Fermi Dyad Research Articles

Theoretical study of resonant vibrational excitation ofCO2by electron impact

We report the results of a fully ab initio study of resonant vibrational excitation of CO 2 by electron impact via the 3.8 eV 2 A 1 shape resonance. First, we solve the fixed-nuclei, electronic scattering problem using the complex Kohn variational method for a variety of symmetric-stretch geometries and for a range of bending angles. We then carry out a three-mode treatment of the nuclear dynamics using a complex local potential or boomerang model using resonance parameters derived from our calculated fixed-nuclei cross sections. The results show that a multidimensional treatment of the nuclear motion is essential for a proper description of the vibrational dynamics of CO 2 , in particular for describing resonant excitation of the two components of the well-known lowest Fermi dyad.

Selectivity in the excitation of fermi-coupled vibrations in CO2 by impact of slow electrons.

Improvement of resolution of a gas phase hemispherical electron spectrometer (to 7 meV FWHM) permitted separate measurements of the excitation of each member of the well known Fermi dyad in CO2 by impact of slow electrons. Absolute differential cross sections at a scattering angle of 135 degrees were measured as a function of electron energy. The excitation was found to be highly selective both via the 2Pi(u) shape resonance around 3.6 eV and via the virtual CO2- state at low energy. The selectivity is surprising because both vibrational states ensuing from the Fermi resonance involve the same type of nuclear motion (bending and stretch) and excitation of both is symmetry allowed.

Raman spectral changes of neat CO 2 across the ridge of density fluctuation in supercritical region

Density dependence of Raman spectra for carbon dioxide was studied along the isotherm in the temperature region 0.96⩽ T/ T c⩽1.06 and the density region 0< ρ/ ρ c<2. Spectrum in the small-wavenumber region below 100 cm −1 and that in the region of the 2 ν 2 intramolecular band, i.e. one of the Fermi dyad, were carefully measured and analyzed. The results are interpreted by assuming the presence of the gas- and liquid-like regions in the supercritical region separated by the ridge of density fluctuation.

Vibrational and rotational collisional relaxation in CO2–Ar and CO2–He mixtures studied by stimulated Raman-infrared double resonance

The collisional relaxation among vibrational levels of the Fermi dyad of CO2 mixed with Ar and He (10% CO2, 90% rare gas) has been studied at room temperature with a double resonance experiment. Stimulated Raman effect from the ground state achieved the pumping process with a Nd:YAG laser and a pulse amplified dye laser. After pumping the v1 or 2v2(Σ+g) level, a cw CO2 laser was used to probe either the depopulation rates of the pumped levels (vibrationally or rotationally resolved) or the energy transfer rates to neighboring states. The vibrational energy relaxation has been studied from experimental depopulation of v1 and population of 2v2 levels through a five-level model. A full set of vibrational rates has been determined and compared with other experimental and theoretical works when available. Our measurements could stimulate new accurate calculations. The rotational energy transfer among the J-resolved rotational levels of 2v2 has been observed for J=14 to 34 with a maximum difference between pumped and probed levels of ΔJ=20. The numerous experimental data have been modeled through a relaxation model based on the energy corrected sudden (ECS) approximation. The adjustable parameters of the ECS matrix have been directly determined by fitting the experimental time-dependent population curves. The diagonal elements of this matrix agree well with experimental linewidths. The resulting ECS relaxation matrix can be used to calculate line shapes in high-pressure coherent Raman spectra of v1 and 2v2 bands or infrared absorption spectra. In contrast, the inelastic linewidths of 2v2 deduced from depopulation data are in disagreement with available experimental linewidths, as already shown in numerous previous studies of gases and mixtures.

Excitation of laser-induced thermal gratings in the gas phase via Raman-active transitions

A systematic account of the properties of a recently developed coherent Raman technique is given. This is a time-resolved technique, based on the generation of thermal gratings due to a population change induced by stimulated Raman pumping of molecular levels. Excitation of gratings is achieved by spatially and temporally overlapping intensity interference patterns independently generated by two lasers with appropriate wavelengths. By employing this technique, it is possible to investigate gas transport properties and molecular energy relaxation processes, as has been shown for carbon dioxide. The transitions of the Q-branches of the ν 1/2 ν 2 Fermi dyad were used for Raman pumping in neat gas and in mixtures with argon. A possibility to perform spectroscopy of Raman-active transitions has also been demonstrated.

Intramolecular V– V transfer between the components of the (3 1/2 14 15 1) and (3 14 1/2 14 25 1) Fermi dyads in acetylene in C 2H 2–C 2H 2 collisions

Infrared–ultraviolet double resonance experiments have been performed to determine rate coefficients for collisional intramolecular vibration–vibration transfer in pure acetylene within two Fermi dyads: (a) that formed from almost equal mixtures of the zero-order, normal-mode states |3 1〉 and |2 1(4 15 1) 0〉 and (b) that which is composed predominantly of the |3 14 1 1〉, |2 14 2 25 1 −1〉 and |2 14 2 05 1 1〉 states. Pulses of tunable IR excited molecules to the lower component (II) of one of the Fermi dyads and the evolution of population in the upper component (I) was observed by exciting laser-induced fluorescence (LIF) from this level using tunable UV laser radiation 1 In this Letter, we employ the notation for vibrational states whereby, for example, 3 1 denotes one quantum of excitation in the ν 3 normal mode. (3 1/2 14 15 1) I,II denotes the Fermi dyad in which the principal contributions to the vibrational eigenstates are from the normal mode wavefunctions describing the zeroth-order 3 1 fundamental and 2 14 15 1 combination vibrational states. In each dyad, the subscript II is used to denote the lower of the two component states, I the higher. 1 . Analysis of the LIF signals vs. time yields the following rate coefficients ( k id) for intradyad transfer at 295 K: for (3 1/2 14 15 1) I↔II, k id=(2.1±0.2)×10 −10 cm 3 molecule −1 s −1; for (3 14 1/2 14 25 1) I↔II, k id=(3.2±0.6)×10 −11 cm 3 molecule −1 s −1. These results are discussed in terms of the matrix elements for such collision-induced transitions and differences in the mixing of the zero-order states in these two pairs of Fermi dyads.

Collisional shifting and broadening coefficients for the rovibrational anisotropic lines of the ν1/2ν2 fermi dyad in CO2 gas studied by stimulated Raman spectroscopy

High-resolution stimulated Raman spectroscopy was applied to the study of collisional broadening and shifting for rovibrational anisotropic Raman lines of the Fermi dyad of molecular carbon dioxide. The O(J) lines of the ν1 band and the S(J) lines of the 2ν2 band were recorded at 295 K. The pressure-induced line shifts were obtained and compared with the overall shift of the high-density Raman Q-branch. A rotational quantum number dependence of the rovibrational line broadening coefficients was observed. The experimental line broadening coefficients were used in order to check the ability of two theoretical methods (random phase approximation and sum rule) for calculating the line broadening coefficients in anisotropic Raman scattering. © 1998 John Wiley & Sons, Ltd.

Relaxation within and from the (31/214151) and (3141/214251) Fermi dyads in acetylene: Vibrational energy transfer in collisions with C2H2, N2 and H2

Infrared–ultraviolet double resonance (IRUVDR) experiments have been performed on samples of pure C2H2 and on C2H2 diluted in N2 and H2. Pulses of tunable IR radiation from an optical parametric oscillator (OPO) excited molecules of C2H2 to one component state of one of two Fermi dyads in the 1Σg+ electronic ground state, i.e. (31/214151)II or (3141/214251)II, and tunable UV laser radiation was used to observe the evolution of population either in that state or in the other component state of the same Fermi dyad. In this paper,‡ rate coefficients are reported for two kinds of processes: (a) vibration-to-vibration (V–V) transfer between the two component states of the same Fermi dyad induced by collisions with C2H2, N2 and H2, and (b) vibrational relaxation from the coupled pair of Fermi dyad states in collisions with the same gases. In addition, populations have been observed in the (4251), (4151) and (42) states of C2H2 during relaxation from the (3141/214251) dyad and rate coefficients for self-relaxation from the first two of these states have been derived. The results for both V–V intradyad transfer and for vibrational relaxation are discussed in terms of the vibrational matrix elements for such collision-induced transitions and differences in the mixing of the zero order states in the Fermi dyads.

Rotational energy transfer and rotationally specific vibration–vibration intradyad transfer in collisions of C2H2 X̃1Σg+(31/214151, J=10) with C2H2, Ar, He and H2

Infrared–ultraviolet double resonance (IRUVDR) experiments have been performed on samples of pure C2H2 and on C2H2 diluted in Ar, He and H2. Pulses of tunable IR radiation from an optical parametric oscillator (OPO) excited molecules of C2H2 to the J = 10 rotational level of the lower component state (II) of the (31/214151)II Fermi dyad in the 1Σg+ electronic ground state of C2H2 and tunable UV radiation was used to record laser-induced spectra at short delays. In this way, state-to-state rate coefficients have been determined for two kinds of processes:§ (a) rotational energy transfer (RET) induced by collisions with C2H2, Ar, He and H2 from the initial level Ji = 10 to other levels (Jf = 2–8, 12–20) within the same component (II) of the (31/214151) Fermi dyad, and (b) intradyad transfer in C2H2–C2H2 collisions to specific levels (Jf = 2–14, 18) in the other component (I) of this Fermi dyad. Transfer from II to I is found to account for ca. 16% of the total relaxation from (II, Ji = 10). The distribution of state-to-state rate coefficients for RET becomes broader as the mass of the collision partner increases, in accord with the predictions of a simple classical model. Absolute values of the state-to-state rate coefficients are determined by scaling the results to the previously determined rate coefficients for rotational relaxation by the same collision partner. It is suggested that intradyad transfer is relatively facile because of the difference in the two diagonal terms in the vibrational matrix element for the transition, with the 〈214151∣V∣214151〉 component being larger than the 〈31∣V∣31〉 component.

Interbranch line-mixing in CO2 (101) and (021) combination bands

Absorption spectra from a mixture of 320 ppm CO2 in synthetic air (79% N2, 21% O2) were collected in the region from 3500 cm−1 to 4000 cm−1 under conditions in the range of 100–1000 atm and 295–900 K. At 295 K, both bands of the (1001), (0201) Fermi dyad show the collapse of P and R branches into a single nearly Lorentzian spectral feature as a result of interbranch line-mixing. At elevated temperatures, the presence of interbranch mixing is also clearly evident as is the presence of several hot bands. The experimental data are modeled using two methods for simulating line-mixed spectra; first, the usual line-by-line approach which relies on the binary impact approximation, and second, a simple band-averaged model proposed by Hartmann and L’Haridon [J. Chem. Phys. 103, 6467 (1995)]. The energy corrected sudden (ECS) approximation is used to generate the relaxation matrix in the first approach. Comparison with the measurement shows that the ECS method does not fit the high density data satisfactorily when adjustable parameters from the literature are used; the level of interbranch mixing must be decreased by about a factor of 2 relative to intrabranch mixing and at least 5% dephasing must be added to the ECS matrix. With these changes, the room temperature data are modeled satisfactorily, but significant discrepancies are still present in the high temperature spectra. On the other hand, the simpler band-averaged model does provide a reasonable estimate of the spectra for all temperatures when best fit values are used for mixing and broadening, but the low density data are not reproduced as well as with the ECS model. Data from high pressure absorption measurements in a 1% NO in N2 mixture as well as a 0.5% CH4 in N2 mixture are also presented without analysis, showing the effects of interbranch line-mixing in these spectra.

High-resolution CARS spectroscopy of small carbon dioxide clusters: investigation of the CO 2 dimer in the [formula omitted] Fermi dyad

High-resolution CARS spectroscopy has been employed to study the formation of small carbon dioxide clusters in a supersonic jet near the lower frequency component of the ν 1 2ν 2 Fermi dyad at 1285.41 cm −1. A pronounced structure was found at 1284.73 cm −1, redshifted by 0.68 cm −1 from the monomer Q-branch. Analysis of the complete set of experimental data and comparison with kinetic calculations indicate that the new feature must be attributed to the CO 2 dimer.

Methyl Isocyanide Hot Bands in the Region 1300–1560 cm−1

The hot bands accompanying the fundamentals ν6and ν3of CH3NC in the region 1300–1560 cm−1observed in high-resolution Fourier transform recordings complemented by diode laser spectra have been analyzed. The observed transitions comprise 16 subbands of the pair of perpendicularE–Ebands ν6±+ ν8±− ν8±and ν7∓+ 2ν80− ν8±whose upper states form a Fermi dyad, 18 subbands of theA1,2–Eperpendicular bands ν6∓+ ν8±− ν8±/ν7±+ 2ν8±2− ν8±with upper states forming another Fermi dyad, and 8 subbands of the bi-parallelE–Eband ν3+ ν8±− ν8±. The anharmonic, Coriolis, andl-type interactions which couple these upper states with each other and with the states ν7∓+ 2ν8±2, ν4+ 3ν8±1, and ν4+ 3ν8±3have been included in an 18 × 18 Hamiltonian matrix whose eigenvalues model the upper levels of the observed transitions. The values of 46 upper state spectroscopic constants and interaction constants have been adjusted by least squares to 950 observed lines. The results provide a reliable quantitative picture of the interacting states and yield accurate values for the spectroscopic constants of the various states and for the anharmonic constantsx68,x68(g68), andx38.

Laser-induced gratings in the gas phase excited by Raman-active transitions

We report on a new time-resolved coherent Raman technique that is based on the generation of thermal gratings following a population change among molecular levels that is induced by stimulated Raman pumping. This is achieved by use of spatially and temporally overlapping intensity interference patterns generated independently by two lasers. When this technique is used in carbon dioxide, making use of transitions that belong to the Q branches of the v(1)/2v Fermi dyad, it is possible to investigate molecular energy transfer processes. A further unique feature of this method is spectral resolution that is better than that achieved by coherent anti-Stokes Raman scattering.

Saturation behavior in degenerate four-wave mixing with nonmonochromatic, non-Lorentzian fields

We report experimental studies of the degenerate four-wave mixing (DFWM) response in weak field (no saturation) and strong field (saturation) regimes for the case of nonmonochromatic, non-Lorentzian fields. The saturation behavior of line-center intensities and linewidths of rovibrational transitions in the ν3/ν2+ν4+ν5 Fermi dyad region of jet-cooled C2H2 are in good agreement with nondegenerate two-level saturation models, suggesting that the on-resonance DFWM response is weakly dependent on laser line shape. We find that DFWM line shapes in the weak field regime are determined by the infrared power spectrum and cubic intensity dependence, as illustrated using broadband (0.35 cm−1) and narrowband (0.04 cm−1) infrared radiation. The saturation intensity (I0sat) is observed to decrease with decreasing bandwidth, in qualitative agreement with theoretical predictions.

Infrared degenerate four wave mixing spectroscopy of jet-cooled C 2H 2

We report the application of infrared degenerate four-wave mixing (IR DFWM) spectroscopy to probe rotational-vibrational transitions in the v 3/ v 2 + v 4 + v 5 Fermi dyad region of jet-cooled C 2H 2. The spectral intensities show a quadratic population dependence, and are well reproduced by a Boltzmann distribution of J state populations at T rot = 25 K. Intensity dependence measurements and lineshape analysis show a cubic dependence of the DFWM signal on laser intensity, as expected from theory in the weak field limit ( I ⪡ I sat). We compare DFWM signals in jet versus bulk experiments.

Line coupling effects in anisotropic Raman Q branches of the ν1/2ν2 Fermi dyad in CO2

The generalized energy corrected sudden model is used to calculate the Q branch of the anisotropic coherent anti-Stokes Raman scattering spectra corresponding to the ν1 and 2ν2 transitions of the Fermi dyad of CO2. The corresponding experimental spectra have been recorded for pressures leading to a consistent overlapping between the rotational components. This leads to a new experimental evaluation of the relaxation time of the second-order tensor associated with the rotational angular momentum. The value is in excellent agreement with that already obtained from the study of the infrared absorption Q branch, the Rayleigh scattering, and the viscomagnetic effect.

Rovibrational Spectroscopy of C 35Cl 4

High-resolution rotationally resolved infrared spectra of the spherical-top rotor C 35Cl 4 (in samples of natural isotopic composition) were obtained both in static cells by FTIR spectroscopy (ν 4, ν 1 + ν 4) and in a supersonically cooled expansion with tunable diode lasers (ν 3). For the ν 3 fundamental at 799 cm −1, quantum assignments were made for individual transitions from P(20) to R(24), and the partially resolved Q branch was matched with synthesized spectra. The bands ν 4 (316 cm −1) and ν 1 + ν 4 (774 cm −1) exhibit much reduced manifold splitting, and scalar fits were made to the R(24)- R(70) and P(38)- R(56) frequencies, respectively. The ν 3/(ν 1 + ν 4) Fermi dyad yields Coriolis constants ζ 3 = 0.621 and ζ′ 4 = −0.145 that satisfy the harmonic sum rule, but are perturbed by the Fermi resonance and are inconsistent with intramolecular force fields previously reported based on isotope shifts in matrix spectra. The true bending-mode Coriolis constant ζ 4 = −0.414, obtained from analysis of the isolated and unperturbed ν 4 band, agrees well with the isotope shifts. CCl 4 and other tetrahedral XY 4 molecules are shown to vibrate according to a simple vector-displacement normal-mode model for which ζ 3 ≈ 4/[3( m x / m y ) + 4].

Intracavity absorption spectroscopy of the third stretching overtone transition of jet cooled methane

The third stretching overtone transition of jet cooled methane has been recorded between 11 170 and 11 315 cm−1 by intracavity laser absorption spectroscopy associated with a supersonic slit jet expansion. By varying the methane percentage seeded in the carrier gas, we have studied the evolution of the spectrum vs the rotational temperature. The rotational cooling drastically reduces the congestion of the spectrum and only a few lines are observed in the spectrum corresponding to the lowest rotational temperature. In the 11 245–11 315 cm−1 range, the rotational structure of two superimposed bands is clearly observed. The lowest rotational levels of each band are assigned and the corresponding band origins, rotational constants and Coriolis parameters are obtained. The two bands are assigned to the two components of a Fermi dyad corresponding to the interaction of the 3ν1+ν3 (F2) stretching level carrying the oscillator strength with a near resonant vibrational state of the background. The high mixing of the vibrational wave functions is reflected by the close values of the rotational constants obtained for the two bands. In the lower energy range of the spectrum (11 170–11 245 cm−1), two weaker vibrational bands are tentatively assigned.

Rotational and vibrational relaxation of the ν1/2ν2 Fermi dyad in CO2 gas from Raman-infrared double resonance experiments

Time-resolved Raman-infrared double resonance experiments have been conducted on CO2 gas in order to determine collisional relaxation rates of energy levels. These total depopulation constants are measured in a three-level double resonance scheme. A pulsed Raman excitation populates the studied state over a brief time interval (7 ns). The ensuing collisional depopulation of this level is monitored by a continuous probe CO2 laser whose transition originates in the same level. The transient absorption on the probe laser gives the time dependent population behavior. The high selectivity of the lasers allows the study of vibrational and rotational levels. The relaxation rates, of the (1000) vibrational state and, for the first time, of the J=14–34 rotational levels of the (0200) vibrational state, have been measured. The derived broadening coefficients have been compared to those calculated by a semiclassical model.

Study of collisional effects on band shapes of the ν1/2ν2 Fermi dyad in CO2 gas with stimulated Raman spectroscopy. III. Modeling of collisional narrowing and study of vibrational shifting and broadening at high temperature

High resolution stimulated Raman spectra (SRS) of the ν1/2ν2 Fermi dyad of CO2 have been recorded in the 0.4–22. amagat density range at 700 K and in the 0.6–16 amagat density range at 900 K. The data have been successfully analyzed with a theoretical model taking into account both rotational line mixing through the energy corrected sudden-polynomial (ECS-P) law for the relaxation matrix and vibrational line broadening γv and line shifting δv. The two vibrational parameters have been accurately determined from fit to the experimental spectra. These new high temperature data together with previous data obtained at 295 and 500 K [B. Lavorel et al., J. Chem. Phys. 93, 2176 (1990); B. Lavorel et al., J. Chem. Phys. 93, 2185 (1990)] entirely determine the temperature dependence in the 295–900 K range of Raman band shapes of ν1 and 2ν2 in a large pressure range. These results will be very useful in CARS thermometry. A few coherent anti-Stokes Raman spectra (CARS) recorded in the 1100–1300 K domain are consistent with extrapolations of the 295–900 K data.