Semirigid Bender Research Articles

CHFCO: Further studies of its microwave spectrum

We report here the microwave spectra of some isotopic species and vibrational satellites of fluoroketene, CHFCO. From the 13C and 18O species we calculate r s (CC) = 131.7 pm, r s (CO) = 116.7 pm, and ∠CCO = 178.0(5)°. The following r 0 parameters were also obtained: r(CH) = 108.0 pm.; r(CF) = 135.6 pm.; ∠FCC = 119.5°; ∠HCC = 122.3°; ∠CCO = 178.0° (away from F). These values of bond lengths are close to those of ketene itself but the HCF angle of 118.2° differs noticeably from the HCH angle in ketene, although it is not as small as the ∠HCF in fluoroallene (113.8°). The semirigid bender analysis of the vibrational satellites of the in-plane CCO bending motion ( v 7 = 1, 2, 3) gives a very shallow single-minimum potential: V = 4765 τ 2 + 40002 τ 4 cm −1 (τ in rad). The two low-frequency out-of-plane vibrations have frequencies similar to those of ketene. We estimate them to be 380 cm −1 for v 9 and 600 cm −1 for v 8.

A theoretical calculation of the rotation-vibration energies for lithium hydroxide, LiOH

We have calculated ab initio the three-dimensional potential energy surface of the LiOH molecule at 166 nuclear geometries spanning energy ranges of about 2500 cm−1 for the LiO stretch, 7500 cm−1 for the OH stretch, and 4000 cm−1 for the bend. The ab initio configuration interaction calculations were performed within the framework of the average coupled pair functional method [R. J. Gdanitz and R. Ahlrichs, Chem. Phys. Lett.143, 413–420 (1988)]. The equilibrium structure is linear, but we found a very strong interaction between the LiO stretch and the bend such that at longer LiO distances the optimal structure is bent. The rotation and vibration energies for 7Li16OH, 7Li16OD, and 7Li18OH were calculated variationally using the Morse oscillatorigid bender internal dynamics Hamiltonian (MORBID) [P. Jensen, J. Mol. Spectrosc.128, 478–501 (1988); J. Chem. Soc. Faraday Trans. 284, 1315–1340 (1988)]. For 7Li16OH we find that ν1 = 3831 cm−1, ν2 = 289 cm−1, and ν3 = 923 cm−1, and we obtain Be = 1.183 cm−1. The MORBID results are compared with rotation-vibration energies calculated with the nonrigid bender [P. Jensen and P. R. Bunker, J. Mol. Spectrosc.118, 18–49 (1986)] and semirigid bender [P. R. Bunker and B. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonians.

OCCCS, NCNCS, NCNCO, and NCNNN as semirigid benders

The semirigid bender model has been developed for a general planar molecule. It is used here to determine the ν 7 (linear convention) or ν 9 (bent convention) bending potential functions of the molecules OCCCS, NCNCS, NCNCO, and NCNNN by fitting the model to the observed microwave spectra. These four molecules illustrate the passage from a linear limit (OCCCS), through quasilinearity (NCNCS, NCNCO), to the bent limit (NCNNN).

ChemInform Abstract: The Vibrational State Dependence of the 14N Quadrupole Coupling Tensor in Aniline. A Microwave Fourier‐Transform Study Combined with Semirigid Bender Calculations.

ChemInformVolume 19, Issue 39 Physical Organic Chemistry ChemInform Abstract: The Vibrational State Dependence of the 14N Quadrupole Coupling Tensor in Aniline. A Microwave Fourier-Transform Study Combined with Semirigid Bender Calculations. B. + KLEIBOEMER, B. + KLEIBOEMER Abt. Chem. Phys., Inst. Phys. Chem., Christian-Albrechts-Univ. Kiel, D-2300 KielSearch for more papers by this authorD. H. SUTTER, D. H. SUTTER Abt. Chem. Phys., Inst. Phys. Chem., Christian-Albrechts-Univ. Kiel, D-2300 KielSearch for more papers by this author B. + KLEIBOEMER, B. + KLEIBOEMER Abt. Chem. Phys., Inst. Phys. Chem., Christian-Albrechts-Univ. Kiel, D-2300 KielSearch for more papers by this authorD. H. SUTTER, D. H. SUTTER Abt. Chem. Phys., Inst. Phys. Chem., Christian-Albrechts-Univ. Kiel, D-2300 KielSearch for more papers by this author First published: September 27, 1988 https://doi.org/10.1002/chin.198839046AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume19, Issue39September 27, 1988 RelatedInformation

Ab initio rotational energy levels and internal rotation splittings in protonated acetylene C 2H 3+

The C 2H 3 + ion has an unusual internal-rotation tunneling degree of freedom in which the three protons rotate around the C 2 core with the molecule remaining planar. We have used our semirigid bender Hamiltonian (R. Escribano and P.R. Bunker, J. Mol. Spectry. 122 (1987) 325), with the results of an ab initio calculation of this tunneling potential (R. Lindh et al., Chem. Phys. Letters 139 (1987) 407), to calculate the rotational energy levels and internal-rotation splittings.

ChemInform Abstract: An ab initio Study of the Molecular Structure and Vibration‐Rotation Spectrum of the Triplet Radical HCCN.

The bent triplet cyanocarbene H-C-C≡N and the linear triplet allene H-C=C=N have been studied by the CASSCF and CI methods, using a DZP basis. Relaxation of all geometrical parameters for the CASSCF energy results in a bent molecule with CCH angle 133° and a barrier to linearity of 6.4 kcal/mol, which was lowered to 2.3 kcal/mol in a subsequent CI calculation. The Davidson correction lowered it further to 1.8 kcal/mol. A 26-term analytical potential energy surface (PES) was fitted to CASSCF, CI, and Davidson corrected CI energies in 94 different geometries. Using these three potentials, the semi-rigid bender model predicts a CCH bending frequency of 782, 505, and 503 cm−1, resp., which compares favourably with an experimentally observed IR transition line at 458 cm−1. For the deuterated species, the corresponding frequencies are 610, 407, and 402 cm−1, to be compared with two possible absorption lines at 405 and 317.5 cm−1. The PES was then parametrized by adding a variable CCH angle dependence, and a comprehensive vibration-rotation spectrum was calculated variationally, using the exact 4-atom vibration-rotation kinetic Hamiltonian, for a range of barrier heights. Comparison with experiment indicates a barrier in the range 1±0.5 kcal/mol.

The Vibrational State Dependence of the 14N Quadrupole Coupling Tensor in Aniline . A Microwave Fourier-Transform Study Combined with Semirigid Bender Calculations

Abstract Experimental values for the diagonal elements of the 14N quadrupole coupling tensor derived from analysis of the hyperfine structure of low-J rotational transitions are reported for the two lowest states of the amino wagging mode. They show the expected difference due to averaging over the large amplitude amino wag. A semirigid bender analysis of previously published infrared data provides the inversion angle expectation values for use in a quantum-chemical calculation of the corresponding effective Cou­lomb field gradients at the nitrogen nucleus. The results are compared to those obtained earlier for the related molecules vinylamine, cyanamide and ammonia.

Effects of orbital angular momentum in CH2The Renner-Teller effect

The vibrational and K-type rotational levels of the a 1 A 1 and the [btilde] 1 B 1 state of CH2 have been fitted by least squares to give a pair of Born-Oppenheimer potential curves for the combining electronic states. An accurate description of the effects of orbital angular momentum on the energy level positions has been obtained. We have been able to relate the force constants used in the calculation of the bond length variation in the semi-rigid bender model to the parameters derived from the deperturbation of the Fermi resonance interaction, and have shown that there is reasonable agreement between them. Finally we have been able to link the amount of unpaired angular momentum ⟨Lz ⟩ produced by the vibronic coupling to the degree of magnetic activity observed in the vibronic sub-bands, and in rotational energy levels of the a, v 2 = 0 state.

An ab initio study of the molecular structure and vibration-rotation spectrum of the triplet radical HCCN

The bent triplet cyanocarbene H-C-C≡N and the linear triplet allene H-C=C=N have been studied by the CASSCF and CI methods, using a DZP basis. Relaxation of all geometrical parameters for the CASSCF energy results in a bent molecule with CCH angle 133° and a barrier to linearity of 6.4 kcal/mol, which was lowered to 2.3 kcal/mol in a subsequent CI calculation. The Davidson correction lowered it further to 1.8 kcal/mol. A 26-term analytical potential energy surface (PES) was fitted to CASSCF, CI, and Davidson corrected CI energies in 94 different geometries. Using these three potentials, the semi-rigid bender model predicts a CCH bending frequency of 782, 505, and 503 cm−1, resp., which compares favourably with an experimentally observed IR transition line at 458 cm−1. For the deuterated species, the corresponding frequencies are 610, 407, and 402 cm−1, to be compared with two possible absorption lines at 405 and 317.5 cm−1. The PES was then parametrized by adding a variable CCH angle dependence, and a comprehensive vibration-rotation spectrum was calculated variationally, using the exact 4-atom vibration-rotation kinetic Hamiltonian, for a range of barrier heights. Comparison with experiment indicates a barrier in the range 1±0.5 kcal/mol.

Rotation and internal rotation in ArH 3+ and ArD 3+

We have developed a semirigid bender model Hamiltonian to calculate the rotation and internal-rotation energy levels of ArH 3 + and ArD 3 +. We have used this Hamiltonian to fit the data reported in M. Bogey, H. Bolvin, C. Demuynck and J.L. Destombes, Phys. Rev. Letters 58 (1987) 988. From the results of the fitting we can predict other rotation and internal l-rotation states that are amenable to experimental study. We predict that the torsional fundamental band of ArH 3 +, and the Ar-H3+ stretching fundamental band, will be in the 450–550 cm −1 region; these bands will interact as a result of c-type Coriolis coupling.

ChemInform Abstract: The Rotation‐Vibration Spectrum and Double‐Minimum ν12 Potential Function of Propadienone: A Semirigid Bender Analysis

Abstract 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 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 ν 12, 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 C 1C 2C 3 = 142°. In the ground state the interconversion frequency is 3.7 GHz and the ν 12 fundamental frequency is predicted to be 160 cm −1. Analysis of other vibrational satellites involving the lowest-frequency out-of-plane mode ν 8 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.

Rotational, structural, ab initio, and semirigid bender analysis of the millimeter wave spectrum of H 2COHF

The hydrogen-bonded species H 2COHF has been studied in a conventional microwave absorption cell. The dimer was produced under equilibrium conditions at −78°C from a mixture of H 2CO and HF. Spectra from H 2COHF, H 2CODF, and D 2CODF are reported. Rotational spectra from two low-energy excited vibrational states, which involve the hydrogen bond, have been observed. Structural analysis was performed by fitting rotational constants after correcting the observed rotational constants for contributions from the low-energy vibrational states. The semirigid bender model was fitted to the observed rotational structure of the bending vibrational levels. The bending potential function and the intermolecular distance were determined in the fittings. SCF ab initio calculations were used to model the bending vibrational dynamics and the potential functions of the three in-plane intermolecular vibrations.

The kinetic energy contribution U( ρ) to the potential energy in the Hougen-Bunker-Johns Hamiltonian

The pseudo potential energy term U( ρ) obtained from the kinetic energy term of the Hougen-Bunker-Johns (HBJ) rotation-vibration Hamiltonian has been obtained in general to order of magnitude κ 2 T v . The expression obtained is relatively easy to evaluate and should be used in any semirigid bender or nonrigid bender Hamiltonian that is derived from the HBJ Hamiltonian.

Rotation and internal rotation in the vinyl cation C 2H 3+

In the vinyl cation C 2H 3 + it is believed that there is a low barrier hindering the rotation of the three protons around the CC core, with the molecule remaining planar during this internal rotation. In this paper the semirigid bender formalism is adapted to calculate the rotation and internal-rotation energy levels of this species. Numerical results are presented for a variety of different hindering potentials. The symmetries of the levels, the nuclear spin statistical weights, and the selection rules for allowed electric dipole transitions are all determined.

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 ( ν 15) and two quanta of the in-plane ( ν 21) 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 v 15 = 3, v 21 = 0 state with the v 15 = 0, v 21 = 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 ν 15 and ν 21 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.

The rotation-inversion spectrum of ketenimine, H2CCNH

Abstract High-resolution measurements of μc-type transitions of ketenimine in the 4- to 7-GHz region revealed a splitting of each line caused by the inversion motion of the imino hydrogen. The inversion splitting amounts to 66 kHz. Data from ab initio molecular orbital calculations for the changes of the geometrical parameters during the inversion motion have been used to carry out semirigid bender calculations. A barrier height of 4700 ± 200 cm−1 and an equilibrium HNC angle of 115.4 ± 0.6° have been derived. In addition, the microwave spectrum of the N-deuterated species has been assigned. The inversion splitting could not be resolved but the quadrupole coupling of the deuterium nucleus has been observed. Attempts to detect the inversion splitting in methanimine, H2CNH, have been unsuccessful, suggesting a higher barrier than in ketenimine.

Ab initio rotation-vibration energies of HOC+ calculated using the nonrigid bender Hamiltonian

Abstract In a previous paper [W. P. Kraemer and P. R. Bunker, J. Mol. Spectrosc. 101, 379–394 (1983)] the results of configuration interaction calculations, performed in order to investigate the bending potential of the molecular ion HOC+, were reported. In the present paper we give the results of such calculations including additional points on the potential surface chosen mainly in order to study the HO and OC stretching potentials at longer bond lengths. We have determined the rotation-vibration energies from this extended potential surface using a newly written computer program that diagonalizes the nonrigid bender Hamiltonian. We compare the results with those obtained using the second-order rotation-vibration perturbation Hamiltonian, the rigid bender Hamiltonian, and the semirigid bender Hamiltonian.

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

Abstract The infrared spectrum of carbon suboxide, C 3 O 2 , 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 12 C 3 16 O 2 . These consist of the ν 6 fundamental band and some of the hot bands associated with the ν 7 , 2 ν 7 , and 3 ν 7 states. The data obtained on the ν 6 + nν 7 states were used as input for a semirigid bender fit yielding the effective CCC bending potential energy function in the ν 6 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 C 3 O 2 is bent at equilibrium with an equilibrium CCC bond angle of 156° and a barrier to linearity of 28 cm −1 .

Microwave spectrum and structure of cyanamide: Semirigid bender treatment

An extensive study of the microwave spectrum of cyanamide has been undertaken, the analysis being based in part on semirigidbender calculations by the methods of Bunker and Szalay. Inversion lines of NH 2CN, K −1 = 2 aQ branches and a number of vibrational satellites of the J = 2−1 transition were observed. A two-vibrational-state Hamiltonian was used to fit simultaneously the 0 + and 0 − microwave data and yielded rotational constants X, Y, Z, D J , D JK , d 1, H JK as well as the inversion splitting and the μ yz -connecting matrix element. Vibrational satellite data of seven isotopic species and infrared frequencies of NH 2CN were included in the semirigid bender calculations: The NCN spine is nonlinear by ca. 5° in the equilibrium structure of the molecule. Also, r NH A ̊ = 0.9994 + 0.0144ϱ 2 ; <HNH/2 = 60.39° − 0.1134ϱ 2; r NC A ̊ = 1.3301 + 0.0327ϱ 2 (ϱ is the inversion angle in rad); r CN = 1.1645 A ̊ fixed. The inclusion of the NC bond flexing was necessary in order to reproduce the observed vibrational satellite patterns of NH 2CN, NHDCN, and ND 2CN. The barrier to inversion of the amino group is 510 ± 6 cm −1 with minima at ±45.0 ±0.2°. The inversion dipole moment is 0.91 ± 0.02 Debye.