1. 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

2. Outline The ExoMol project Theoretical approach adopted
Preliminary results for NiH

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

5. 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

6. Transition metal molecules
Transition metals: many low-lying electronic states
E.g.: Carbon has 3 energy levels with E < 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

7. +(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+)

8. 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

9. 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

10. 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

11. 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

12. Potential energy curves

13. Spin-orbit and angular momentum couplings

14. 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

15. 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