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.     

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.     

The bending-rotation spectrum of fulminic acid and deuterofulminic acid

A quasilinear molecular model is needed to account for the infrared absorption spectrum of HCNO and DCNO in the spectral region from 100 cm^?1 to 1000 cm^?1. The observed systems of infrared bands arising from the ν₅ vibrational manifold have all been assigned. The rotational structure of the absorption bands at 225 cm^?1, 275 cm^?1, 315 cm^?1, and 317 cm^?1 for HCNO has been resolved using a Fourier spectrometer. The rotational constants and the band centers have been determined for the above bands, which represent the transitions(0000⁰1¹)_c←0000⁰0⁰(0000⁰2²)_c,d←(0000⁰1¹)_c,dboth components(0000⁰3³)_c,d←(0000⁰2²)_c,d0000⁰2⁰←(0000⁰1¹)_c.By means of the Ritz combination principle the infrared transitions could be used to build up the vibrational energy level scheme of the ν₅ vibrational mode for HCNO and DCNO. The data are only reconcilable with a potential function for ν₅ which exhibits a low barrier opposing linearity. Preliminary values of the potential parameters were obtained using different approximate theoretical approaches.A reinterpretation of the r₈ structure parameters of fulminic acid in the light of the quasilinear model leads to an explanation of the extraordinarily short CH internuclear distance of 1.027 Å as the projection of a CH bond length of 1.060(5) Å upon the heavy-atom axis.The isotopic shift upon deuteration observed in the infrared data indicate that the ν₅ fundamental vibration is primarily an HCN bending motion. The ν₄ fundamental vibration (skeletal bending motion) of HCNO is located at 537 cm^?1 and does not exhibit any hot band structure which would be indicative of a perturbed potential function.     

The two-dimensional anharmonic oscillator: Vibration-rotation constants of fulminic acid,HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν₅, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v₅, l₅), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q_5x, Q_5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle (～170°) with a maximum at the linear configuration about 2 cm^?1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants.We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.     

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.     

The infrared spectrum of fulminic acid,HCNO, in the ν4 fundamental region

The infrared spectrum of fulminic acid, HCNO, was measured with high resolution in the region 500–657 cm^?1. The spectrum was obtained with a Bomem interferometer, at a reslution of about 0.006 cm^?1. Thirteen bands could be identified and assigned to rovibrational transitions of HCNO. These are the fundamental ν₄ and some of its hot bands, and the overtone 2ν₅ and some of its hot bands. Because ν₅ is a quasilinear bending mode, the identification and measurement of the various hot bands is especially important for locating the combination states of ν₄ with various quanta of ν₅.     

Carbon suboxide as a quasilinear molecule with a large amplitude bending mode: Determination of the molecular constants and the ν7 potential function

The model of a quasilinear molecule with a large amplitude bending mode is used to treat C₃O₂. The Hamiltonian operator, including the rotation-vibration interaction, is derived allowing only a single vibrational degree of freedom, namely, the ν₇ mode corresponding to the bending at the central carbon atom. The CCO angle is constrained to be 180°. With this model the rotational energy levels and, thus, the molecular constants can be computed for any ν₇ level once the ν₇ potential is specified. The l-doubling is included only for π states. The model contains three adjustable parameters: the rotational constant in the linear configuration and two terms in the potential function, and these are determined by fitting three experimental quantities: the rotational constants in and the separation between the ground and 2ν7⁰ states. The resulting ν₇ potential has a 30.56 cm^?1 barrier at α = 0 with a minimum at α = 11.04°, where 2α is the angular deviation from linearity. The model gives a good fit to the 2ν₇ Raman data and to the rotational and centrifugal distortion constants in all of the nν7^l states which have been analyzed. A similar analysis is applied with equal success to the states with ν₄, the asymmetric CC stretch mode at 1587 cm^?1, simultaneously excited with a ν₇ mode. The potential in this case has a 56.58 cm^?1 barrier at α = 0 with a minimum at α = 13.02°.     

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.     

Determination of the skeletal bending potential function for SiH3NCO from the microwave spectrum

The rotation-bending-torsion Hamiltonian (M. Kr?glewski, J. Mol. Spectrosc., in press) is used to simultaneously fit observed rotational transitions (J. A. Duckett, Ph.D. thesis, University of Reading, 1976) of silyl isocyanate SiH₃NCO in 18 vibrational states involving excited quanta of the ν₁₀ SiNC skeletal bending mode. The effective SiNC bending potential energy function and the geometry of the molecule in the small amplitude vibrational ground state are determined from the microwave data.     

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.     

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.     

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.     

Analysis of the ν2 + ν3 band of 12CH4 and 13CH4

The ν₂ + ν₃ bands of ¹²CH₄ and ¹³CH₄ occurring in the region 4400–4650 cm^?1 have been studied from spectra recorded with a high-resolution Fourier transform spectrometer (resolution better than 0.01 cm^?1). Champion's Hamiltonian expansion, Canad. J. Phys.55, 1802 (1977), is applied to the problem of the two interacting F₁ and F₂ vibrational sublevels of this type of a band. As the P branch of ν₂ + ν₃ is strongly overlapped by neighboring bands, a combination-difference method, adapted to tetrahedral XY₄ molecules has been developed to help assignments of lines. A fit of 700 transitions has been performed using 13 new effective constants in the case of ¹²CH₄. In the case of ¹³CH₄, 532 transitions have been fit to 18 constants. The known parameters, relative to the vibrational ground state and the ν₃ state for both methanes, and the ν₂ state for ¹²CH₄ were fixed throughout. Most of the perturbed levels, up to J′ = 12, are well reproduced and the general agreement between experimental and calculated transitions is satisfactory with standard deviations of 0.047 cm^?1 (¹²CH₄) and 0.041 cm^?1 (¹³CH₄). The results (order of magnitude of obtained (ν₂ + ν₃) parameters and comparison of observed and computed intensities) indicate that the ν₂ + ν₃ band is perturbed by many other bands.     

The ν7 vibrational states of C3O2: A least-squares fit of the rigid-bender model to the v7ν7l7 energies and rotational constants

The rigid-bender model is used to treat the large-amplitude, low-frequency, bending vibration ν₇ of C₃O₂. Different parameterizations of the bending potential function are considered, and a simple two-term power series is found to give the best fit. With this parameterization, using a least-squares fit to energies and B values, the ν₇ potential function is determined for the ground state as well as for the states in which ν₂, ν₃, ν₄, ν₆, 2ν₆, ν₁ + ν₃, ν₁ + ν₄, ν₂ + ν₃, and 2ν₂ + ν₄ are excited. The excitation of other vibrations has in some cases a drastic effect on the ν₇ potential. In the ground state the potential has a 29 cm^?1 barrier at the linear position, in ν₁ + ν₃ the barrier increases to 79 cm^?1, while in 2ν₂ + ν₄ the barrier vanishes. An equilibrium potential is determined by correcting the ground state potential for the effects of zero-point motion of the normal vibrations ν₁, …, ν₆. This potential has a 35.6-cm^?1 barrier with a minimum at α = 11.14°, where 2α is the angular deviation from linearity. The model accurately predicts the quartic and sextic centrifugal distortion terms for the low-lying v₇ν₇^l₇ states. Second-order l-type coupling is included in the calculations of the quartic terms. The effects of this coupling, which are most pronounced for the ν₇ ≥ 2 states, adequately explain the negative D term recently reported for the ν₂ + 4ν₇⁰ state.     

Theoretical integrated intensities for the 2ν2 and 2ν2-ν2 bands of HCN and DCN

Dipole moment functions, both perpendicular and parallel to the molecular axis, are calculated from the SCF and MRD-CI results of a previous study for the normal ν₂ bending vibrations of HCN and DCN. Vibrationally averaged dipole moments and the infrared transition matrix elements are then obtained from the dipole moment functions and vibrational wave functions. MRD-CI results, with known experimental values in parentheses, for HCN are 〈0|μ|0〉 = ?2.954(?2.985) D, 〈1|μ|1〉 = ?2.915(±2.942) D, 〈0|μ|1〉 = 0.148(0.147) D, 〈0|μ|2〉 = ?0.027 D, 〈1|μ|2〉 = 0.210 D. Calculated absolute intensities at 1 atm and 0°C for the (02⁰0) ← (000), (02⁰0) ← (010), and (02²0) ← (010) bands of HCN are 25 (40 ± 10 as estimated from spectra), 8.5, and 17.0 atm^?1 cm^?2, respectively. Results for DCN are also reported.     

The infrared spectrum of carbon suboxide in the ν6 fundamental region: Experimental observation and semirigid bender analysis

The infrared spectrum of carbon suboxide, C₃O₂, was measured at high resolution in the region from 500 to 600 cm⁻¹. The spectrum was recorded with a Bomem interferometer at a resolution of about 0.004 cm⁻¹; after deconvolution a resolution of about 0.002 cm⁻¹ was attained. Seven bands were identified and assigned to rovibrational transitions of ¹²C₃¹⁶O₂. These consist of the ν₆ fundamental band and some of the hot bands associated with the ν₇, 2ν₇, and 3ν₇ states. The data obtained on the ν₆ + nν₇ states were used as input for a semirigid bender fit yielding the effective CCC bending potential energy function in the ν₆ state together with a number of related parameters. From the results of the present work together with the results of previous semirigid bender fits it was found that C₃O₂ is bent at equilibrium with an equilibrium CCC bond angle of 156° and a barrier to linearity of 28 cm⁻¹.     

A refined potential energy function for the electronic ground state of H2Se

The potential energy surface for the electronic ground state of the hydrogen selenide molecule has been determined previously by Jensen and Kozin [J. Mol. Spectrosc. 160 (1993) 39] in a fitting to experimental data by means of the MORBID computer program. We report here a further refinement of this surface, also made with the MORBID program. With the refined potential surface, we can make predictions of rotation-vibration transition wavenumbers for H₂Se, D₂Se, and HDSe, and with these predictions we can assign weak spectra of these molecules. We assign here two very weak bands of HD⁸⁰Se, ν₁+ν₂+ν₃ and 2ν₁+ν₃. The refinement of the potential energy surface was made possible because (1) the number of vibrational states characterized experimentally for various isotopomers of H₂Se has approximately doubled since 1993, and (2) we now have access to larger computers with which we can fit energy spacings of states with J?8, whereas Jensen and Kozin could only use J?5. In the present work, we fitted rotation-vibration energy spacings associated with 24 vibrational states of H₂⁸⁰Se with v₁?6, v₂?3, and v₃?2; 11 vibrational states of D₂⁸⁰Se with v₁?2, v₂?3, and v₃?2, and 17 vibrational states of HD⁸⁰Se with v₁?3, v₂?3, and v₃?3. The input data set comprised 3611 energy spacings. In the fitting, we could usefully vary 29 potential energy parameters. The standard deviation of the fitting was 0.12 cm⁻¹ and the root-mean-square deviation for 49 vibrational term values was 0.59 cm⁻¹.     

A multispectrum analysis of the ν2 band of HCN: Part II. Theoretical calculations of self-broadening, self-induced shifts, and their temperature dependences

A semiclassical theory based upon the Robert-Bonamy formalism has been developed to explain the experimental measurements of self-broadening, self-induced pressure shift coefficients in the ν₁,ν₂, 2ν₂ bands of H¹²C¹⁴N and the 2ν₁ band of H¹³C¹⁴N, as well as the temperature dependences of these parameters with special emphasis on the ν₂ band. Our calculations include only electrostatic interactions and neglect the vibrational dependence of the isotropic part of the intermolecular potential, which probably has a weak contribution to the HCN self-shifts for the bands investigated in this study. The agreement between theory and measurements is good in the cases of self-broadening coefficients and their variation with temperature, as well as the self-shift coefficients determined at room temperature. However, the observed temperature dependence of self-shift coefficients in the ν₂ band is different from that derived theoretically.     

Identification and intensities of the “forbidden” 3ν23 band of 12C16O2

Lines of the 3ν₂³ “forbidden” band of ¹²C¹⁶O₂ have been identified in the 2000-cm^?1 region of a long-path, 0.01-cm^?1 resolution laboratory absorption spectrum. This band has detectable intensity due to Δl = 2 Fermi interactions between the upper level and the nearby ν₁ + ν₂ and 3ν₂¹ levels. Intensities of 18 lines of this band have been measured using a nonlinear least-squares spectral fitting technique. The intensities are enhanced at high J and an expression for the intensity distribution as derived by Toth [Appl. Opt.23, 1825–1834 (1984)] is used for the analysis. In terms of the total sample pressure, the vibrational band intensity is 0.194 ± 0.008 × 10^?30 cm^?1/molecule-cm^?2 at 296 K. The coefficient in the F factor is analogous to the Coriolis coefficient ξ and has been determined to be ?0.0413 ± 0.0015. As expected by theory, its value is very close to that of ξ for the related ν₁ + ν₂ band.     

The ν5 band of CH3CH3: High resolution stimulated Raman spectrum and global three band analysis

Rotationally resolved spectrum of ¹²CH₃¹³CH₃ in the region of ν₅ vibrational fundamental (CC stretch) was observed using stimulated Raman spectroscopy. This spectrum was analyzed with data from the ν₁₂ fundamental and transitions from the ν₆, 2ν₆-ν₆, and 3ν₆ torsional bands using a 3-state fit. One torsional component of the ν₅ fundamental is perturbed, interacting with its partner in the ν₆=4 of the torsional stack of the ground vibrational state. As for normal ethane, the coupling was successfully modeled using a Fermi-type interaction. The results mirror that of ¹²CH₃¹²CH₃ in that the inclusion of the Fermi-type interaction reduces the required number of terms in the Fourier expansion of the torsional potential for the ground vibrational state from three (in the 2-state fit) to one, only the term in the barrier height is required.