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/Visible excitation 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 ISM more 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 ps fs μs - s non- adiabatic processes (IC,ISC) intramolecular vibrational relaxation (IVR) IR photon emission dissociation isomerisation time

Journée Simulations Numériques 2013 Simulation protocol Step 1: compute micro-canonical quantities Basire et al. JCP (2008). Basire et al. JPCA (2009). Basire et al. EAS Publications Series (2011) vibrational density of states absorption spectra stimulated emission spectra spontaneous emission 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 (2008). Basire et al. JPCA (2009). Basire et al. EAS Publications Series (2011) absorption spectra stimulated emission spectra spontaneous emission 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 vibrational density of states Step 1: compute micro-canonical quantities

Journée Simulations Numériques 2013 Simulation protocol Basire et al. JCP (2008). Basire et al. JPCA (2009). Basire et al. EAS Publications Series (2011) vibrational density of states absorption spectra stimulated emission spectra spontaneous emission 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 {n i } Monte-carlo simulation with Ensure flat histogram : with Typical number of steps in a MC simulation: N≈10 7

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 (N at <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 ω 0 (sim) = cm -1 α (sim) = −1.56 ×10 -2 cm -1.K -1 ω 0 (exp) = cm -1 α (exp) = −1.39 ×10 -2 cm -1.K -1 canonical spectra Absorption spectroscopy

Journée Simulations Numériques 2013 Results: naphthalene (S 0 ) without collision Parneix et al. CTC 990, 112 (2012) Time-resolved IR emission spectroscopy

Journée Simulations Numériques 2013 Results: naphthalene (S 0 ) with collision Parneix et al. JCP 137, (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 S 0 vs T 1 Influence of the electronic state in the emission spectra Falvo et al. JCP (2012) ICISC 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 Basire Cyril 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 {n k } → construction of the effective Hamiltonian matrix around an initial state {n k } → diagonalisation of the effective Hamiltonian diagonal terms: Dunham expansion remaining 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......