ExoMol: molecular line lists for astrophysical applications ExoMol: molecular line lists for astrophysical applications. A theoretical line list for NiH Lorenzo Lodi University College London, Dept of physics & Astronomy, London, UK

Outline The ExoMol project Theoretical approach adopted Preliminary results for NiH

Exoplanets 1995: first exoplanet discovered, 51 Pegasi b 2007: IR spectra for planets HD 189733 b and HD 209458 b Today: 778 planets discovered and counting! Linelists needed for spectral characterisation and simulation of atmospheric models

Molecule List Already available ExoMol Source Primordial (metal-poor) Terrestrial planets Giant planets & cool stars Already available H2, LiH, HeH+, H3+, H2D+ OH, CO2, O3, NO,  H2O, HDO, NH3 H2, CN, CH, CO, CO2, TiO,  HCN/HNC, H2O, NH3 ExoMol O2, CH4, SO2, SO3 HOOH, H2CO, HNO3 CH4, PH3 C2, C3, HCCH, H2S, C2H6, C3H8, VO, O2, AlO, MgO, CrH,  MgH, FeH, CaH, AlH, SiH, TiH, NiH, BeH, YO Computed at UCL Available elsewhere Being studied now at UCL

Transition metal molecules Transition metals: many low-lying electronic states E.g.: Carbon has 3 energy levels with E < 22000 cm-1, titanium has an infinite number! Multi-reference character → electronic structure calculations difficult Strong spin-orbit interaction Strong relativistic effects Electronic states are strongly coupled

+(L+S-+L-S+) –(J+L-+J-L+) –(J+S-+J-S+) Diatomic molecules Hamiltonian for diatomic molecule (no spin-orbit) H = Tr + V(r) + B(r) R2 R2 = (J – L – S)2 R2 = J2 + S2 + L2 -2LzSz – Lz2 – 2Sz2 + +(L+S-+L-S+) –(J+L-+J-L+) –(J+S-+J-S+)

H = -(1/2 m) d2/dr2 + V(r) + B(r) J(J+1) Diatomic molecules 1S states → decoupled equations for each potential V(r) H = -(1/2 m) d2/dr2 + V(r) + B(r) J(J+1) and one can use, e.g., LeRoy’s LEVEL Non-singlet, non-S states → coupled problem Our approach Solve uncoupled problem Use solutions as basis for the coupled problem We use Hund’s case a function |J, S, L, S, n > as basis

Our computer code Our group (mainly Sergey Yurchenko) developed new code for coupled problem Input: potential energy curves (PECs), spin-orbit coupling curves (SOC), angular momentum coupling curves (AMC) Output: Ro-vibrational energy levels & wavefunctions for the coupled problem Input (optional): experimental energy levels or line positions Output (optional): PECs, SOCs, AMCs fitted to experimental data

NiH introduction Ni : 3F, 3D and 1D states within 3600 cm-1 Wigner-Witmer rules: 39 spin-orbit-split curves correlate to these asymptotes, total degeneracy is 82

NiH curves Ground 2D state observed in 1930s, low-lying 2P and 2S+ observed in the 1980s, notably by Gray and Field at MIT and by Marian Very recently Ross in Lyon observed higher-lying states We computed PECs, SOCs and AMCs for the three lowest states using CASSCF/CASPT2, 6-z basis sets, DKH2 Hamiltonian

Potential energy curves

Spin-orbit and angular momentum couplings

Preliminary results Using ab initio data gives unsatisfactory results Fitting the PECs improves results somewhat but is difficult Working on better PECs and couplings, including more states, improving the fitting method

Summary and acknowledgements ExoMol: easy access to linelists of molecules Code for coupled problem in diatomics Study of NiH began but not easy Project funded by the European Research Council