1. International Symposium on Molecular Spectroscopy, June 22-26, 2015 1 First high-resolution analysis of the ν 21 band of propane at 921.4 cm -1 : Evidence of large amplitude motion tunneling effects A. Perrin, F. Kwabia Tchana, J.-M. Flaud LISA, CNRS, Universités Paris Est Créteil et Paris Diderot, Créteil, France L. Manceron CNRS-MONARIS UMR 8233 and Beamline AILES, Synchrotron Soleil, Saint Aubin, France J. Demaison, N. Vogt Universität Ulm, Section of Chemical Information Systems, Ulm, Germany P. Groner Department of Chemistry, University of Missouri – Kansas City, Kansas City, MO, USA W. Lafferty Optical Technology Dividion, National Institute of Standards and Technology, Gaithersburg, MD, USA

2. International Symposium on Molecular Spectroscopy, June 22-26, 20152 Importance of IR Spectroscopy of propane Gaseous propane, C 3 H 8, isPrevious high-resolution studies present in the atmospheres of Earth (biomass burning) Giant planets Some of their moons (Titan) Principal method to study abundance & distribution: High-resolution IR spectroscopy. a F. Kwabia Tchana, J.-M. Flaud, W.J. Lafferty, L. Manceron, P. Roy. J. Quant. Spectrosc. Rad. Transf. 111 (2010) 1277–1281 b G. Glasser, B. Reissenauer, W. Hüttner, Z. Naturforsch A 44 (1989) 316–24 c J.-M. Flaud, F. Kwabia Tchana, W.J. Lafferty and C.A. Nixon, Mol. Phys. 108 (2010) 699–704 d J.-M. Flaud, W.J. Lafferty, M. Herman, J. Chem. Phys. 114 (2001) 9361-9366 SymE v / cm -1 TorsObserved ResonancesRef. 9191 A1A1 369.222n.o.a 26 1 B2B2 748.531b 9292 A1A1 740.292 9 2  (A-Corio)  26 1 c 26 1 B2B2 748.531 19 1 B1B1 1338.965d 18 1 B1B1 1376.850local 5151 A1A1 1461.072 5 1  (A-Corio)  24 1 d 17 1 B1B1 1462.488 4 1  (Anh)  5 1 24 1 B2B2 1471.8745 4 1  (A– Corio)  24 1 4141 A1A1 1476.384 4 1  (C-Corio)  17 1 17 1  (B-Corio)  24 1

3. International Symposium on Molecular Spectroscopy, June 22-26, 20153 IR Spectrum of propane Bruker IFS 125HR FT spectrometer SOLEIL–LISA cryo-cell AILES Beamline at SOLEILOptical path length:45.14 m HgCdTe (MCT) detector cooled by liquid N 2 Temperature:142 ± 2 K Resolution 0.0015 cm -1 Sample pressure:14.0 ±0.3 Pa

4. International Symposium on Molecular Spectroscopy, June 22-26, 20154 IR Spectrum of propane Two fundamental bands between 820 and 960 cm -1 a-type band at 921.38 cm -1 ν 21 (in-plane CH 3 rock) b-type band at 870.35 cm -1 ν 8 (sym CC stretch) Both bands have split rotational transitions due to interactions between overall and internal rotations of the methyl groups ν 21 : Summary of “First high resolution analysis of the ν 21 band of propane CH 3 CH 2 CH 3 at 921.382 cm −1 : Evidence of large amplitude tunneling effects” A. Perrin et al. (2015) doi:10.1016/j.jms.2015.02.010doi:10.1016/j.jms.2015.02.010 ν 8 : Preliminary analysis using ERHAM (Effective Rotational Hamiltonian) P. Groner, J. Chem. Phys. 107 (1997) 4483-4498; J. Mol. Spectrosc. 278 (2012) 52-67

5. International Symposium on Molecular Spectroscopy, June 22-26, 20155 Internal rotation in propane Point group symmetry at equilibrium:C 2v Molecular symmetry group with 2 LAM’s (CH 3 groups):G 36 or [33]C 2v Each energy level in C 2v splits into four components E  E 00  E 01  E 11  E 12 (subscripts refer to σ 1 σ 2 ) C 2v G 36 ShorthandAAEEAEEA (σ 1 σ 2 )(00) (01), (10), (02), (20) (11), (22)(12), (21) A1A1 A1A1 GE1E1 E3E3 A2A2 A3A3 GE2E2 E3E3 B1B1 A4A4 GE2E2 E4E4 B2B2 A2A2 GE1E1 E4E4 K a K c GS nuclear spin weights of rotational energy levels e e / o o13636642016 e o / o e12028641216

6. International Symposium on Molecular Spectroscopy, June 22-26, 20156 Analysis of ν 21 band “Conventional” analysis A. Perrin et al. (2015) doi:10.1016/j.jms.2015.02.010doi:10.1016/j.jms.2015.02.010 Based on combination differences GS parameters from [1] kept constant 3 band centers identified for AA, EE & AE+EA substates Rotational & centrifugal distortion constants for each substate (  J  & sextic & octic CD constants kept constant at GS value) a Kept at value for EE substate [1]B. J. Drouin, J. C. Pearson, A. Walters, V. Lattanzi, J. Mol. Spectrosc. 240 (2006) 227–237. AAEEAE+EA EVEV 921.3724(38)921.3821(33)921.3913(44) A0.9831356(3600)0.9828286(1100)0.9827518(3700) B0.28153860(2200)0.28153000(1700)0.28151473(2400) C0.24841758(1100)0.24842073(1200)0.24842144(1100)    10 6 a12.714(560) a  KJ  10 7 a -4.51(180) a  J  10 7 a 2.2756(730) a    10 7 a 15.186(550) a

7. Simulation Fig. 1 : Overview of the ν 21 band of propane. The distinctive shape of this typical A-type band is reproduced well. The experimental spectrum is compared to the calculation performed during this study. International Symposium on Molecular Spectroscopy, June 22-26, 20157

8. Simulation details Portions of R-branch near 931.4 cm -1 (left) and of P-branch near 915.2 cm -1 (right) [J, K a, K c ] = assignment in ν 21 state, “d” stand for degenerate K a. Non-degenerate K a : calculated intensities (spin weights ratio) for AA, EE and AE+EA components lead to reasonable agreement between observed and calculated spectra. Degenrate K a : agreement is not good (purple dots for [18,8,d]), triangles for [11,5,d], and diamonds for [11, 6, d].. International Symposium on Molecular Spectroscopy, June 22-26, 20158

9. Simulation details Portion of R branch near 933.2 cm -1 (left) and central part of Q branch (right). [J, K a, K c ] = assignment in ν 21 state. Q-branch: The K a stacks with K a > 11 are not well reproduced. International Symposium on Molecular Spectroscopy, June 22-26, 20159

10. 10 Origin of torsional splittings Comparison of torsional splittings E 01/EE – E 00/AA Torsional splitting in ν 21 expected to be comparable to splitting in GS without additional torsional interaction. However, it is about 8 times as large as in the torsional excited states ν 14 and ν 27. Why? E 01 –E 00 (cm -1 ) GS3.69E-05 ν 14 -0.0011 ν 27 -0.0013 ν 21 0.0097

11. International Symposium on Molecular Spectroscopy, June 22-26, 201511 Torsional energy levels and splittings for J = 0 Literature analysis of torsional Raman spectra [1], [2] ab initio calculations [3] New fit of Raman data [1], [2] and splittings from rot. spectra in GS, ν 14 & ν 27 [4] ν 14 + 3ν 27, ν 21 FR 2ν 14 + 2ν 27, ν 8 FR 3ν 14 + ν 27 4ν 14 [1]J. R. Durig, P. Groner, and M. G. Griffin, J. Chem. Phys. 66 (1977) 3061-3065; analysis of torsional Raman spectra, no splittings [2]R. Engeln, J. Reuss, D. Consalvo, J.W.I. Van Bladel, A. Van Der Avoird, V. Pavlov-Verevkin, Chem. Phys. 144 (1990) 81–9; analysis of torsional Raman spectra [3]M. Villa, M.L. Senent, M. Carvajal, Phys. Chem. Chem. Phys. 15 (2013) 10258–10269; ab initio methods, only up to 770 cm-1 [4]B. J. Drouin, J. C. Pearson, A. Walters, V. Lattanzi, J. Mol. Spectrosc. 240 (2006) 227–237.

12. International Symposium on Molecular Spectroscopy, June 22-26, 201512 Origin of larger torsional splittings Comparison of torsional splittings E 01/EE – E 00/AA Fermi resonance ν 14 + 3ν 27  ν 21 could increase such negligible splitting in the observed direction if ν 14 +3ν 27 had lower energy than ν 21 (instead of the predicted higher energy) Other perturbations Resonces have been observed particularly for 01/EE state transitions (though not for 00/AA). Coriolis interaction is allowed for some but not all torsional substates, particularly not for AA. E 01 –E 00 (cm -1 ) GS3.69E-05 ν 14 -0.0011 ν 27 -0.0013 ν 21 0.0097 ν 14 +3ν 27 0.5234

13. International Symposium on Molecular Spectroscopy, June 22-26, 201513 Analysis of ν 8 band with ERHAM Initial assignments by combination difference method (CDM) Much less satisfactory than for ν 21 band (b/c splittings larger than in ν 8 band) Analysis with ERHAM [1] * Modified to allow prediction & fitting of rovibrational spectra * Initial assignments from CDM * Trial calculation of the most intense high-K a P- & R-branch transitions to establish direction of splitting patterns (6 lines): K a -degenerate transitions generate 6 characteristic lines, the strongest 3 with equal intensities (2 01/EE and 1 degenerate 00/AA) Example for 6 60 - 5 51 & 6 61 – 5 50 at right: 2 predictions with opposite sign of ε 10, bottom: observed spectrum * Assignments with CAAARS [2] using Loomis-Wood diagrams [1] P. Groner, J. Chem. Phys. 107 (1997) 4483-4498; J. Mol. Spectrosc. 278 (2012) 52-67 [2] I. R. Medvedev, M. Winnewisser, B. P. Winnewisser,,F. C. De Lucia, E. Herbst., J. Mol. Struct. 742 (2005 229-236

14. International Symposium on Molecular Spectroscopy, June 22-26, 201514 Analysis of ν 8 band with ERHAM Current status 4185 transitions assigned, many blends (not fit as blends yet, incl. K a -degeneracy), max J = 30, max K a = 15 3959 with non-zero weight 00/AA :1390 01/EE: 2103 11/AE: 393 12/EA: 73 ρ, β, GS constants from rotational spectroscopy [1] kept fixed sextic CD constants same as in GS 17 variable parameters 0.00184 cm -1 standard deviation Many resonances (level crossings) with unknown dark state [1] B. J. Drouin, J. C. Pearson, A. Walters, V. Lattanzi, J. Mol. Spectrosc. 240 (2006) 227–237 ρ 0.15611 β / deg 8.68 A / MHz29207.46449 29224.007(78) B / MHz 8445.968098 8401.424(34) C / MHz 7459.003026 7422.685(29) Δ J / kHz 7.201377 7.359(23) Δ JK / kHz -26.97966 -20.85(15) Δ K / kHz 159.59173 155.71(43) δ J / kHz 1.396750 1.431(19) δ K / kHz 3.10017 12.4(13) ε 00 / cm -1 870.3501243(94) ε 1-1 / MHz -44.00(82) ε 10 / MHz -0.3682 -230.5(11) ε 11 / MHz -76.5(12) ε 20 / MHz -8.98(85) ε 30 / MHz -3.87(64) [A-(B+C)/2] 10 / MHz -0.095(15) [(B+C)/2] 10 / MHz -0.0414(21) [(B-C)/4] 10 / MHz -0.0282(20)

15. International Symposium on Molecular Spectroscopy, June 22-26, 201515 Comparisons of observed and calculated spectrum Overview Q-branch J 0J – J 1,J-1 (J=9 → J=1)Q-branch J 1,J-1 -J 2,J-2 (J=16 → J=8  ) Circle: level crossing 00 01 12 11 16 15 14 13 12 11 10 9 8 3 4 5 6 7 00 01 12,11

16. International Symposium on Molecular Spectroscopy, June 22-26, 201516 More comparisons R-branches J+1 1,J+1 -J 0J (J=10 → J=13) and J+1 0,J+1 -J 1J (J=11 → J=13) [last line also 15 1,14 -14 2,13 ) 23 0,23 -22 1,22 & 23 1,23 -22 0,22 (left) 6 6. -5 5. (middle) 9 5. -8 4., 18 3,16 -17 2,15, 23 1,22 -22 2,21 (right) 11 & 00 components have 2 degenerate transitions, intensities should be double! 10 11 11 12 12 13 1314 00 01 12 11 12 01 11 00 01,12

17. International Symposium on Molecular Spectroscopy, June 22-26, 201517 Origin of larger torsional splittings Comparison of torsional splittings E 01 -E 00 Fermi resonance ν 14 + 3ν 27  ν 21 could increase such negligible splitting in the observed direction if ν 14 +3ν 27 had lower energy than ν 21 (instead of the predicted higher energy) Similarly, FR 2ν 14 + 2ν 27  ν 8 could increase negligible native splitting in the observed direction if 2ν 14 +2ν 27 had lower energy than ν 8 (instead of the predicted higher energy) E 01 –E 00 (cm -1 ) GS3.69E-05 ν 14 -0.0011 ν 27 -0.0013 ν 21 0.0097 ν 14 +3ν 27 0.5234 ν8ν8 0.0360 2ν 14 +2ν 27 1.0801

18. International Symposium on Molecular Spectroscopy, June 22-26, 201518 Discussion & conclusion A start is made!But a lot more needs to be done. a) More assignments necessary to higher J and K a more 11/AE and 12/EE components (more difficult b/c they are weaker) b) More parameters to try, particularly tunneling parameters c) Identify system of level crossings (01/EE and 12/EA components are much more susceptible to Coriolis interactions) d) With enough level crossings, it might be possible to approximate the dark state 2ν 14 +2ν 27 (and get a better torsional potential function). m) Work out some kinks in this modified version of ERHAM. z) Revisit ν 21 and try to characterize the dark state ν 14 +3ν 27.

19. International Symposium on Molecular Spectroscopy, June 22-26, 201519 Thank you