Semiclassical Theory of Spectra and Relaxation in Molecular Gases

Time-Domain Self-Broadened and Air-Broadened Nitrogen S-Branch Raman Linewidths at 80-200 K Recorded in an Underexpanded Jet

We report pure-rotational N2-N2, N2-air, and O2-air S-branch linewidths for temperatures of 80-200 K by measuring the time-dependent decay of rotational Raman coherences in an isentropic free-jet expansion from a sonic nozzle. We recorded pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps CARS) spectra along the axial centerline of the underexpanded jet, within the barrel shock region upstream of the Mach disk. Dephasing of the pure-rotational Raman coherence was monitored using probe-time-delay scans at different axial positions in the jet, corresponding to varying local temperatures and pressures. The local temperature was obtained by fitting CARS spectra acquired at zero probe time delay, where the impact of collisions was minimal. The measured decay of each available Raman transition was fit to a dephasing constant and corrected for the local pressure, which was obtained from the CARS-measured static temperature and thermodynamic relationships for isentropic expansion from the known stagnation state. Nitrogen self-broadened transitions decayed more rapidly than those broadened in air for all temperatures, corresponding to higher Raman linewidths. In general, the measured S-branch linewidths deviated significantly in absolute and relative magnitudes from those predicted by extrapolating the modified exponential gap (MEG) model to low temperatures. The temperature dependence of the Raman linewidth for each measured rotational state of nitrogen ( J {less than or equal to} 10) and oxygen ( N {less than or equal to} 11) was fit to a temperature-dependent power-law over the measurable temperature domain (80-200 K) and extrapolated to both higher rotational states and to room temperature.

Lindblad parameters from high resolution spectroscopy to describe collision-induced rovibrational decoherence in the gas phase-Application to acetylene

Within the framework of the Lindblad master equation, we propose a general methodology to describe the effects of the environment on a system in the dilute gas phase. The phenomenological parameters characterizing the transitions between rovibrational states of the system induced by collisions can be extracted from experimental transition kinetic constants, relying on energy gap fitting laws. As the availability of these kinds of experimental data can be limited, this work relied on experimental line broadening coefficients, however still using energy gap fitting laws. The 3 μm infrared spectral range of acetylene was chosen to illustrate the proposed approach. The method shows fair agreement with available experimental data while being computationally inexpensive. The results are discussed in the context of state laser quantum control.

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).

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 Gordon's 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.

Spectral shapes of Ar-broadened HCl lines in the fundamental band by classical molecular dynamics simulations and comparison with experiments

Spectral shapes of isolated lines of HCl perturbed by Ar are investigated for the first time using classical molecular dynamics simulations (CMDS). Using reliable intermolecular potentials taken from the literature, these CMDS provide the time evolution of the auto-correlation function of the dipole moment, whose Fourier-Laplace transform leads to the absorption spectrum. In order to test these calculations, room temperature spectra of various lines in the fundamental band of HCl diluted in Ar are measured, in a large pressure range, with a difference-frequency laser spectrometer. Comparisons between measured and calculated spectra show that the CMDS are able to predict the large Dicke narrowing effect on the shape of HCl lines and to satisfactorily reproduce the shapes of HCl spectra at different pressures and for various rotational quantum numbers.

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.

Line interference effects using a refined Robert-Bonamy formalism: the test case of the isotropic Raman spectra of autoperturbed N2

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

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.

Molecular dynamics simulations for CO2 spectra. IV. Collisional line-mixing in infrared and Raman bands

Ab initio calculations of the shapes of pure CO2 infrared and Raman bands under (pressure) conditions for which line-mixing effects are important have been performed using requantized classical molecular dynamics simulations. This approach provides the autocorrelation functions of the dipole vector and isotropic polarizability whose Fourier-Laplace transforms yield the corresponding spectra. For that, the classical equations of dynamics are solved for each molecule among several millions treated as linear rigid rotors and interacting through an anisotropic intermolecular potential. Two of the approximations used in the previous studies have been corrected, allowing the consideration of line-mixing effects without use of any adjusted parameters. The comparisons between calculated and experimental spectra under various conditions of pressure and temperature demonstrate the quality of the theoretical model. This opens promising perspectives for first principle ab initio predictions of line-mixing effects in absorption and scattering spectra of various systems involving linear molecules.

Binary-collision-induced longitudinal relaxation in gas-phase 83Kr

Density dependent NMR relaxation measurements of noble gases can provide complementary information to that obtained from relaxation studies of molecular gases. However, conventional noble gas NMR is typically hindered by low sensitivity or prohibitively long relaxation times. In this work, the low sensitivity of (83)Kr (I=92) was overcome by spin exchange optical pumping, and the quadrupolar interaction dominated (83)Kr T(1) times of 40-400 s enabled rapid collection of relaxation data. The density dependence of the (83)Kr longitudinal relaxation in pure krypton was found to be about 1.6 x 10(-3) amagat(-1) s(-1). Experiments were also performed in krypton mixtures containing either helium or nitrogen as a buffer gas. By varying the composition and the density of these mixtures, the density dependence of buffer gas induced relaxation and the relaxation efficiency of (83)Kr-buffer gas collisions were determined. The results from these gas mixtures are compared with those from pure krypton.