Vibrational Term Values Research Articles

The High-Resolution Fourier Transform Spectrum of Dideuterated Methane CH2D2in the Region between 1900 and 2400 cm−1

The infrared spectrum of doubly deuterated methane CH2D2has been recorded in the region from 1900 to 2400 cm−1at almost Doppler-limited resolution by using two high-resolution Fourier transform spectrometers. The vibrational bands observed include 2ν4, ν4+ ν7, 2ν7, ν2, ν8, ν4+ ν9, and ν7+ ν9, which were analyzed by taking into account Coriolis and Fermi interactions among them and also those with ν4+ ν5, ν3+ ν7, and ν5+ ν7. Most of the centrifugal distortion constants were constrained to appropriate values, while the vibrational term value and three rotational constants in each of the seven excited states were adjusted along with Coriolis and Fermi interaction parameters by the least-squares analysis of the observed spectrum. The vibration–rotation interaction constants αsthus determined for the ν2and ν8states were combined with those of other fundamental states already published to calculate the equilibrium C–H distance.

Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions

Anion photoelectron spectra of Ge−n, n=2–15, have been measured using an incident photon energy of 4.66 eV. In addition, the spectra of Ge−2, Ge−3, and Ge−4 have been measured at photon energies of 3.49 and 2.98 eV. From these spectra the electron affinity of the corresponding neutral cluster has been determined. Vibrational frequencies and term values for several electronic states of Ge−2 and Ge−3 have been determined. Vibrational structure in the 3B3u excited state of Ge4 has been resolved using zero electron kinetic energy (ZEKE) photoelectron spectroscopy. The assignment of the spectra of Ge−3 and Ge−4 is facilitated by a comparison to the similar spectra of Si−3 and Si−4, respectively. The spectra of the larger clusters, Ge−n, n=5–15, are characterized by many broad structureless features which indicate the presence of multiple electronic transitions. Several of these were assigned based on comparison with previous ab initio calculations on germanium and silicon clusters.

Initiation and Abstraction Reactions in the Pyrolysis of Acetone

The rates of the reactions, (CH3)2CO → CH3 + CH3CO (1) and CH3 + (CH3)2CO → CH4 + CH2COCH3 (3) have been studied in the flow pyrolysis of acetone at 825−940 K and 10−180 Torr. Yields of products were measured by gas chromatography. The rate constant, k1, for the initiation reaction, determined from the sum of the yields of the termination products, was observed to be pressure dependent at 928 K. The Arrhenius expression for this reaction at the high-pressure limit (obtained from a nonlinear least-squares fit to the experimental data using the Troe factorization procedure) was found to be k1∞ (s-1) = 1017.9±0.8 exp(−353 ± 14 kJ mol-1/RT). The Troe method has also been used to find the high-pressure limits of the cross-combination ratio for CH3 and CH3COCH2 radicals (1.9 ± 0.1) and of the quotient k5/k32, where reaction 5 is 2CH3 → C2H6. Calculated rate constants for reaction 3, when combined with values reported from photolysis experiments at lower temperatures, were found to exhibit a curved Arrhenius plot. A transition state theory model was fitted to the data for k3 to determine the average transitional vibrational term value in the transition state (279 ± 8 cm-1), the effective activation barrier height (46 ± 1 kJ mol-1), and the full width of the barrier at half its height (52 ± 3 pm).

An ab Initio Calculation of the Rovibronic Energies of the Ch +2 Molecule

In a previous paper (W. P. Kraemer, P. Jensen, and P. R. Bunker, Can. J. Phys. 72, 871-878, 1994) we reported the results of an ab initio calculation of the vibronic (i.e., N = 0) energy levels of the CH + 2 molecular ion in both the X̃ 2 A 1 and à 2 B 1 electronic states. These two electronic states become degenerate ( 2Π ) when the molecule is linear, and in the vibronic calculation we used the theory that we have given in another paper (P. Jensen, M. Brumm, W. P. Kraemer, and P. R. Bunker, J. Mol. Spectrosc. 171, 31-57, 1995) in order to allow for the effects of the electronic angular momentum in this situation (i.e., the Renner effect). In the present paper we extend the CH + 2 calculation to include N > 0 rovibronic energies and we take into account the effect of spin-orbit coupling by using the ab initio value of the spin-orbit matrix element from W. Reuter and S. D. Peyerimhoff ( Chem. Phys. 160, 11-24, 1992). The only experimental data available for CH + 2 come from a measurement of the ν 3 fundamental band of the ground state (M. Rösslein, C. M. Gabrys, M.-F. Jagod, and T. Oka, J. Mol. Spectrosc. 153, 738-740, 1992) in which the ν 3 vibrational term value was determined to be 3131.37 cm −1. In our ab initio calculation we obtain 3114.1 cm −1 for this term value. Thus, to make our predictions as reliable as possible, we calculate the rovibronic energies after adjusting one parameter in the potential so that we fit the observed value of the ν 3 vibrational term value. Using this slightly adjusted ab initio potential we predict a large number of rovibronic term values in the X̃ and à states that have not yet been spectroscopically characterized, and we compare our results for the line positions and spin splittings in the ν 3 band with the observations.

Laser induced fluorescence spectroscopy of the C̃ 1B 2X̃ 1A 1 band of jet-cooled SO 2: rotational and vibrational analyses in the 235-210 nm region

Laser induced fluorescence spectra of the C̃ 1B 2X̃ 1A 1 band of SO 2 in the 235-210 nm region were measured under jetcooled conditions. By high-resolution (≈ 0.08 cm −1) measurements of the vibronic transitions, which were well separated from each other due to rotational and vibrational cooling, the rotational constants and term values for the 33 vibrational levels were determined. For the other four levels, only the term values were determined. A total of 573 ro-vibronic transition wavenumbers are presented. It was found that the C rotational constants exhibit considerable fluctuation over the whole observed energy range due to the C-axis Coriolis interaction. The observed vibrational term values were utilized for the extension of the secure vibrational assignments to the higher energy region. However, due to the strong 1:2 Fermi interaction between v 1 (symmetric stretch) and v 3 (anti-symmetric stretch), definitive vibrational assignments for the transitions to the vibrational levels above 2000 cm −1 were found to be intrinsically impossible except for the C ̃ (v 1, v 2, v 3) = (1, n, 0) , (2, n, 0), (3, n, 0) and (1, n, 2) vibrational levels. By constructing the three-dimensional Hamiltonian with a vibrational potential expanded to the fourth-power of the normal coordinates, the expansion coefficients were determined by the least-square fitting to the observed term values and those of several known lowlying vibrational levels. The Franck-Condon intensity pattern calculated using the vibrational wavefunctions derived as eigenfunctions was consistent with the observed pattern below the C̃(1, 4, 2) band, above which the predissociation occurs. The derived vibrational eigenfunctions showed that the v 1 and v 3 modes mix with each other significantly in the higher energy region above 2000 cm −1, which is consistent with the difficulty encountered in assigning the definitive v 1 and v 3 vibrational quantum numbers. The vibrational wavefunctions were further utilized to analyze the C-axis Coriolis interaction, and the counterpart levels of the perturbation having an odd v 3 quantum number were identified for the lowlying vibrational levels. By measurements of the hot-band transitions from X̃(0, 1, 0), the v 2 (bend) fundamental wavenumber of the electronic ground X̃ 1A 1 state was determined to be 517.90(3) cm −1.

Fermi resonances and local modes in pyramidal XH3 molecules: An application to arsine (AsH3) overtone spectra

A simple vibrational Hamiltonian expressed in terms of curvilinear internal coordinates has been used to model both stretching and bending vibrations in pyramidal XH3 molecules. The pure stretching part is expressed as harmonically coupled anharmonic oscillators and the pure bending part as harmonically coupled harmonic oscillators. The stretching and the bending modes are coupled with each other by Fermi resonance terms which contain contributions both from the kinetic and potential energy part of the full vibrational Hamiltonian. Only resonance couplings are included. The Hamiltonian matrices are symmetry factorized by employing symmetrized basis functions which consist of products of stretching oscillator and valence angle bending oscillator functions. This model is applied to observed vibrational term value data of arsine (AsH3). The least squares method is used to optimize potential energy parameters. The results obtained are in good agreement with ab initio calculations. All observed arsine overtone and combination bands have been assigned.

The Potential Energy Function of CS2 Derived from Rovibrational Data

We have derived the potential energy surface up to 5000 cm−1 of the X̃1Σ+g electronic ground state of CS2 by fitting to experimental rotation-vibration data using a variational approach. We use the Morse oscillator rigid bender (MORBID) Hamiltonian, with a basis set composed of Morse oscillator and rigid bender eigenfunctions, to fit 40 vibrational term values and 40 rotational levels with J < 6. We obtain a root mean square deviation of 2.12 cm−1 for the vibrational energy spacings. In determining the potential energy function we obtain the equilibrium bond length Re = 1.5549 ± 0.0040 Å, and predict the position of 22 l = 0 vibrational levels, below 5000 cm−1 that have not been observed. The large masses of the terminal sulphur atoms lead to difficulties in basis set convergence at high energies because of large bend-stretch and stretch-stretch coupling in the kinetic energy operator, and for this reason we only fit to levels up to 5000 cm−1; these are converged to better than 1 cm−1. This difficulty with convergence does not occur for hydrides such as CH2, H2O, H2S, and H2Se, but is a general problem in heavy-light-heavy triatomic molecules. It is particularly difficult to fit the l = 1 vibrational energies.

The Rotational and Rotation‐Bending Spectrum of HC15NO: An Extended Analysis of the Spectral Regions 18‐40 GHz, 90‐440 GHz and 170‐1300 cm−1

AbstractThe rotational spectrum of the 15N‐substituted quasilinear molecule fulminic acid, HCNO, has been measured in the frequency range from 90 to 440 GHz covering rotational transitions up to J = 19←18. Rotational transitions arising from HC15NO molecules in 52 vibrational levels were detected and assigned. Additional information was obtained by measuring the direct l‐type transitions for v5 = 1 and 3 and for v4 = 1 in the frequency range from 18 to 40 GHz. With the information from the rotational spectrum the analysis of the far and mid‐infrared spectra (170‐1300cm−1), which was started by Wagner et al. [J. Mol. Spectrosc. 162, 82 (1993)], could be extended so that the vibrational term values of HC15NO were determined for almost every state below 2500cm−1. The assignment of the 114 subbands involved allowed in turn the assignment of 25 subbands in the mid‐infrared from the data of Quapp et al. [J. Mol. Spectrosc. 160, 540 (1993)]. The infrared spectra were recorded with a Bruker IFS 120 HR interferometer at resolutions between 0.0019 and 0.0034 cm−1. For the vibrational states (v1 v2v3v4v5) = (00000), (00001), (00002), (00003), (00004), (00010), (00011) an (00100) the spectroscopic constants of an effective Hamiltonian for linear molecules could be improved by combining the already published infrared data with the millimeter wave, microwave and newly assigned infrared data presented in this work. For the states (00013) and (00101) these constants were also calculated. A calibration problem with the infrared data became obvious and important. The effects of a Fermi‐type resonance between the vibrational levels (00004)oe and (00100)oe and a Coriolis resonance between the states (00002) and (00010) on the rotational and rovibrational spectra were observed and analysed. The difficulties encountered in determining the Coriolis resonance parameters are discussed.

Laser excitation and dispersed fluorescence investigations of the system of SrOH

Abstract The 1 0 1 bond of the A 2 Π − X 2 Σ + system of SrOH has been observed at Doppler-limited resolution using cw dye laser excitation coupled with selective detection. Using a digitally interfaced scanning monochromator, rotationally resolved dispersed fluorescence spectra of the 1 1 1 , 1 2 1 , and 2 3 1 bands have also been recorded and analyzed. Vibrational term values and rotational constants for several vibrational levels in the A 2 Π and X 2 Σ + states are determined. Coriolis interactions arising from the near degeneracy of the (200) and (03 1 0) levels is found to have a negligible effect on the rotational energy level structure of the (200) level.

A Characterization of the CH2ã1A1(1,2,0),(2,0,0),(0,5,0),(1,3,0) and b̃1B1(1,142,0),(0,180,0),(0,191,0) Vibronic Levels by Fourier-Transform Dispersed Fluorescence Spectroscopy

The CH2ã1A1, (1, 2, 0), (2, 0, 0), (0, 5, 0), (1, 3, 0) and b̃1B1 (1, 142, 0), (0, 180, 0), (0, 191, 0) levels are characterized by Fourier-transform dispersed fluorescence spectroscopy (FTDFS). Rotational transitions in the b̃ ← ã 1102140, 2180, and 2190 fluorescence excitation bands and those of the b̃ → ã 1012162, 1012172, 1022160, 2185, 2195, 1012183 and 1102193 bands in dispersed fluorescence spectra have been assigned. The rotational constants and vibrational term values for these vibrational levels have been obtained. Due to the limits brought by Renner-Teller coupling and Franck-Condon factors, this work, along with previous studies on lower vibrational levels, has characterized almost all ã vibrational levels detectable in the b̃↔ã transitions.

A spectroscopically determined potential energy surface for the ground state of H216O: A new level of accuracy

The potential energy function for the electronic ground state of the water molecule has been obtained by fitting rotation-vibration term values involving J≤14 for 24 vibrational states of H216O together with 25 additional vibrational term values belonging to higher excited states. The fitting was carried out by means of an exact kinetic energy Hamiltonian. It was found that the differences between the exact kinetic energy calculations and calculations with the morbid program (i.e., calculations with an approximate kinetic energy operator) depend only very slightly on the parameters of the potential. This fact allowed us to make an inexpensive fitting using the morbid approach and still get the accuracy obtainable with the exact kinetic energy Hamiltonian. The standard deviation for 1600 term values was 0.36 cm−1. For 220 ground state energy levels the standard deviation was 0.03 cm−1. With the fitted potential, calculations of term values with J≤35 were carried out. This showed the excellent predictive power of the new potential. For the J=20 term values in the vibrational ground state, the deviations from experiment are typically below 0.2 cm−1. The discrepancy for the observed level with the highest Ka value, JKaKc = 20200, is only 0.008 cm−1. The calculated term value for the observed level with the highest J, 35035, deviates 0.1 cm−1 from experiment. Because of the level of accuracy achieved in these calculations, we can for the first time demonstrate the breakdown of the Born–Oppenheimer approximation for the water molecule. The high Ka level calculations allow us to show that the rotational energy level structure in water is at least of a very different nature than the fourfold cluster structures observed for H2Se and calculated for H2S, H2Se, and H2Te.

New stretching vibrational basis functions for vibrational variational calculations in curvilinear internal coordinates

New basis functions for the stretching degrees of freedom for vibrational variational calculations in curvilinear internal coordinates are proposed. Analytical kinetic energy matrix elements for the curvilinear internal coordinate vibrational Hamiltonian for triatomic molecules are derived. Use of the basis functions in practical calculations is demonstrated by calculating vibrational term values for H 2 16O variationally up to 30000 cm −1.

Improvements in a Curvilinear Internal Coordinate Model for the CH Stretching and Bending Vibrations in Trihalomethanes

The interactions between the CH stretching and bending vibrations in CH X 3-type symmetric-top molecules have been studied. The previous curvilinear internal coordinate vibrational Hamiltonian (E. Kauppi and L. Halonen, J. Chem. Phys. 90, 6980-6992, 1989) has been improved by including contributions arising from the nonlinearity of the redundancy relation between the curvilinear internal coordinates. This affects the anharmonic kinetic energy terms of the pure CH bending Hamiltonian. Vibrational energy levels have been calculated variationally. The model has been applied to data for CHF 3, CHCl 3, CHBr 3, and (CF 3) 3CH. The potential energy parameters have been optimized by a nonlinear least-squares method using vibrational term values as data. In the cases of CHF 3, CHCl 3, and CHBr 3 data for bath 12C and 13C isotopomers have been treated with one set of isotope invariant potential energy parameters. Good fits have been obtained by using five or six adjustable parameters. The values for the quartic bending force constants change considerably from the values obtained by ignoring the nonlinear redundancy contributions.

Vibration-Rotation Interactions in Bending and CBr Stretching Fundamental Band Systems ν 3, ν 4, and ν 5 of Monobromoacetylene

High-resolution vibration-rotation spectra of a sample of natural monobromoacetylene (HCCBr) have been recorded with the Bruker IFS 120 Fourier spectrometer in the region of the bending and CBr stretching fundamentals. Altogether 23 bands belonging to HCC 79Br and 23 bands belonging to HCC 81Br isotopic species have been analyzed rotationally, yielding accurate vibrational term values and rotational constants. Coriolis-, rotational l-, and Fermi-resonance interactions have been observed and analyzed in some of the bands.

Potential energy surface of the H+3 ground state in the neighborhood of the minimum with microhartree accuracy and vibrational frequencies derived from it

The potential energy surface (PES) of the H+3 ground state is computed by means of the single and double excitation configuration interaction with an explicit linear r12 term in the wave function (CISD-R12) developed recently by the present authors, with a nearly saturated basis set. The points of the PES suggested by Meyer, Botschwina, and Burton (MBB) were chosen and the fitting procedure of the same authors was followed. The present PES has both on an absolute and a relative scale (i.e., relative to the minimum) an error of a few microhartrees (μEh) in the relevant region, an accuracy that has never before been achieved in a quantum chemical calculation for a triatomic molecule. From the fit the vibrational term values for the fundamental bands and some overtones of H+3, H2D+, HD+2, and D+3 were computed by means of the TRIATOM package of Tennyson and Miller. The computed frequencies are in better agreement with experiment (maximum error ∼0.5 cm−1) than those of all previous ab initio calculations (without empirical adjustment). To achieve this accuracy, it is necessary to go beyond the Born–Oppenheimer approximation and to take care of the finite mass ratio between nuclei and electrons.

Electron spin resonance study of the reaction of hydrogen atoms with methane

The reaction: H + CH4 → CH3 + H2 has been investigated in a flow system between 348 and 421 K. Hydrogen atoms were generated in a microwave discharge, introduced to the reactor through a movable injector, and monitored by electron spin resonance. After an initial decay attributed to reaction with impurity, the hydrogen atom concentration decayed in a pseudo-first-order manner. Ethane was detected by gas chromatography, consistent with its formation by the following reaction: 2CH3 → C2H6. The amount of ethane formed at 421 K was only 0.015 times the amount of hydrogen atoms reacting. Most methyl radicals were assumed to have been removed by the process: H + CH3 + M → CH4 + M. Because of this process, two hydrogen atoms were removed each time the title reaction occurred. Applying this stoichiometric factor, the rate constant for the elementary reaction was calculated to be 2.5 × 103 L mol−1 s−1 at 348 K, increasing to 2.0 × 104 L mol−1 s−1 at 421 K. Most of the previous discrepancy between kinetics and thermochemistry has been eliminated; the exothermicity at 0 K was reduced to 0.8 ± 0.4 kJ mol−1, which corresponds to a standard heat of formation of the methyl radical of 145 kJ mol−1. Properties of the activation barrier have been inferred from the experimental data with the aid of transition state theory. The fitted barrier height was 63 ± 1 kJ mol−1, the average of five low-frequency vibrational term values was 640 ± 30 cm−1, and the characteristic tunnelling temperature was 500 ± 30 K.

High resolution photoacoustic overtone spectroscopy of monofluoroacetylene, HCCF, with a titanium:sapphire ring laser

Intracavity photoacoustic overtone spectrum of monofluoroacetylene, HCCF, has been recorded in the wave number region 10 750–14 500 cm−1 with a titanium:sapphire ring laser. The spectrum contains many dense vibration–rotation band systems which can be resolved with Doppler limited resolution. Altogether 58 individual overtone bands have been analyzed rotationally. Many of the observed bands show perturbations of which some have been attributed to anharmonic resonance interactions. A Fermi resonance model based on conventional rectilinear normal coordinate theory has been used to assign vibrationally bands from this work and from earlier studies. Many of the observed vibrational term values and rotational constants can be reproduced well with this model. The results show the importance of the Fermi resonance interactions at the high overtone excitations.

Fluorescence Excitation Spectra of the b̃1B1 ← ã1A1 2 n0 ( n = 18-23) Bands of CD 2

Some 100 transitions in the six b̃ 1 B 1 ← ã 1 A 1 2 n ( n = 18-23) bands in the fluorescence excitation spectrum of CD 2 have been assigned. Stimulated emission pumping through the b̃ 1 B 1 ← ã 1 A 1 2 22 3 band confirmed the assignment for the laser-induced fluorescence transitions. Approximate rotational constants and vibrational term values for the ã (0, 0, 0) and (0, 3, 0) and the b̃ (0, 18, 0), (0, 20, 0), and (0, 22, 0) levels have been determined.

Fourier transform dispersed fluorescence spectroscopy: Observation of new vibrational levels in the 5000–8000 cm−1 region of ã 1A1 CH2

Dispersed fluorescence spectra from the CH2 b̃ 1B1 state to highly excited vibrational levels of the ã 1A1 state were recorded by a new technique, Fourier transform dispersed fluorescence spectroscopy. The spectra obtained clearly show the advantages of using a Fourier transform spectrometer for dispersing fluorescence, namely emission over a wide spectral range can be efficiently detected with high sensitivity and resolution. These advantages allow four new vibrational levels in the CH2 ã 1A1 state to be observed; the (2,0,0) and (0,5,0) vibrational overtones and the (1,2,0) and (1,3,0) combination bands. The vibrational term values for these levels are given, along with the harmonic frequencies and anharmonicities for the v1 and v2 modes. From the (0,5,0) term value an improved estimate of the barrier height to linearity in the CH2 ã 1A1 state is made.

Threshold photoelectron and TOF photoelectron spectra of Ar2+ and Kr2+

The threshold electron spectra of Ar2 and Kr2 were measured using synchrotron radiation. The vibrational structures of the ground states of Ar2+ and Kr2+ ions were clearly observed. The present results for the Ar2+ ionic state confirmed previous ones. For the Kr2+ ionic state, the vibrational term values are determined to be (103695+or-8)+(188+or-1)( nu +1/2)-(0.9+or-0.03)( nu +1/2)2 (cm-1) from the zero vibrational state of Kr2. The TOF photoelectron spectra of Ar2 and Kr2 were measured at several wavelengths of autoionizing states of Ar2 and Kr2, using pulsed photons from a synchrotron. In the photoelectron spectra, several vibrational levels were clearly recognized to support the authors' vibrational analysis of the threshold electron spectra.