Christian Boulet

Line broadening of confined CO gas: From molecule-wall to molecule-molecule collisions with pressure

The infrared absorption in the fundamental band of CO gas confined in porous silica xerogel has been recorded at room temperature for pressures between about 5 and 920 hPa using a high resolution Fourier transform spectrometer. The widths of individual lines are determined from fits of measured spectra and compared with ab initio predictions obtained from requantized classical molecular dynamics simulations. Good agreement is obtained from the low pressure regime where the line shapes are governed by molecule-wall collisions to high pressures where the influence of molecule-molecule interactions dominates. These results, together with those obtained with a simple analytical model, indicate that both mechanisms contribute in a practically additive way to the observed linewidths. They also confirm that a single collision of a molecule with a wall changes its rotational state. These results are of interest for the determination of some characteristics of the opened porosity of porous materials through optical soundings.

Refinement of the Robert-Bonamy formalism: Considering effects from the line coupling

Since it was developed in 1979, the Robert-Bonamy (RB) formalism has been widely used in calculating pressure broadened half-widths and induced shifts for many molecular systems. However, this formalism contains several approximations whose applicability has not been thoroughly justified. One of them is that lines of interest are well isolated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from the line mixing are ignored. Second, when they applied the linked cluster theorem to remove the cutoff, they have assumed the matrix elements of the operator exp(-iS1 - S2) can be replaced by the exponential of the matrix elements of -iS1 - S2. With this replacement, effects from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. In the present study, we have developed a new method to evaluate the matrix elements of exp(-iS1 - S2) and have refined the RB formalism such that line coupling can be taken into account. Our numerical calculations of the half-widths for Raman Q lines of the N2-N2 pair have demonstrated that effects from the line coupling are important. In comparison with values derived from the RB formalism, new calculated values for these lines are significantly reduced. A recent study has shown that in comparison with the measurements and the most accurate close coupling calculations, the RB formalism overestimates the half-widths by a large amount. As a result, the refinement of the RB formalism goes in the right direction and these new calculated half-widths become closer to the true values.

An experimental investigation of rare gases pressure effects on the rovibrational line intensities of HCl

A measurement method has been set up for the accurate determination of vibration–rotation line strengths. It has been applied to a careful analysis of the intensities of HCl lines pressurized by Ar or Xe. Several mixtures have been studied corresponding to pressures of the perturber ranging from 5 to 15 atm. It is shown that the line intensities S appear to vary linearly (within the accuracy of experimental measurements) with the density of the perturbing species. For each one of the investigated lines, a least squares fit allows one to retrieve the ’’standard’’ S0 value corresponding to pure HCl and excellent agreement with previous determinations is obtained. In addition, the rate of variation of S as a function of the density of the rare gas is determined and shown to be strongly m dependent.

Two dimensional symmetric correlation functions of the Ŝ operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the Ŝ operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

Effects on calculated half-widths and shifts from the line coupling for asymmetric-top molecules

The refinement of the Robert-Bonamy formalism by considering the line coupling for linear molecules developed in our previous studies [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013); 140, 104304 (2014)] have been extended to asymmetric-top molecules. For H2O immersed in N2 bath, the line coupling selection rules applicable for the pure rotational band to determine whether two specified lines are coupled or not are established. Meanwhile, because the coupling strengths are determined by relative importance of off-diagonal matrix elements versus diagonal elements of the operator -iS1 - S2, quantitative tools are developed with which one is able to remove weakly coupled lines from consideration. By applying these tools, we have found that within reasonable tolerances, most of the H2O lines in the pure rotational band are not coupled. This reflects the fact that differences of energy levels of the H2O states are pretty large. But, there are several dozen strongly coupled lines and they can be categorized into different groups such that the line couplings occur only within the same groups. In practice, to identify those strongly coupled lines and to confine them into sub-linespaces are crucial steps in considering the line coupling. We have calculated half-widths and shifts for some groups, including the line coupling. Based on these calculations, one can conclude that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and reductions of calculated half-widths due to including the line coupling could reach to 5%. Meanwhile, effects on the calculated shifts are very significant and variations of calculated shifts could be as large as 25%.

The relaxation matrix for symmetric tops with inversion symmetry. I. Effects of line coupling on self-broadened ν1 and pure rotational bands of NH3.

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

The relaxation matrix for symmetric tops with inversion symmetry. II. Line mixing effects in the ν1 band of NH3

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

Line coupling effects in the isotropic Raman spectra of N2: A quantum calculation at room temperature

We present quantum calculations of the relaxation matrix for the Q branch of N2 at room temperature using a recently proposed N2-N2 rigid rotor potential. Close coupling calculations were complemented by coupled states studies at high energies and provide about 10,200 two-body state-to state cross sections from which the needed one-body cross-sections may be obtained. For such temperatures, convergence has to be thoroughly analyzed since such conditions are close to the limit of current computational feasibility. This has been done using complementary calculations based on the energy corrected sudden formalism. Agreement of these quantum predictions with experimental data is good, but the main goal of this work is to provide a benchmark relaxation matrix for testing more approximate methods which remain of a great utility for complex molecular systems at room (and higher) temperatures.

Line mixing effects in isotropic Raman spectra of pure N2: A classical trajectory study

Line mixing effects in the Q branch of pure N2 isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordons classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N2 molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.

Collision‐induced absorption by N2 near 2.16 µm: Calculations, model and consequences for atmospheric remote sensing

Classical Molecular Dynamics Simulations (CMDS) are used for calculations of the Collision Induced Absorption (CIA) by pure N2 in the (2.1-2.2u2009µm) region of the first overtone band. They lead to reasonable (±15%) agreement with the only two laboratory measurements available, at 97u2009K and room temperature. Based on these experiment/theory comparisons, empirical corrections are made to the CMDS-calculated CIA of pure N2 in the 200-300u2009K temperature range. In addition, the contribution of N2-O2 collisions is, in the absence of any laboratory measurement, calculated and a simple semi-empirical model (the first of its kind) is built in order to predict the CIA of N2 under Earth atmosphere conditions. This is successfully validated by comparisons with ground based atmospheric transmission spectra in the 2.1-2.2u2009µm region.