International Symposium on Molecular Spectroscopy, June 22-26, First high-resolution analysis of the ν 21 band of propane at 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

International Symposium on Molecular Spectroscopy, June 22-26, 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) SymE v / cm -1 TorsObserved ResonancesRef A1A n.o.a 26 1 B2B b 9292 A1A  (A-Corio)  26 1 c 26 1 B2B B1B d 18 1 B1B local 5151 A1A  (A-Corio)  24 1 d 17 1 B1B  (Anh)  B2B  (A– Corio)  A1A  (C-Corio)   (B-Corio)  24 1

International Symposium on Molecular Spectroscopy, June 22-26, 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 cm -1 Sample pressure:14.0 ±0.3 Pa

International Symposium on Molecular Spectroscopy, June 22-26, IR Spectrum of propane Two fundamental bands between 820 and 960 cm -1 a-type band at cm -1 ν 21 (in-plane CH 3 rock) b-type band at 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 cm −1 : Evidence of large amplitude tunneling effects” A. Perrin et al. (2015) doi: /j.jms doi: /j.jms ν 8 : Preliminary analysis using ERHAM (Effective Rotational Hamiltonian) P. Groner, J. Chem. Phys. 107 (1997) ; J. Mol. Spectrosc. 278 (2012) 52-67

International Symposium on Molecular Spectroscopy, June 22-26, 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 o e o / o e

International Symposium on Molecular Spectroscopy, June 22-26, Analysis of ν 21 band “Conventional” analysis A. Perrin et al. (2015) doi: /j.jms doi: /j.jms 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 (38) (33) (44) A (3600) (1100) (3700) B (2200) (1700) (2400) C (1100) (1200) (1100)    10 6 a12.714(560) a  KJ  10 7 a -4.51(180) a  J  10 7 a (730) a    10 7 a (550) a

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

Simulation details Portions of R-branch near cm -1 (left) and of P-branch near 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

Simulation details Portion of R branch near 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 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 ν ν

International Symposium on Molecular Spectroscopy, June 22-26, 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 ν 27, ν 21 FR 2ν ν 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) ; 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.

International Symposium on Molecular Spectroscopy, June 22-26, Origin of larger torsional splittings Comparison of torsional splittings E 01/EE – E 00/AA Fermi resonance ν ν 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 ν ν ν 14 +3ν

International Symposium on Molecular Spectroscopy, June 22-26, 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 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) ; J. Mol. Spectrosc. 278 (2012) [2] I. R. Medvedev, M. Winnewisser, B. P. Winnewisser,,F. C. De Lucia, E. Herbst., J. Mol. Struct. 742 (

International Symposium on Molecular Spectroscopy, June 22-26, 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 = with non-zero weight 00/AA : /EE: /AE: /EA: 73 ρ, β, GS constants from rotational spectroscopy [1] kept fixed sextic CD constants same as in GS 17 variable parameters 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 β / deg 8.68 A / MHz (78) B / MHz (34) C / MHz (29) Δ J / kHz (23) Δ JK / kHz (15) Δ K / kHz (43) δ J / kHz (19) δ K / kHz (13) ε 00 / cm (94) ε 1-1 / MHz (82) ε 10 / MHz (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 (15) [(B+C)/2] 10 / MHz (21) [(B-C)/4] 10 / MHz (20)

International Symposium on Molecular Spectroscopy, June 22-26, 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 ,11

International Symposium on Molecular Spectroscopy, June 22-26, 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, ,13 ) 23 0, ,22 & 23 1, ,22 (left) (middle) , 18 3, ,15, 23 1, ,21 (right) 11 & 00 components have 2 degenerate transitions, intensities should be double! ,12

International Symposium on Molecular Spectroscopy, June 22-26, Origin of larger torsional splittings Comparison of torsional splittings E 01 -E 00 Fermi resonance ν ν 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 ν 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 ν ν ν 14 +3ν ν8ν ν 14 +2ν

International Symposium on Molecular Spectroscopy, June 22-26, 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.

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