Ab initio classical dynamics simulations of CO 2 line-mixing effects in infrared and Raman bands Julien LAMOUROUX, Jean-Michel HARTMANN, Ha TRAN L.I.S.A., Universités Paris Est Créteil et Paris Diderot, Créteil, FRANCE Marcel SNELS ISAC-CNR, Via del Fosso del Cavaliere, Rome, ITALY Stefania STEFANI, Giuseppe PICCIONI IAPS-IASF, Via del Fosso del Cavaliere, Rome, ITALY 68th International Symposium on Molecular Spectroscopy

Collisional line-mixing For a collisionally isolated transition, the main effects of intermolecular collisions are the Lorentz broadening and shifting of the line Collisions induce transfers of populations between the levels of the two lines that lead to transfers of intensity between the lines This effect is called line- mixing.

Why this study ?  Requantized Classical Molecular Dynamics Simulations (rCMDS) were sucessfully applied for predictions for pure CO 2 : - Line broadening coefficients; - Collision-induced absorption; - Far wings of absorption and scattering band; - Individual line shapes;  Limitations - Single branch calculation (identical P/R); - Positions and intensities for a strictly rigid rotor; Line-mixing effects are not accounted for See Hartmann and Boulet, J. Chem. Phys. 134 (2011), Hartmann et al., Phys. Rev. A 87 (2013),

Absorption Isotropic Raman Spectral Shape where... denotes an average over the molecular system, ω and are the angular frequency and wave vector of the electromagnetic field, and is the molecule position. The spectrum F(ω) is given by the Laplace transform of the auto- correlation function Φ(ω,t)

Classical equations (M and I: molecular mass and moment of inertia) - Center of mass: - Molecule orientation: The state of each molecule m (linear, treated as a rigid rotor) is parameterized by : - Center of mass (CoM) position and velocity - Molecule orientation: unit vector along axis - Molecule rotational speed: (alternatively ) Force Various center of force sites s (r s from CoM) on molecule and site-site potential Molecular dynamics simulations 2,j

N M molecules ( ∼ 10 6 ) treated simultaneously - Placed in a cubic box with periodic conditions - When a molecule gets out of the box, it comes back-in from the opposite box Initialization (time t=0) - Random CoM positions and axis orientations - CoM velocity and rotation : random orientations, modules from Maxwell-Boltzmann Time evolution for all molecules treated sequentially (with small enough time step dt) - At each time t compute force and torque on each molecule from sum of potential gradient of over surrounding neighbors (cut-off sphere of 20 Å) - Then compute acceleration of CoM and of orientation - Then compute molecule parameters at t+dt from those at t - Ab-initio CO 2 -CO 2 potential [Bock et al. Chem. Phys. 257, 147 (2000) ] Molecular dynamics simulations

Associate to Determine the line involved L m Calculate the positions of the line L m [J m (t)] Requantization

Absorption ACF Isotropic Raman ACF Complex autocorrelation functions

For all the results presented not a single parameter has been adjusted Everything taken from litterature - Intermolecular potential - Molecule geometry and mass - Spectroscopic parameters - Electric multipoles

Calculations rCMDS calculations for infrared and Raman bands : isotropic Raman Q branch of 2ν 2 The effects of the other bands are taken into account using the Energy Corrected Sudden model and tools of Tran et al. JQSRT 112 (2011), 925 Calculations at room and hot temperatures

CO 2 - CO 2, , T=294K Experimental rCMDS 22.7Am 35.5Am 51.3Am Tran et al., JQSRT 112 (2011), 925 Voigt The line-mixing effects are taken into account correctly by the rCMDS in the 3ν 3 region

CO 2 - CO 2, 2 2 isotropic Raman Q branch, T=295K Experimental rCMDS Lavorel et al., J. Chem. Phys. 93 (1990), 2176 Voigt 0.5Am 2.0Am 10.0Am As in the infrared region, the line-mixing effects are well modeled by the rCMDS calculations

Conclusion  Line-mixing effects can be modeled using classical molecular dynamics simulations  The comparisons between predicted and measured infrared absorption and isotropic Raman scattering spectra demonstrate the quality of the proposed rCMDS model.  rCMDS are a robust and flexible tool for the description of the consequences of inter-molecular collisions on CO 2. JL is pleased to acknowledge support of this research by the French National Research Agency (ANR) through the project ASGGRS (ANR- 12-PDOC ).

CO 2 - CO 2, , T=473K Experimental CMDS Tran et al., JQSRT 112 (2011), 925 Voigt  CMDS for  ECS calculations for the other bands

CO 2 - CO 2, , T=295K Experimental CMDS Tran et al., JQSRT 112 (2011), 925 Voigt  CMDS for  ECS calculations for the other bands 20.6Am 33Am 56.7Am

N M molecules treated simultaneously -Placed in a cubic box (size determined from N M and molecular density n ) -Periodic boundary (treated box surrounded by 26 identical other boxes) -When a molecule gets out of the box, it comes back-in from the opposite box Initialization (time t=0) -Random CoM positions and axis orientations -CoM velocity : random orientation and module from Maxwell-Boltzmann -Rotation : random orientation [ ┴ to ], module from Maxwell-Boltzmann Time evolution For all molecules treated sequentially (with small enough time step dt ) -At each time t compute force and torque on each molecule from sum of potential gradient of over surrounding neighbors (cut-off sphere of 20 Å ) -Then compute acceleration of CoM and of orientation -Then compute molecule parameters at t+dt from those at t Several millions of molecules treated Ab-initio CO 2 -CO 2 potential [Bock et al. Chem. Phys. 257, 147 (2000) ] Implementation