Transcript Recent advances in the simulation of the absorption and emission

Un apport de la simulation numérique à
l’astrochimie des PAHs
P. Parneix and C. Falvo
ISMO, Université Paris Sud, Orsay, France
Unidentified Infrared Bands (UIBs)
•
Interstellar medium (ISM) : cold and
dilute medium
•
Emission bands first observed by
Gillett and coworkers
•
Polycyclic aromatic hydrocarbons
(PAHs) could be carriers of UIBs
•
Stochastic heating process of PAHs
could be responsible for IR emission.
Tielens, Annu. Rev. Astron. Astrophys. 46, 289 (2008)
IR emission
UV/Visible
excitation
internal
conversion
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Unidentified Infrared Bands (UIBs)
•
No unambiguous identification of PAHs have been made yet !
•
Many questions regarding the UIBs carriers remain open:
⇒ size distribution, aromaticity, charge, hydrogenation, protonation and electronic
state...
•
To relate specific molecular structure to IR emission spectra
 Measure experimental IR emission spectra in the laboratory (G. Féraud, ISMO)
• difficult experiments (very few), not isolated molecules, other processes play a
role (collision)

Use ab-initio simulations
• complex calculations which require many approximations ....
harmonic approximation can give knowledge on the state of PAHs in the ISM
more detailed modeling is necessary to obtain quantitative information
⇒description of anharmonicity
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Simulation of IR emission spectra of PAHs
•
Numerous processes occurring from
femtoseconds to milliseconds
 electronic excitation
 non-adiabatic intramolecular processes
 IR emission
 dissociation
 isomerisation
 ....
• Molecules range from 18 atoms to several
hundreds
• Full ab-initio calculation should describe several
complex potential energy surfaces (PES)
coupled through non-adiabatic processes
• Calculation impossible on medium sized
molecules such as PAHs
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Micro-canonical approach
fs
ps
μs - s
time
nonadiabatic
processes
(IC,ISC)
intramolecular vibrational
relaxation (IVR)
IR photon emission
dissociation
isomerisation
•
The electronic energy is quickly converted into vibrational energy on the
femtosecond timescale
→ Born-Oppenheimer approximation, the system evolves on a single PES
•
The intramolecular vibrational relaxation is much faster than the IR emission, the
dissociation and the isomerisation processes
→ IVR occurs between each photon emission, dissociation or isomerisation process
•
⇒ All molecular properties depends on the internal energy E
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Simulation protocol
Step 1: compute micro-canonical
quantities
micro-canonical spectra
vibrational
density of
states
absorption
spectra
stimulated
emission
spectra
spontaneous
emission
spectra
dissociation
rate
isomerisation
rate
absorption spectroscopy
Step 2: combine the micro-canonical data to compute spectra
Basire et al. JCP 129 081101 (2008).
Basire et al. JPCA 113 6947 (2009).
Basire et al. EAS Publications Series 46 95 (2011)
Journée Simulations Numériques 2013
Simulation protocol
Step 1: compute micro-canonical
quantities
micro-canonical spectra
vibrational
density of
states
absorption
spectra
stimulated
emission
spectra
spontaneous
emission
spectra
dissociation
rate
isomerisation
rate
emission spectroscopy
kinetic Monte-Carlo (kMC) simulations
Step 2: combine the micro-canonical data to compute spectra
Basire et al. JCP 129 081101 (2008).
Basire et al. JPCA 113 6947 (2009).
Basire et al. EAS Publications Series 46 95 (2011)
Journée Simulations Numériques 2013
Simulation protocol
Step 1: compute micro-canonical
quantities
micro-canonical spectra
vibrational
density of
states
absorption
spectra
stimulated
emission
spectra
spontaneous
emission
spectra
dissociation
rate
isomerisation
rate
IRMPD action
spectroscopy
kinetic Monte-Carlo (kMC) simulations
Step 2: combine the micro-canonical data to compute spectra
Basire et al. JCP 129 081101 (2008).
Basire et al. JPCA 113 6947 (2009).
Basire et al. EAS Publications Series 46 95 (2011)
Journée Simulations Numériques 2013
Wang-Landau simulations
•
Requires knowledge of the anharmonic density of state : computed with the WangLandau algorithm (biased MC simulation)
•
A large quantum space needs to be explored
•
Vibrational quantum state {ni}
•
Monte-carlo simulation
•
Ensure flat histogram :
•
Typical number of steps in a MC simulation: N≈107
with
with
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Multi-canonical simulations
•
Micro-canonical spectra are computed using multi-canonical simulations
•
Transitions energies obtained from second order perturbation theory (VPT2)
Dunham
expansion
harmonic
•
anharmonic
Einstein coefficients obtained using harmonic approximation
→ fundamental transitions:
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Electronic structure calculations
•
•
•
Input of the simulation
-
harmonic frequencies
-
anharmonic parameters
-
Einstein coefficients
All these parameters can be obtained from electronic structure calculation
-
harmonic frequencies requires second derivatives of the potential energy
surface
-
harmonic Einstein coefficients requires first derivatives of the dipole moment
-
anharmonic parameters requires third and fourth derivatives of the potential
energy surface
Density functional theory (DFT) allow anharmonic calculations for medium-size
molecule (Nat<50 )
No parameters
Anharmonicity is included explicitly, no scaling factor
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Results: naphthalene molecule
CH stretching modes
0.01
0.008
0.006
0.004
3065
3060
3055
3050
3045
0.002
0
2990
Theory
Exp
-1
0.012
Peak frequency (cm )
Intensity (arb. units)
0.014
3070
T=600 K
T=700 K
T=800 K
T=900 K
3000
3010
3020
3030
3040
3050
3060
3070
-1
Wavenumber (cm )
3040
500
600
700
800
900
1000
Temperature (K)
canonical spectra
Absorption spectroscopy
Basire et al. JPCA 113, 6947 (2009)
Joblin et al. A&A 299, 835 (1995)
ω0(exp) = 3066.9 cm-1
α(exp) = −1.39 ×10-2 cm-1.K-1
ω0(sim) = 3061.0 cm-1
α(sim) = −1.56 ×10-2 cm-1.K-1
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Results: naphthalene (S0) without collision
Time-resolved IR emission spectroscopy
Parneix et al. CTC 990, 112 (2012)
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Results: naphthalene (S0) with collision
Time-resolved IR emission spectroscopy
Good agreement with experimental data (asymmetric profile, FWHM and spectral
position)
Very few emitted IR photons
Parneix et al. JCP 137, 064303 (2012)
Williams et al ApJ 443, 675 (1995)
need for a large statistics in the kMC simulation
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Results: naphthalene S0 vs T1
•
Influence of the electronic state in the emission spectra
IC
ISC
310 nm
248 nm
193 nm
S0
Intensity (arb. units)
´10
T1
´10
400
500
600
700
800
Frequency (cm -1)
2900
3000
3100
Emission spectroscopy
Falvo et al. JCP 137 064303 (2012)
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Absorption spectroscopy: preliminary results
•
Absorption spectra: Full anharmonic calculation (with Fermi resonances and overtones)
for the ground state (T=0 K)
6
2.5
0.5
0.4
0.3
0.2
0.1
0
-0.1
4
3
1500
2
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
2
1600
1700
1800
1900
Intensity (arb. units)
Intensity (arb. units)
5
1.5
1
1500 1600 1700 1800 1900
0.5
1
0
0
600
800 1000 1200 1400 1600 1800 2000
Frequency (cm -1)
3000 3200
800
1000
1200
1400
1600
1800
2000 3000
3200
Frequency (cm -1)
Red: Theory, T=0 K, DFT/B97-1/TZ2P, phenomenological linewidth
Black: Experiment, T=373 K and 573 K, Joblin et al. 1994, Joblin et
al. 1995
•
Almost perfect agreement between theory and experiment for band position and
intensities
•
No scaling factor !
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Conclusions & Perspectives
•
Conclusions
•
A micro-canonical approach have been developed to simulate absorption, emission and
action IRMPD spectra based on multi-canonical simulations
•
Vibrational transitions are computed using perturbation theory
•
The effect of anharmonicity on the redshift and linewidth of vibrational bands is well
reproduced
•
Fermi resonances, overtones and combination bands have been recently included with
very promising results
•
Perspectives
•
Full anharmonic calculation of micro-canonical spectra.
→ include resonances in absorption and emission spectra
•
Study isomerisation as a competing mechanism against IR emission
•
Towards the PAH formation mechanism from AIREBO reactive potenial
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Acknowledgments
Marie Basire
Cyril Falvo (ISMO, Orsay)
Florent Calvo (ILM, Lyon)
Giacomo Mulas (INAF, Cagliari)
Financial support : ANR
GASPARIM
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THANKS FOR YOUR
ATTENTION
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Including Fermi resonances
•
Perturbation theory gives the Dunham expansion
•
Perturbation theory cannot account for resonances
• → e.g. Fermi resonances
•
In general resonant couplings terms are excluded from the Dunham coefficients
•
Only few coupling terms cannot be treated by perturbation theory (naphthalene ~20
terms)
•
Van-Vleck theory
-
unitary transformation
-
effective Hamiltonian
diagonal terms: Dunham expansion
•
remaining coupling terms
Automatic search of quantum states coupled to a specific state {nk}
→ construction of the effective Hamiltonian matrix around an initial state {nk}
→ diagonalisation of the effective Hamiltonian
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Including overtones and combination bands
•
Harmonic approximation on the dipole
-
•
First order perturbation theory using the perturbative transformation T
-
•
fundamental bands
overtones
-
combination bands
-
difference bands
Einstein coefficients e.g.
......
•
Einstein coefficients can be extracted from electronic structure calculation
requires second derivatives of the dipole moment obtained from numerical
differentiation
Journée Simulations Numériques 2013