1. QED of H 3 + Oleg L. Polyansky 1,2 1 Institute of Applied Physics, Russian Academy of Sciences, Uljanov Street 46, Nizhnii Novgorod, Russia 603950 2Department of Physics and Astronomy, University College London, London WC1E 6BT, UK. 9 th February, 2012

3. Part of the table of Morong, Gottfried and Oka, JMS, v.255, p.13, (2009)

4. Carrington-Kennedy of H 3 + spectrum at dissociation – 27 000 lines

5. ACCURACY H 2 + H 2 H 3 + H 2 O 10 -6 cm -1 10 -4 cm -1 0.1 cm -1 0.1 cm -1 0.01 cm -1 Both necessary and intuitively natural

6. QED H2 Comparison Theory/Experiment (Theory: Pachucki, Komasa, Jeziorski et al.)

8. mode E obs / cm  1 MBB CP RKJK PT(BO) PT(nBO) 01 1 2521.409 2.5 5 0.3 -0.11 +0.056 10 0 3178.290 0.1 7 0.09 -1.3 +0.025 02 0 4778.350 5.4 21 1.1 0.0 +0.020 02 2 4998.045 5.0 6 0.8 -0.3 +0.010 11 1 5554.155 3.2 14 0.07 -1.4 0.000 7870.020 -0.81 9113.080 +0.93 11323.100 +0.55 11658.400 +7.58 THUS the reason for this large discrepancy – BO PES used in PT Ab initio vibrational band origins MBB - - Meyer, Botschwina, Burton, JCP, v.84, 891 (1986) CP – Carney, Porter, JCP, v.65,3547(1976) RKJK- - Roese, Kutzelnigg, Jaquet, Klopper, JCP, v.101, 2231 (1994) PT - Polyansky and Tennyson, J. Chem. Phys., 110, 5056 (1999) – based on the points of CRJK - Cencek,Rychlewski, Jaquet, Kutzelnigg, JCP, v.108, 2831 (1998)

10. The highest H 3 + line. -3.0 and +8.5 cm -1 – previous predictions

11. Obs-calc. BO+adiabatic –grey, full model – red and yellow

12. Relative contribution of BO-PES, adiabatic, nonadiabatic and relativistic corrections to the accuracy of optical lines calculations

13. Formula for the QED as a percentage of Darwin relativistic term (P.Pyykko,K.Dyal,A.Csaszar,G.Tarczay, O.L.Polyansky, J.Tennyson, Phys.Rev., v.63,024502 (2001))

14. Accurate calcs of H 2 QED Due to J. Komasa et al. JCTC, (2011)

15. Obs / cm  1 CBS+CV 1 +relativity +QED +BODC 2 PS 3 (010) 1594.75 +0.48  (020) 3155.85 +1.16  (030) 4666.73  (040) 6134.01 +3.21  (050) 7542.44 +4.82  (101) 7249.82  +1.70 +1.45 +0.60  4.78 (201) 10613.35  +  +1.23  6.96 (301) 13830.94  8.98 +4.59 +4.06 +2.05  8.41 (401) 13805.22  +2.74  9.47  all  Ab initio calculations for water 1 Complete Basis Set (CBS) limit plus Core  Valence (CV) correction 2 Born-Oppenheimer Diagonal Correction (BODC) 3 Partridge & Schwenke, J Chem Phys, 106, 4618 (1997). OL Polyansky, AG Csaszar, SV Shirin, NF.Zobov, J Tennyson, P Barletta, DW Schwenke & PJ Knowles Science, 299, 539 (2003)

16. Ab initio + Lamb Obs / cm  1 (010) 1598.19  0.09 1594.75 (020) 3158.49  0.18 3151.63 (030) 4677.22  0.29 4666.79 (040) 6148.29  0.43 6134.01 (050) 7561.09  0.60 7542.44 (060) 8894.52  0.86 8869.95 (101) 7249.52 +0.37 7249.82 (201) 10612.70 +0.54 10613.35 (301) 13829.31 +0.71 13830.94 (401) 16896.50 +0.83 16898.84 (501) 19776.00 +1.01 19781.10 (601) 22519.69 +1.19 22529.44 (701) 25105.51 +1.29 25120.28 One-electron Lamb shift effects in water P. Pyykko, K.G. Dyall, A.G. Csaszar, G. Tarczay, O.L. Polyansky and J. Tennyson, Phys. Rev. A, 63, 024502 (2001)

18. Cancellation of two components

20. Formula for the QED as a percentage of Darwin relativistic term (P.Pyykko,K.Dyal,A.Csaszar,G.Tarczay, O.L.Polyansky, J.Tennyson, Phys.Rev., v.63,024502 (2001))

22. Errors in H 3 + vibrational band origin (J = 0) energy levels computed from FCI nonrelativistic energy curves and various basis sets. All values are in cm −1.

23. Formula for the QED as a percentage of Darwin relativistic term (P.Pyykko,K.Dyal,A.Csaszar,G.Tarczay, O.L.Polyansky, J.Tennyson, Phys.Rev., v.63,024502 (2001))

24. QED corrections for H 2 for J = 0 vibrational levels. All energies are in cm−1.

25. QED corrections (in cm −1 ), computed at the 69 MBB geometries using a MOLPRO and an a5z FCI wave function.

26. Vibrational band origins for H 3 + calculated with various models of nonadiabatic effects and with or without QED corrections. All energies are in cm −1.

28. CONCLUSIONS 5 components of H 3 + calcs BO, adiabatic, relativistic, QED All of them contribute more than 0.1 cm -1 Are now known with 0.01 cm -1 Remaining 0.2 cm -1 are due to nonadiabatic- the only thing left. Nonadiabatic contribution is 1 cm -1, so we now know it with the accuracy ~80%