1. High-accuracy ab initio water line intensities Lorenzo Lodi University College London Department of Physics & Astronomy

2. Talk summary Variational methods for vibration-rotation spectra Electronic structure treatment Results for water line intensities

3. What we are aiming at? Line intensities are extremely important. They are also difficult to measure accurately. Aim: accuracy of 1% (for majority lines). We used the very best level of theory to achieve this goal. Line intensities likely to be in error can be identified.

4. General scheme of solution Solve the electronic problem, obtaining Potential Energy Surface E(R) and Dipole Moment Surface  (R). Use E(R) for the motion of the nuclei. From  (R) and nuclear-motion wavefunctions calculate line intensities. Born-Oppenheimer approximation.

5. Solving for the nuclear motion An efficient technique to do this is the Discrete Variable Representation method. The resulting 3-dimentional Schrödinger equation can be solved numerically. Molecule-fixed, J-dependent effective hamiltonians can be derived. Accuracy of line positions and intensities is limited by quality of PES and DMS.

6. Transition intensities Transition intensity for the transition n → m is given by  (R) is the Dipole Moment Surface (DMS) function and is given by We compute the DMS for many selected geometries and then interpolate between these values.

7. Multi-reference methods Standard methods such as DFT, MP2 etc are not suitable. Multi-reference methods are needed. We used IC-MRCI+Q[8,10], 6Z basis set. Relativistic effects accounted for.

10. Equilibrium water dipole From L. Lodi and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys. 43, 133001 (2010)

11. Fitting the points Intensities are very sensitive to oscillations in the DMS.

12. Lisak, Harvey and Hodges D. Lisak, D. K. Harvey and J.T. Hodges, Phys. Rev. A 79, 052507 (2009) 15 line intensities between 7170-7183 cm -1 Declared error of 0.4%.

14. Lisak, Harvey and Hodges 15 very accurate lines One line where theory is consistently stronger by 30% For the other 14 lines: average 1.01(1)

15. Ponsardin & Browell P.L. Ponsardin and E. V. Browell, J. Mol. Spectr. 185, 58-70 (1997) 40 line intensities around 12,200 cm -1. Declared error of 2%.

20. Summary comparison with HITRAN2008 Total lines analysed: 26,957 Stable lines: 19,056 Unstable lines: 7,901 Average of ratios for stable lines: 1.00(4)

21. Final words New high-accurate intensity linelist Error of 1% in most cases “Resonant” lines with large errors can be identified