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.     

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.     

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.     

振动和转动激发对N2在Fe(111)表面解离吸附的影响

N₂的解离化学吸附是工业合成氨的速控步骤. 基于最近构建的六维势能面,本文研究了N₂的初始振动激发和转动激发在Fe(111)表面的反应性的作用. 由于该反应具有重要的量子效应,通过六维量子动力学计算研究了入射能量低于1.6 eV 时振动激发的效应. 并采用准经典轨线计算揭示了高入射能量下的振动和转动激发的影响. 通过这些研究发现增加平动能量在一定程度上能提高解离几率,振动激发或转动激发能更有效地促进解离. 这项研究为重原子分子-表面反应的模式特异性动力学提供了有价值的见解.     

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.     

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.     

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.     

Semiclassical line broadening calculations,using an ab initio potential energy surface,in Q‐branch and S‐branch of N2 perturbed by H2

In order to improve the accuracy of Raman combustion diagnostics, the broadening coefficients of N₂ perturbed by H₂ for Q‐branch and S‐branch have been calculated by the semiclassical Robert–Bonamy model using an ab initio potential energy surface. The calculations have been performed for a large range of temperatures (from 77 to 800 K) and J rotational quantum numbers (from 0 to 60). This paper shows that our results and their temperature dependence are in good agreement with earlier published experimental and theoretical data. Moreover, our results improve the semiclassical calculations made earlier with an adapted analytical potential. The results, obtained at high temperatures and for a large range of rotational quantum numbers, are presented in order to be implemented for optical diagnostics in combustion media. Copyright © 2012 John Wiley & Sons, Ltd.     

N2- and O2-broadening coefficients and profiles for millimeter lines of N2O

For the purpose of atmospheric applications, we have measured N₂- and O₂-induced broadenings and shapes of rotational lines of N₂O in the 235-350 K temperature range, precisely the J=8←7, J=22←21, and J=23←22 lines, located near 201, 552, and 577 GHz, respectively. The analysis of experimental lineshapes shows up significant deviations from the Voigt profile, which are characteristic of line narrowing processes. In a first step, the Voigt profile was considered for the determination of pressure broadening parameters and of their temperature dependencies. Results are in good agreement with the dependence from rotational quantum number previously observed for other rotational and rovibrational lines. They are well explained by calculations based on a semiclassical formalism that includes the atom-atom Lennard-Jones potential in addition to electrostatic interactions up to hexadecapolar contributions. In a second step, observed lineshapes were analyzed by using the Galatry profile and a speed-dependent Voigt profile. The nonlinear pressure behavior observed for the diffusion rate β involved in the Galatry profile leads to rule out the possible role of velocity/speed changing collisions, and to infer that discrepancies from the Voigt profile result from the dependence of relaxation rates on molecular speeds. This interpretation is supported by the comparison of optical and kinetic radii and confirmed by theoretical calculations of relaxation rates. Finally, it can be claimed that, for the N₂O-N₂ and N₂O-O₂ systems, deviations from the Voigt profile are explained by a speed-dependent Voigt profile.     

H2-broadening coefficients in the ν3 band of CH3D at low temperatures

Using a diode-laser spectrometer, we have measured H₂-broadening coefficients of CH₃D at low temperatures (153.5, 183.5, and 223.5 K) for four lines in the ν₃ band. The collisional widths are obtained by fitting each absorption line with three lineshape models: the Voigt, Rautian, and Galatry profiles. The broadening coefficients are also calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to electrostatic contributions. By comparing the broadening coefficients at room and low temperatures the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.     

Temperature dependence of pressure broadening of NH3 perturbed by H2 and N2

The temperature dependence of pressure broadening of 134 rovibrational transitions of several branches in the ν₄ and 2ν₂ bands of ammonia perturbed by H₂ and N₂ has been measured using a high-resolution Fourier transform spectrometer. The temperature range covered during the experiments was between 235 and 296 K. The pressure-broadening linewidths were obtained using the method of multipressure fitting to the measured shapes of the lines. These broadenings were also calculated using a semiclassical model leading to a reasonable agreement with the observations and reproduces well the strong systematic experimental J and K quantum number dependencies. The retrieved values of the linewidths, along with those previously determined from the spectra at room temperature, were used to derive the temperature dependence of both H₂ and N₂ broadening of NH₃ lines. The broadening coefficients were shown to fit closely the well-known exponential law. For both experimental and theoretical results, the temperature exponent n has been obtained. Careful inspection of the experimental values shows that, contrary to the linewidths, the coefficient n is nearly K independent within each J multiplet. Also for a given J it does not seem to exhibit any noticeable variation with the type of rotational transition. On the other hand, the calculated n values exhibit a strong J and K systematic dependencies. n increases with K for a given J, decreases with J for a given K and are independent of the type of rotational transition.     

Collisional broadening of nitrous oxide transition lines in the ν1 + 2ν2 band by noble gases

A tunable diode laser is used to measure the foreign gas broadening for several rotational states in the R branch of the 12⁰0-00⁰0 vibration-rotation band of N₂O. The results indicate that rotational relaxation is the chief pressure broadening mechanism. The resulting cross sections for He and Ne turn out to be almost independent of the rotational quantum number. Ar and Kr, however, show a clear dependency. This seems to contradict the results of the infinite order sudden approximation.     

Comparison of classical, semiclassical and quantum methods in hydrogen broadening of acetylene lines

Quantum close coupling (CC) calculations of H₂-broadening coefficients of infrared and isotropic Raman lines of acetylene (C₂H₂) are performed for temperatures between 77 and 2000 K. They are used to test three more approximate methods, the quantum coupled states (CS) theory, the semiclassical Robert-Bonamy (RB) formalism and the full classical (FC) model of Gordon. In order to allow a clear and well founded comparison, all the dynamical calculations were performed employing the same ab initio potential energy surface free of any adjustable parameters. It is shown that below room temperature both the coupled states method and full classical method fail at reproducing the close coupling pressure broadening coefficients while above room temperature they are correct and predict comparable accurate values for temperatures greater than about 1000 K. The values provided by the RB method are clearly not satisfactory even at the highest temperature examined. However, the temperature dependence of the RB results follows the functional form used for interpolating and extrapolating CC, CS and FC pressure broadening coefficients.     

Energy transfer processes in linear triatomic molecule-solid surface collisions

The semiclassical stochastic trajectory method is extended to the study of rotational and vibrational transitions for linear triatomic molecules colliding with non-rigid solid surfaces. Rotational and vibrational motion are treated by quantum mechanics, translational motion by classical mechanics, and surface atom motion by the classical generalized Langevin equation. Self-consistent coupling of all motions is enforced via Ehrenfest's theorem. Calculations of the kinetic energy and gas temperature dependence of trapping probabilities, vibrational relaxation probabilities and final vibrational state distributions are presented for the CO₂-Ag(111) system at surface temperatures of 0 and 600 K. The trapping probabilities are greatly enhanced by the rotational motion and also vary to some degree with the initial vibrational state of the CO₂. Total vibrationally inelastic probabilities are on the order of 10⁻² for a single collision event with an initial state (00°1). For the initial state (01¹0) these are much larger, ~ 10⁻¹, due to the nature of bending mode motion. In conjunction with the large trapping probabilities, the mechanism of vibration to vibration, rotation, translation, phonon energy transfer can provide vibration relaxation probabilities in the range of those measured experimentally. A pseudo-selection rule for conservation of vibrational angular momentum is found.     

Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines

We use an accurate N₂-H₂ab initio potential energy surface (PES) in order to inter-compare various methods commonly employed to calculate pressure broadening coefficients. Close-coupling (CC) calculations of the collisional linewidths of the isotropic Raman lines of N₂ perturbed by H₂ are performed for temperatures between 77 and 2000 K. The CC results compare well with available experimental values. Three less exact methods of calculation are also used: the full classical (FC) model of Gordon, the semiclassical (SC) formalism of Robert and Bonamy and the quantum dynamical coupled states (CS) method. The CS method provides good agreement with CC calculations for all studied temperatures, FC calculations can be considered as accurate above room temperature while the SC method gives overestimated values by about 20-30% in all cases. The temperature dependences of pressure broadening coefficients provided by each method are very similar at elevated (above room) temperatures.     

Semiclassical stochastic trajectory approach to molecule-solid surface scattering

A semiclassical stochastic trajectory (SST) approach to the sudy of collision induced transitions in gas molecule-solid surface scattering is presented. The time-dependent Schrödinger equation provides the time-evolution of the transition amplitudes for the molecular internal states. Classical mechanics is used to describe the molecule's center of mass motion as well as the surface atoms' motion — the latter through the generalized Langevin equation (GLE) method which allows the treatment of non-rigid surfaces (i.e. surface temperature effects). These quantum and classical equations of motion are coupled through the use of a time-dependent interaction potential in the Schrödinger equation and the use of the expectation value of the interaction potential in the classical equations of motion. Advantages of the SST approach include: (1) flexibility in the choice of quantum versus classical coordinates; (c) strict energy conservation for non-dissipative system; and (3) realistic treatment of surface many-body effects within the GLE. The SST technique is applied to the study of vibrational and rotational inelasticity in a model H₂Pt(111) system. As an initial test, results obtained assuming a rigid, smooth surface with an exponentially repulsive potential are compared to exact quantal and quasi-classical trajectory values to determine the accuracy and utility of the SST approach. A limited practical application is presented for the same H₂Pt(111) system but for a non-rigid surface. These results, calculated at low gas kinetic energies, indicate that surface energy transfer and surface temperature effects should be minimal for this type of system, even though the energy gaps are quite similar for rotational and phonon degrees of freedom.     

Collisional line widths of autoperturbed N2: Measurements and quantum calculations

In this work we present new experimental and theoretical values for the line broadening coefficients of the Q-branch Raman lines of autoperturbed N₂. For the experimental determination of the coefficients, high resolution stimulated Raman spectra of the Q-branch of N₂ at different pressures were obtained at 77, 194 and 298 K. Simultaneously, quantum dynamical calculations, performed on two potential energy surfaces, were carried out for the system between 77 and 298 K, rendering a set of theoretical line broadening coefficients that could be directly compared to those obtained from the present measurements and the previous ones. Within the limit of considering the colliding molecules distinguishable we discuss the ortho and para contributions to the pressure broadening cross-sections. Because such calculations are time consuming we indicate routes to circumvent this difficulty. We observe a reasonable agreement between theoretical and experimental values of the collisional line broadening coefficients at all the studied temperatures.