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

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


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


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


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


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


Simulation protocol


absorptionspectra



dissociation rate

isomerisation rate



emission spectroscopy

kinetic Monte-Carlo (kMC) simulations


states



Simulation protocol



states

absorptionspectra



dissociation rate

isomerisation rate



IRMPD action spectroscopy

kinetic Monte-Carlo (kMC) simulations



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


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


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


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


Results: naphthalene (S0) without collision

Parneix et al. CTC 990, 112 (2012)

Time-resolved IR emission spectroscopy


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


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


• 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


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


Acknowledgments

Marie BasireCyril Falvo (ISMO, Orsay)Florent Calvo (ILM, Lyon)Giacomo Mulas (INAF, Cagliari)

Financial support : ANR GASPARIM


THANKS FOR YOUR

ATTENTION


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


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

......

Documents

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