Un apport de la simulation numérique à l’astrochimie des PAHs

1. Un apport de la simulation numérique à l’astrochimie des PAHs • P. Parneix and C. Falvo ISMO, Université Paris Sud, Orsay, France

2. IR emission internal conversion UV/Visible excitation 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)

3. 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

4. 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

5. Micro-canonical approach ps μs - s fs • 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 time non-adiabatic processes (IC,ISC) intramolecular vibrational relaxation (IVR) IR photon emission dissociation isomerisation

6. 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)

7. 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)

8. 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)

9. 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

10. 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: Dunham expansion harmonic anharmonic

11. 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

12. Results: naphthalene molecule CH stretching modes canonical spectra ω0(exp) = 3066.9 cm-1 α(exp) = −1.39 ×10-2 cm-1.K-1 Absorption spectroscopy ω0(sim) = 3061.0 cm-1 α(sim) = −1.56 ×10-2 cm-1.K-1 Basire et al. JPCA 113, 6947 (2009) Joblin et al. A&A 299, 835 (1995)

13. Results: naphthalene (S0) without collision Time-resolved IR emission spectroscopy Parneix et al. CTC 990,112 (2012)

14. 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 need for a large statistics in the kMC simulation Parneix et al. JCP 137,064303 (2012) Williams et al ApJ 443, 675 (1995)

15. Results: naphthalene S0 vs T1 • Influence of the electronic state in the emission spectra IC ISC Emission spectroscopy Falvo et al. JCP 137064303 (2012)

16. Absorption spectroscopy: preliminary results • 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 ! 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

17. 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

18. Acknowledgments Marie Basire Cyril Falvo (ISMO, Orsay) Florent Calvo (ILM, Lyon) Giacomo Mulas (INAF, Cagliari) Financial support : ANR GASPARIM

19. THANKS FOR YOUR ATTENTION

20. 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 remaining coupling terms diagonal terms: Dunham expansion

21. 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 ......