AYTY: A new hot line- list for formaldehyde A. F. Al-Refaie, S. N. Yurchenko, A. Yachmenev, J. Tennyson Department of Physics Astronomy - University College London - Gower Street - London - WC1E 6BT

The Exomol project Goals: Produce high quality theoretical molecular line-lists Line-lists for studying and modelling cool stars and exoplanet atmospheres Applicability to high temperature modelling (e.g 1500K) Aim for completeness. Data can be found at Provide partition functions, cross sections and k-coefficients

Formaldehyde A poisonous molecule in the aldehydes group Main source of OH in atmosphere via photo-dissociation Formed from photo-oxidation of methane Astrophysical: First polyatomic molecule detected in interstellar medium (ISM) and is abundant Precursor to complex organic molecules in ISM (e.g amino acids, glycolaldehyde) Detected in abundance in comets (e.g 103P/Hartley 2, Hale-Bopp) Detected in protoplanetary disks around young low mass stars. Formaldehyde masers from 19 extra-galactic sources.

Spectroscopy of exoplanets: Emission of XO-1b H 2 O CO 2 CO CH 4 Primary transit spectrum of XO-1b: Tinetti, ApJ 2010 Hubble–NICMOS instrument

Spectroscopy of exoplanets: Emission of XO-1b H 2 O CO 2 CO CH 4 Hubble–NICMOS instrument Primary transit spectrum of XO-1b: Tinetti, ApJ 2010

Spectroscopy of exoplanets: Emission of XO-1b H 2 O CO 2 CO CH 4 Hubble–NICMOS instrument Primary transit spectrum of XO-1b: Tinetti, ApJ 2010

Spectroscopy of exoplanets: Emission of XO-1b H 2 O CO 2 CO CH 4 Primary transit spectrum of XO-1b: Tinetti, ApJ 2010

Formaldehyde Prolate symmetric top molecule C2v(M) symmetry molecular group A1A2A1A2 B1B2B1B2 ‘para’ singly degenerate ‘ortho’ triply degenerate symmetric C-H stretching (v 1 )A cm -1 C-O stretching (v 2 )A cm -1 symmetric O-C-H bending (v 3 ) A cm -1 out-of-plane bending (v 4 )B cm -1 asymmetric C-H stretching (v 5 ) B cm -1 asymmetric O-C-H stretching (v 6 ) B cm -1

Why Formaldehyde?

Formaldehyde Prolate asymmetric top molecule C2v(M) molecular symmetry group A1A2A1A2 B1B2B1B2 ‘para’‘ortho’

HITRAN spectrum Pure rotational band v 2 band v 1 and v 5 band Missing v 3, v 4 and v 6 !!!

Production Outline Experimental values Refine Refined PES Compute and diagonalise hamiltonian Energy states Line list Compute line-strengths and Einstein-A coefficients Goal for synthetic spectrum to reach up to cm -1 TROVE Software Suite [1] Ab-initio PES (Potential Energy Surface) Ab-initio DMS (Dipole Moment Surface) [1] S. Yurchenko et al. J. Mol. Spectrosc (2007)

Production Potential Energy Surface (PES) Ab-initio computed using CCSD(T)/aug-cc-pVQZ method Root mean squared (RMS) deviation is 5.1 cm -1 for all observed term values below 7200 cm -1 RMS deviation for observed fundamental term values is cm -1 Ab-initio: Refinement: Refined using least-squares fitting to experimental data Resulting PES RMS deviation for observed term values is 0.04 cm -1 A good line-list starts with a high quality PES!!!!!!

J=12 A1 symmetry Production Computation and Diagonalization Hamiltonian computed for increasing rotational excitation Computed up to J=70 and maximum energy at cm -1 Matrices can get very big!!!! J=70 biggest!!!!!! Diagonalization using LAPACK, SCALAPACK, PLASMA and PARPACK Sparsity grows with J and number of eigenvalues required decreases 300,000 J= GB

Production Compute Einstein-A coefficients Dipole Moment Surface (DMS): Ab-initio computed using CCSD(T)/aug-cc-pVQZ level of theory. RMS deviation of Debye Absolute intensities and Einstein-A coefficients: Selection rules: Computation:

Result AYTY-0 line-list 3 billion transitions6 million states Applicable to 1000 K

Result v 3, v 4 and v 6 band

Result Careful of aggressive refinement of PES Re-refined PES rms error changed to 0.18 cm -1 Transition moments can change drastically for some bands!!! Discovered in our v 3, v 4 and v 6 bands!!! Over-refined PESCarefully refined PES

Result AYTY line-list 10 billion transitions10 million states Applicable to 1500 K

Result v 3, v 4 and v 6 band

Result Rotational band

Result v 2 band

Result v 1 and v 5 band

Result More bands!!!

Result Temperature dependance

Future work [WIP] Assigning states High agreement with experimental lines Fitting process is fast and can be done on the fly. This may mean assigning states without usage of an effective rotational hamiltonian!! cm B1( ) cm A1( ) cm B2( ) Preliminary assignments: Wavenumber-JKSym (Vib quanta)

Where can I get AYTY? Data can be found at States and transitions are available in the Exomol format Helper scripts to convert to different formats

Acknowledgements This work was supported by the ERC under the Advanced Investigator Project Made use of STFC HPC facilities CfI Sorry about all the hard drive space!!

Al-Refaie, Yurchenko, Tennyson, Yachmenev MNRAS (2015) #ExoMol Thank you for you time!!