ExoMol: molecular line lists for ExoMol: molecular line lists for astrophysical applications. astrophysical applications. A theoretical line list for NiHA theoretical line list for NiH

Lorenzo LodiUniversity 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 ListSource 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

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 – 2Sz

2 +

+(L+S-+L-S+) –(J+L-+J-L+) –(J+S-+J-S+)

Diatomic molecules

• 1 states → decoupled equations for each potential V(r)

H = -(1/2 ) d2/dr2 + V(r) + B(r) J(J+1)and one can use, e.g., LeRoy’s LEVEL

• Non-singlet, non- states → coupled problemOur approach

1. Solve uncoupled problem2. Use solutions as basis for the coupled problemWe use Hund’s case a function |J, 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

0

5 000

10 000

15 000

20 000

25 000

1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00

bond length in Angstroms

En

erg

y in

cm

-1

From: Zou and Liu, J Comp Chem 28 , 2286 (2007).

NiH curves

• Ground 2 state observed in 1930s, low-lying 2 and 2+ 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- 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