Calculation and analytical representation of self-pressure and air pressure broadening coefficients of ozone spectral lines

The coefficients γ of broadening by self-pressure, and pressure of nitrogen, oxygen, and air are calculated for absorption lines of the rotational band and for the ν₂ band of the ozone molecule for temperatures 296, 252, and 212 K. The calculations are performed by the semiclassical method using rectilinear and exact trajectories for interacting molecules. It is shown that the experimental data obtained for the two bands at T = 296 K can be reconstructed better using different isotropic intermolecular interaction potentials. The experimental and calculated broadening coefficients of ozone absorption lines for the rotational band and for the ν₂ and ν₁ + ν₃ vibrational bands were used to determine the parameters of an analytical model, which permits one to calculate γ in a wide range of rotational quantum numbers, 0 ≤ J ≤ 45, 0 ≤ K _a ≤ 20, and temperatures of 200–296 K.     

Self-Broadening and Carbon-Dioxide Broadening of Lines of the H<Subscript>2</Subscript>S Molecule

Carbon-dioxide-broadening coefficients and self-broadening coefficients of lines of the main isotopic modification of Н₂S are estimated on the basis of literature data. The J′-dependences of the above line-profile parameters of the hydrogen-sulfide molecule are examined. In the case of CO₂ broadening, the half-widths of lines are calculated by a semiempirical method based on a parametric modification of the impact semiclassical model; the model parameters were determined from the fit to experimental data.     

Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: I. C2H2-Ar case

Semiclassical approaches to the computation of spectral line parameters stay up to nowadays one of the working tools complementary to refined but costly quantum-mechanical methods. Using of the trajectory concept together with quantum treatment of internal molecular motions imposes however the hypothesis of rotation-translation decoupling and translational motion governed by the isotropic potential. When a posteori justified for small heavy colliders, this hypothesis appears as doubtful for long polyatomic molecules. At the same time, purely classical methods, even requiring the artificial procedure of the correspondence principle with quantum mechanics, easily take into account the rototranslational energy transfer through the trajectory governed by the full anisotropic potential. The infrared line broadening of a typically classical C₂H₂-Ar system at various temperatures is analyzed here from these two different points of view. When a refined ab initio potential is chosen to represent the interaction energy, the semiclassical approach leads to a visible overestimation of the line broadening for all values of the rotational quantum number and for all temperatures studied whereas the fully classical treatment gives a quite satisfactory prediction. These fully classical computations show that even for C₂H₂-Ar the rototranslational coupling is quite important, and variations of the translational motion parameters during collisions produce detectable changes in rotation. When, for the sake of a meaningful comparison with the semiclassical approach, the isotropic trajectories are imposed within the classical method, this leads to smaller line widths; the effect strongly depends, however, on the peculiarities of potential energy surface, temperature, and rotational quantum number value.     

Calculated line broadening coefficients in the ν2 band of CH3D perturbed by helium

Line broadening coefficients have been calculated, at room temperature, for lines in the P and R branches of the ν₂ band of monodeuterated methane. A properly symmetrized semiclassical model with parabolic relative trajectories has been used. Two interaction potential models have been considered. The first is a Lennard-Jones type atom-atom potential, while the second one was derived from ab initio calculations. The calculated line widths were compared to the available experimental data and a satisfactory agreement was found, although the model contains no other adjustable parameters than the four atomic Lennard-Jones ones. Nonetheless, failures of calculations have also been evidenced for the highest rotational quantum numbers.     

Calculation of line parameters of the ν<Subscript>3</Subscript> band of monodeuterated methane: Nitrogen broadening

Halfwidths and shifts of CH₃D lines are calculated for the case of nitrogen broadening. The calculations are performed for room temperature (296 K) for vibrational–rotational lines in the ν₃ parallel band, with the rotational quantum numbers varying in the ranges of 0 ≤ J ≤ 70 and 0 ≤ K ≤ 20. For each line, the temperature-dependence characteristics are calculated in the range of 200–400 K recommended for the HITRAN database. The calculations are carried out using a semiempirical method with a correction factor the parameters of which are adjusted on a number of experimental values.     

On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: Comparative analysis for C2H2-Ar, He systems

Accuracies of classical, semiclassical and quantum methods are comprehensively examined in calculations of impact line widths of C₂H₂ molecules perturbed by Ar and He. The field of comparative study covers both infrared absorption and Raman scattering lines of acetylene having rotational quantum number J=0-30 at temperatures 173 and 296 K. Calculations have been made by fully classical method and by three basic least approximate semiclassical methods, namely, Neilsen-Gordon (NG) method, peaking approximation (PA) and Smith-Giraud-Cooper (SGC) method. Most accurate ab initio potential energy surfaces (PES) of Yang et al. (1996) [21] and Mozsynski et al. (1995) [22] have been applied to model C₂H₂-Ar and C₂H₂-He interactions. The comparison has been made also with available experimental data and with the results of rigorous fully quantum-mechanical calculations within close coupling and coupled states approaches in identical conditions. Semiclassical methods are proved to be not so much accurate as it is generally believed since all they gave in the cases considered seriously underestimated results. The fundamental issue of the adequacy of simplified trajectories in collision broadening calculations is finally reasonably solved. In cases of C₂H₂-Ar and C₂H₂-He systems the use of the “exact” isotropic trajectories (i.e. driven only by the isotropic part of PES) is the main reason of failing of NG, PA and SGC methods. Thus the neglecting of back-influence of the RT exchange on the classical path is a principal defect of semiclassical methods. Finally, the application of simplified trajectories is recognized as inadequate and risky in broadening calculations for molecules having relatively small rotational constants when accurate ab initio PES are applied.     

Rotational dependence of the broadening of lines of the ν2 band of H2O induced by nitrogen pressure

A semiempirical method for calculating the coefficients of broadening of spectral lines of H₂O molecules subjected to nitrogen pressure is developed. The method involves different corrections associated with deviations from the Anderson approximation. The parameters of the method are determined from the adjustment of the coefficients of broadening to experimental data, which makes it possible to predict fairly accurately the parameters of the contour of a line whose measurements were not performed. On the basis of numerous calculations in terms of this method, a numerical analysis is made that allows one to conclude that the rotational dependence of the half-widths of the lines is more complex than was previously believed and to reveal the basic trends of this dependence.     

Broadening and shifting of vibrational-rotational lines corresponding to the highly excited rotational states of the water molecule

Self-pressure-induced, as well as argon- and nitrogen-induced, broadening γ and shifting δ coefficients of vibrational-rotational lines of the water molecule have been calculated. The asymptotic behavior of the coefficients γ and δ at J → 42 and K _a → J has been studied. For the calculation of the parameters γ and δ, we used the wave functions obtained from the analysis of highly excited rotational states of the H₂O molecule with the maximal ever observed values of rotational quantum numbers J _max = 42, K _amax = 32. Rotational states were analyzed in the method of effective Hamiltonians using generating functions for the first eight vibrational states of the molecule.     

Diode-laser measurements of O2, N2 and air-pressure broadening and shifting of NH3 in the 10 μm spectral region

Using a tunable diode-laser spectrometer, we have measured the O₂, N₂, air-shift and broadening coefficients for 5 lines of ammonia in the R branch of the ν₂ band. These lines are located in the spectral range 1030-1070 cm⁻¹. The pressure shift and broadening are obtained by fitting the measured shapes of these lines by a Voigt profile. The broadening parameters and shift coefficients are compared to the results of theoretical calculations based on the semiclassical Robert-Bonamy formalism (RB) in which the intermolecular potential includes electrostatic, induction, and dispersion energy contributions. The variation of these coefficients with rotational and vibrational quantum numbers is examined. The results are generally in satisfactory agreement with experimental data.     

Broadening and shift of lines of the ν<Subscript>2</Subscript> + ν<Subscript>3</Subscript> band of water vapor induced by helium pressure

The broadening and shift coefficients of more than 100 absorption lines of the ν₂ + ν₃ band of water vapor that are induced by the pressure of helium are measured and calculated. The broadening and shift coefficients are obtained from analysis of the room-temperature absorption spectra of an H₂O-He mixture measured with a resolution of 0.007 cm^?1 on a Fourier spectrometer in a large range of helium pressures. The specific features in the rotational dependence of the line center shifts are determined, which, in contrast to the broadening induced by other gases, are mainly positive. The calculated coefficients of the line broadening and shift of line centers are determined by a semiclassical method. An unusual dependence of the shift coefficients is explained by the rotational dependence of the intermolecular isotropic interaction potential.     

Experimental and theoretical studies of room-temperature sub-millimetre CH3 35Cl line shapes broadened by H2

Hydrogen-broadening coefficients of methyl chloride rotational lines J?=?6?→?7, 10?→?11, 17?→?18, 22?→?23 and 31?→?32 at 296?K are measured as functions of the quantum number K using a sensitive frequency-modulation technique. As expected for this light perturber, the observed line shapes are well described by Voigt profile model. A clear dependence of the collisional broadening on K is observed for most transitions. From a detailed study of the K-components of the transition J?=?6?→?7 situated at 186?GHz no variation of the broadening of the hyperfine components related to ³⁵Cl quadrupole is stated. Given the absence of refined ab initio computed potential energy surfaces and the impracticality of quantum-mechanical calculations for the considered molecular system, theoretical values of these broadening coefficients are estimated by a semi-classical approach with exact trajectories and a model interaction potential including both long-range and short-range (atom-atom) interactions of the active molecule rigorously treated as a symmetric top. It is shown that the short-range forces yield important contributions to the collisional line width for all values of the rotational quantum numbers J and K. Various models are also tested for the isotropic part of the interaction potential which governs the relative translational motion. It is demonstrated that for the very light perturbing molecule H₂ the calculated line widths, practically independent from the rotational quantum number J (for K?≤?J), are particularly sensitive to the position and slope of the repulsive wall. Modifications required in the semi-classical formalism for a correct application of the cumulant expansion are also tested and it is stated that no difference is observed for the CH₃Cl–H₂ system characterised by quite weak interactions.     

Low rotational transitions of the CF3H molecule: The pressure-induced shift and broadening

Using a microwave spectrometer with a radioacoustic signal detection, the absorption profiles in the multiplets of the low rotational transitions J’?J = 2?1, 3?2, 4?3, and 5?4 of the ¹²CF₃H molecule in the ground vibrational state at pressures of pure gaseous CF₃H from 0.1 to 1.3 Torr when all the K components of the multiplets merge into a single spectral line are studied. The parameters of the pressure-induced shift and broadening of the observed lines are determined by comparing the theoretically modeled absorption signal and the experimental spectrum. The model used takes into account weak lines corresponding to the excited vibrational states v₃ and v₆ of the ¹³CHF₃ molecule and the instrumental features of the spectrometer. The observed multiplet is simulated as an isolated Lorentzian line and as a sum of the profiles of the K components with known unshifted positions and known amplitude ratio. The shift and broadening parameters obtained in both cases are shown to agree well with each other. The dependences of the shift and broadening parameters on the quantum number J are analyzed and compared with the previously obtained data for the lines J’?J = 1?0 and 2?1.     

Calculation and simulation of absorption line broadening in water vapor by noble gas atoms

Semiclassical methods have been applied to calculate the collisional broadening of water vapor absorption lines by noble gas atoms (Ar, He, Ne, and Kr). An analytical model has been proposed for line half-widths. The model parameters have been determined for the ν₂ band of the H₂O molecule for all the buffer gases under consideration, as well as for the bands 3ν₁ + ν₃ and 2ν₁ + 2ν₂ + ν₃ in the case of the broadening by argon. In the latter case, the model parameters that determine the temperature dependence of the half-widths of the water vapor lines of the ν₂ band have been found. The model proposed describes well the known experimental data and permits a relatively simple calculation of the H₂O line half-widths for the bands and the buffer gases under consideration in a wide range of rotational quantum numbers. For the ν₂ band, the model calculations in the case of the broadening by argon can be performed up to temperatures of 2500 K.     

Experimental studies by complementary terahertz techniques and semi-classical calculations of N2- broadening coefficients of CH335Cl

Room-temperature N₂-broadening coefficients of methyl chloride rotational lines are measured over a large interval of quantum numbers (6≤J≤50, 0≤K≤18) by a submillimeter frequency-multiplication chain (J≤31) and a terahertz photomixing continuous-wave spectrometer (J≥31). In order to check the accuracy of both techniques, the measurements of identical lines are compared for J=31. The pressure broadening coefficients are deduced from line fits using mainly a Voigt profile model. The excellent signal-to-noise ratio of the frequency-multiplication scheme highlights some speed dependence effect on the line shape. Theoretical values of these coefficients are calculated by a semi-classical approach with exact trajectories. An intermolecular potential including atom–atom interactions is used for the first time. It is shown that, contrary to the previous theoretical predictions, the contributions of short-range forces are important for all values of the rotational quantum numbers. Additional testing of modifications required in the semi-classical formalism for a correct application of the cumulant expansion is also performed. It is stated that the use of the cumulant average on the rotational states of the perturbing molecule leads, for high J and small K values, to slightly higher line-broadening coefficients, as expected for the relatively strong interacting CH₃Cl–N₂ system. The excellent agreement between the theoretical and the experimental results ensures the reliability of these data.     

An analysis of a superweak absorption spectrum of the SO<Subscript>2</Subscript> molecule using the variational procedure

The high resolution structure of a superweak 2ν₁+ν₂+ν₃−ν₂ band of sulfur dioxide, SO₂, is for the first time recorded with a Bruker IFS-120 HR Fourier spectrometer and analyzed using a specially derived procedure and a relevant computer code. As a result of the analysis, 115 lines have been found in the recorded spectrum, which allowed us to obtain high-accuracy values of the vibrational energy and rotational parameters of the highly excited vibrational state, (211).     

Stark broadening of neutral sodium lines

A semiclassical approach has been used to evaluate Stark broadening of atomic lines and also electron-and proton-impact line widths and shifts of 30 neutral sodium lines. The results are used to investigate Stark broadening-parameter regularities within the spectral series.     

Theoretical and experimental analysis of N2–H2 stimulated Raman spectra

The paper reports on a detailed study of the N₂–H₂ collisional line broadening coefficient. High resolution stimulated Raman spectra of nitrogen–hydrogen mixtures have been recorded at liquid nitrogen and room temperatures. Corresponding linewidth calculations have been performed at temperatures between 77 and 500?K using the semiclassical Robert and Bonamy model for J rotational quantum numbers varying between 0 and 11. Comparison between experimental data and calculated results shows good agreement at room temperature using an adjusted value for the kinetic diameter.     

Temperature dependence of pressure broadening and shifts of acetylene at 1550 nm by He, Ne, and Ar

Pressure broadening and shift coefficients for the ν₁+ν₃ band of ¹²C₂H₂ have been measured for He, Ne, and Ar at a temperature of 195 K using high resolution diode laser spectroscopy. The pressure broadening and shifts follow patterns with rotational assignment that are similar to those at room temperature but are generally larger in magnitude. The change in magnitude is qualitatively described by assuming, for each transition, a constant cross section for pressure broadening or shifting. Better agreement may be obtained for pressure broadening coefficients by using empirically determined temperature exponents; better agreement still is obtained from close coupling calculations of the pressure broadening cross sections. PACS 33.70.Jg     

Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: II. C2H2-He case

The comparison of the classical method of Gordon and the semiclassical formalism of Robert and Bonamy was started in part I of this series of papers, dealing with the acetylene molecule perturbed by a heavy atom (Ar). The case of a light buffer gas (He) is considered in the present study. On the basis of a high-quality ab initio interaction potential, as previously, the influence of the roto-translational coupling on the trajectory parameters and its role in the line broadening at various temperatures are studied within the classical method. In addition, the line width contributions coming from the elastic (reorientation and dephasing) and inelastic collisions are separately analysed in the framework of both theoretical approaches. All these points confirm the previously stated conclusion that the roto-translational interactions play a non-negligible role in the collisional line broadening mechanisms. Also, a particular study in the framework of the classical approach enables some supplementary conclusions about the role of the perturber mass.