1. Full Empirical Potential Curves and Improved Dissociation Energies for the A 1 Π and X 1 Σ + States of CH + Young-Sang Cho, Robert J. Le Roy Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada

2. Why are we interested in CH + ? 1

3. Objectives 1. To represent all types of experimental data compactly within uncertainties Should simultaneously treat all types of data (MW, IR, electronic), and data for all isotopologues and multiple connected electronic states in a single analysis. 2. To be able to interpolate reliably for missing observations within the data range. 3. To provide realistic predictions in the ‘extrapolation region’ outside the data range. In effect, this presumes that the analysis provides a realistic global potential energy curve. 4. To provide reliable estimates of physically interesting properties. e.g. r e, D e, force constants, long-range potential coefficients Expectation values, matrix elements and transition intensities. Collisional and dilute (atomic) gas properties (e.g. virial coefficients) 2

4. What is the nature of the data?  Conventional spectroscopic data Electronic A - X Transition: X - state A - state Microwave: /Å/Å 3  Photodissociation observation of predissociating υ ( A ) = 11-14 and of low υ ( A ) levels at very high J ’

5. What is the nature of the data? High-J tunneling pre-dissociation levels of the A-state seen by photofragment spectroscopy a Plus kinetic energy of fragments for selected levels a 4 a H.Helm, P.C. Cosby, M.M. Gaff and J.T. Moseley, Phys.Rev. A25, 304 (1982)

6. What is the nature of the data? Low-J, high-v Feshbach pre-dissociation levels seen by photodissociation spectroscopy b 5 b U.Hechtfischer, C.J. Williams, M.Lange, J.Linkemann, D.Schwalm, R.Wester, A.Wolf and D.Zajfman, J.Chem.Phys. 117 8754 (2002)

7. Direct Potential Fits Simulate transition energies as numerically determined eigenvalues, E ( υ, J ), of some parameterized analytic potential energy function Partial derivatives of observables w.r.t. parameters p j required for fitting are generated readily by the Hellmann-Feynmann theorem: Compare with experiment and iterate the least-squares fit to convergence. 6

8. Direct Potential Fits (cont’) Advantages satisfies all four ‘objectives of spectroscopic data reduction’ full quantum mechanical accuracy Challenge to determine flexible potential functions that are robust and ‘well behaved’ (no spurious behaviour in interpolation or extrapolation regions) can incorporate physical constraints and limiting behaviour Compact and portable – defined by ‘modest’ no. of parameters 7

9. Morse Long-Range Potential (MLR) where theory tells us that we define in which 8

10. Analysis (the X 1 Σ + state) 9

11. /Å/Å What is the best value of p,q? 10

12. /Å/Å 11

13. /Å/Å 12

14. /Å/Å 13

15. /Å/Å 14

16. /Å/Å 15 ab-initio

17. /Å/Å 16 ab-initio Two ab-initio points added to the data set

18. /Å/Å 17 ab-initio

19. Results (the X 1 Σ + state) U LR (r) defined by C 4 =3.872×10 4, C 6 =0.0043×10 6, C 8 =1.6×10 8 Param.No ab-initioWith ab-initio dd 1.6531.655 DeDe 34361.634361.8 rere 1.128456761.1284108 {p,q}{5,1} r ref 1.54×r e 2.54×r e β0β0 -0.067646-0.152 β1β1 12.7382313.71782 β2β2 62.0571.578 β3β3 197.5739216.673013 β4β4 444.94392.4 β5β5 644.2393.7484 β6β6 440.0169.0 18

20. Comparing with previous work Source D 0 /cm -1 D e /cm -1 Method Present work (2014) XAXA 32945.8 ± 3.0 9326.0 ± 3.0 34361.8 ± 3.0 10302.4 ± 3.0 Direct fit to MLR potential function Hechtfischer et al. (2002) XAXA 32946.7 ± 1.1Experimental (photodissociation) Helm et al. (1982)XAXA 32907 ± 23 9351 ± 23 Experimental (photofragment) Barinovs and van Hemert (2004) XAXA 32892.51 9304.6 Theory Kanzler (1991)XAXA 37586.3 12340.6 Theory Sarre et al. (1989)XAXA 34323.81 10263.44 Theory Saxon et al. (1980)XAXA 33392.1 7549.5 Theory Smith et al. (1973)X33842Theory 19

21. Conclusions Obtained accurate potential function that account for all data within their uncertainties This analysis yields improved estimated value of the dissociation energy and other properties of the A 1 Π and X 1 Σ + states This analysis yields the first empirical determination of Born-Oppenheimer Breakdown corrections for CH + This analysis yields a good explanation of lambda-doubling corrections spanning the whole A-state well These potentials will yield linelists that provide improved predictions for astrophysics application 20

22. Acknowledgement Dr. Takayoshi Amano for helpful discussions Research supported by Natural Science and Engineering Research Council of Canada 21

23. Thank you 22

24. What do we have? Isotop. υ (A) υ (X)J”Unc. (cm -1 ) Total # of data used Ref. 12 CH + 0 - 20 - 10 - 110.06 - 0.0894 Douglas and Herzberg (‘42) 0 - 410 - 160.02130127Douglas and Morton (‘60) 005 - 210.53635Grieman et al. (‘81) 0 - 3 0 - 150.004 - 0.01231 Carrington and Ramsay(‘82) 0,20 - 10 - 170.005 – 0.018123119Hakalla et al. (‘06) 0 - 9 0 - 514 - 363.05147Helm et al. (‘82) -0 - 1012 - 3520.0 – 152.432 Helm et al. (‘82) 0 - 2131 - 351.066 Sarre et al. (‘89) 11 - 14 00 – 90.4 – 9.034 Hechtfischer et al. (‘02) -01 - 60.01 - 0.0866Cernicharo et al. (‘97) -000.000000711Amano (‘10) 12 CD + 0 - 3 0 - 140.004 – 0.03264258Bembenek et al. (‘87) 0 - 30 - 10 - 12-1520Antic-Jovanovic et al. (‘79) 008 - 230.54024Grieman et al. (‘81) -000.000000711Amano (‘10) 13 CH + 311 - 40.244Antic-Jovanovic et al. (‘83) 0 - 20 - 10 - 120.004 – 0.01156141Bembenek (‘97) -000.00000111Amano (‘10) 0 - 2131 – 35 1.065Sarre et al.(‘89) 13 CD + 0 - 100 - 160.004 – 0.006 83 Bembenek (‘97) 23

25. Analysis (the A 1 Π state) 24