Ab initio classical dynamics simulations of CO 2 line-mixing effects in infrared and Raman bands...
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Ab initio classical dynamics simulations of CO 2 line- mixing effects in infrared and Raman bands ulien LAMOUROUX , Jean-Michel HARTMANN, Ha TRAN .I.S.A., Universités Paris Est Créteil et Paris Diderot, Créteil, F arcel SNELS SAC-CNR, Via del Fosso del Cavaliere, 100 00133 Rome, ITALY tefania STEFANI, Giuseppe PICCIONI APS-IASF, Via del Fosso del Cavaliere, 100 00133 Rome, ITALY 68th International Symposium on Molecular Spectroscopy
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Transcript of Ab initio classical dynamics simulations of CO 2 line-mixing effects in infrared and Raman bands...
Ab initio classical dynamics simulations of CO2 line-mixing effects in infrared and
Raman bandsJulien 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, 100 00133 Rome, ITALY
Stefania STEFANI, Giuseppe PICCIONI
IAPS-IASF, Via del Fosso del Cavaliere, 100 00133 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.
i
i'
f
f'
line | > f i
line | k > f' i'
Why this study ?
Requantized Classical Molecular Dynamics Simulations (rCMDS) were sucessfully applied for predictions for pure CO2:
- 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), 184312 Hartmann et al., Phys. Rev. A 87 (2013), 013403
0
1( ) Re ( , ) i tF t e dt
)().()().( )0().(),( tqkitqkiP etet
Absorption
Isotropic Raman
)().()().( )0().(),( tqkitqkiD edtdet
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 )
)t(qm
)t(q)t(v mm
)t(um
)t(um
)t(u)t(u)t( mmm
M/)t(f)t(q)t(v mmm
I/)]t(u)t([dt/)t(ud)t(u mmmm
Force
Various center of force sites s (rs from CoM) on molecule and site-site potential
Molecular dynamics simulations
2,j
NM 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
)0(qm
)0(um
)0(q)0(v mm )0(um
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 CO2-CO2 potential [Bock et al. Chem. Phys. 257, 147 (2000) ]
Molecular dynamics simulations
)]([)]()([)]([ tJtJtJ mLowRotmm
UpRotVibtJL mm
Associate to)t(Jm )t(u)t(u)t( mmm
Determine the line involved Lm
Calculate the positions of the line Lm[Jm(t)]
Requantization
||)(||
)0().((t)]cos[ with (t)]cos[)( m0 m)]([ t
utdtt
m
mmt
tJLm mm
tti
Nm
tiqtqki
T
P vibvib
T
mmm eeN
t
,1
)()0()()(1),(
)(0 )]([ dttt
tJLm mm
Absorption ACF
Isotropic Raman ACF
Complex autocorrelation functions
For all the results presentednot 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 :
00031 00001
30012 00001
isotropic Raman Q branch of 2ν2
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
CO2 - CO2, 00031 00001, 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 3ν3 region
CO2 - CO2, 22 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 CO2.
JL is pleased to acknowledge support of this research by the French National Research Agency (ANR) through the project ASGGRS (ANR-12-PDOC-0012-01).
CO2 - CO2, 00031 00001, T=473K
Experimental
CMDS
Tran et al., JQSRT 112 (2011), 925
Voigt
CMDS for 00031 00001
ECS calculations for the other bands
CO2 - CO2, 30012 00001, T=295K
Experimental
CMDS
Tran et al., JQSRT 112 (2011), 925
Voigt
CMDS for 30012 00001
ECS calculations for the other bands
20.6Am
33Am
56.7Am
NM molecules treated simultaneously
-Placed in a cubic box (size determined from NM 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
)0(qm
)0(um
)0(q)0(v mm )0(um
)0(um
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 CO2-CO2 potential [Bock et al. Chem. Phys. 257, 147 (2000) ]
Implementation
