Un apport de la simulation numérique à l’astrochimie des PAHs
P. Parneix and C. Falvo
ISMO, Université Paris Sud, Orsay, France
Journée Simulations Numériques 2013
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)
UV/Visibleexcitation
IR emission
internal conversion
Journée Simulations Numériques 2013
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 ISMmore detailed modeling is necessary to obtain quantitative
information⇒description of anharmonicity
Journée Simulations Numériques 2013
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
Journée Simulations Numériques 2013
Micro-canonical approach
• 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
psfs μs - s
non-adiabatic processes
(IC,ISC)
intramolecular vibrational relaxation (IVR)
IR photon emissiondissociation
isomerisation
time
Journée Simulations Numériques 2013
Simulation protocol
Step 1: compute micro-canonical quantities
Basire et al. JCP 129 081101 (2008).Basire et al. JPCA 113 6947 (2009).Basire et al. EAS Publications Series 46 95 (2011)
vibrationaldensity of
states
absorptionspectra
stimulated emission spectra
spontaneousemission spectra
dissociation rate
isomerisation rate
micro-canonical spectra
Step 2: combine the micro-canonical data to compute spectra
absorption spectroscopy
Journée Simulations Numériques 2013
Simulation protocol
Basire et al. JCP 129 081101 (2008).Basire et al. JPCA 113 6947 (2009).Basire et al. EAS Publications Series 46 95 (2011)
absorptionspectra
stimulated emission spectra
spontaneousemission spectra
dissociation rate
isomerisation rate
micro-canonical spectra
Step 2: combine the micro-canonical data to compute spectra
emission spectroscopy
kinetic Monte-Carlo (kMC) simulations
vibrationaldensity of
states
Step 1: compute micro-canonical quantities
Journée Simulations Numériques 2013
Simulation protocol
Basire et al. JCP 129 081101 (2008).Basire et al. JPCA 113 6947 (2009).Basire et al. EAS Publications Series 46 95 (2011)
vibrationaldensity of
states
absorptionspectra
stimulated emission spectra
spontaneousemission spectra
dissociation rate
isomerisation rate
micro-canonical spectra
Step 2: combine the micro-canonical data to compute spectra
IRMPD action spectroscopy
kinetic Monte-Carlo (kMC) simulations
Step 1: compute micro-canonical quantities
Journée Simulations Numériques 2013
Wang-Landau simulations
• Requires knowledge of the anharmonic density of state : computed with the Wang-Landau algorithm (biased MC simulation)
• A large quantum space needs to be explored
• Vibrational quantum state {ni}
• Monte-carlo simulation with
• Ensure flat histogram : with
• Typical number of steps in a MC simulation: N≈107
Journée Simulations Numériques 2013
Multi-canonical simulations
• Micro-canonical spectra are computed using multi-canonical simulations
• Transitions energies obtained from second order perturbation theory (VPT2)
• Einstein coefficients obtained using harmonic approximation→ fundamental transitions:
harmonic anharmonic
Dunham expansion
Journée Simulations Numériques 2013
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
Journée Simulations Numériques 2013
Results: naphthalene molecule
Basire et al. JPCA 113, 6947 (2009)Joblin et al. A&A 299, 835 (1995)
CH stretching modes
ω0(sim) = 3061.0 cm-1
α(sim) = −1.56 ×10-2 cm-1.K-1
ω0(exp) = 3066.9 cm-1
α(exp) = −1.39 ×10-2 cm-1.K-1
canonical spectra
Absorption spectroscopy
Journée Simulations Numériques 2013
Results: naphthalene (S0) without collision
Parneix et al. CTC 990, 112 (2012)
Time-resolved IR emission spectroscopy
Journée Simulations Numériques 2013
Results: naphthalene (S0) with collision
Parneix et al. JCP 137, 064303 (2012)Williams et al ApJ 443, 675 (1995)
Time-resolved IR emission spectroscopy
Good agreement with experimental data (asymmetric profile, FWHM and spectral position)
Very few emitted IR photons need for a large statistics in the kMC simulation
Journée Simulations Numériques 2013
Results: naphthalene S0 vs T1
• Influence of the electronic state in the emission spectra
Falvo et al. JCP 137 064303 (2012)
IC ISC
Emission spectroscopy
Journée Simulations Numériques 2013
• Absorption spectra: Full anharmonic calculation (with Fermi resonances and overtones) for the ground state (T=0 K)
• Almost perfect agreement between theory and experiment for band position and intensities
• No scaling factor !
Absorption spectroscopy: preliminary results
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
Journée Simulations Numériques 2013
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
Journée Simulations Numériques 2013
Acknowledgments
Marie BasireCyril Falvo (ISMO, Orsay)Florent Calvo (ILM, Lyon)Giacomo Mulas (INAF, Cagliari)
Financial support : ANR GASPARIM
Journée Simulations Numériques 2013
THANKS FOR YOUR
ATTENTION
Journée Simulations Numériques 2013
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
• 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
diagonal terms: Dunham expansionremaining coupling terms
Journée Simulations Numériques 2013
Including overtones and combination bands
• Harmonic approximation on the dipole- fundamental bands
• First order perturbation theory using the perturbative transformation T- 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
......
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