration interaction in CH3OH

The strong torsion-vibration interaction in CH₃OH has traditionally been dealt with by letting the torsional barrier height depend on vibrational excitation, and letting the vibrational energy depend on torsional excitation. By including an explicit interaction term in the Hamiltonian this is avoided, and apart from an anomaly which is presumably caused by the OH bending mode, the relative location of the vibrational ground state and the CO stretch state is well reproduced for torsional states n = 0, 1, and 2 by adjusting a single interaction constant.