Analysis of torsional splitting in the ν8 band of propane near 870 Analysis of torsional splitting in the ν8 band of propane near 870.4 cm-1 caused by Fermi resonance with the 2ν14+2ν27 level P. Groner Department of Chemistry, University of Missouri - Kansas City, Kansas City, MO, USA A. Perrin, F. Kwabia Tchana 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 International Symposium on Molecular Spectroscopy, June 20-24, 2016

Last year: IR Spectrum of propane Bruker IFS 125HR FT spectrometer SOLEIL–LISA cryo-cell AILES Beamline at SOLEIL Optical path length: 45.14 m HgCdTe (MCT) detector cooled by liquid N2 Temperature: 142 ± 2 K Resolution 0.0015 cm-1 Sample pressure: 14.0 ±0.3 Pa International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 IR Spectrum of propane Two fundamental bands between 820 and 960 cm-1 a-type band at 921.38 cm-1 ν21 (in-plane CH3 rock) b-type band at 870.35 cm-1 ν8 (sym CC stretch) Both bands have split rotational transitions due to interactions between overall and internal rotations of the methyl groups Last year (TG04) * ν21 near 920 cm-1: A. Perrin et al. (2015) doi:10.1016/j.jms.2015.02.010 “First high resolution analysis of the ν21 band of propane CH3CH2CH3 at 921.382 cm−1: Evidence of large amplitude tunneling effects” * ν8 near 870 cm-1 : Preliminary analysis using ERHAM (Effective Rotational Hamiltonian) P. Groner, J. Chem. Phys. 107 (1997) 4483-4498; J. Mol. Spectrosc. 278 (2012) 52-67 International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 ν8 Current status Ground state [1] ν8 (last year) ν8 Transitions   4185 / 3959 5107 / 4797 00 species / 1390 1622 / 1596 01 species / 2103 2359 / 2220 11 species / 393 768 / 726 12 species / 73 358 / 255 s / cm-1 0.00184 0.00153 # parameters 17 25 ρ 0.15611 β / deg 8.68 A / MHz 29207.46449 29224.007(78) 29223.728(57) B / MHz 8445.968098 8401.424(34) 8401.321(30) C / MHz 7459.003026 7422.685(29) 7422.792(26) ΔJ / kHz 7.201377 7.359(23) 7.413(18) ΔJK / kHz -26.97966 -20.85(15) -22.04(12) ΔK / kHz 159.59173 155.71(43) 161.02(36) δJ / kHz 1.396750 1.431(19) 1.408(18) δK / kHz 3.10017 12.4(13) 16.89(109) ε00 / cm-1 870.3501243(94) 870.350650(71) ε1-1 / MHz -44.00(82) -50.63(59) ε10 / MHz -0.3682 -230.5(11) -228.9(11) ε11 / MHz -76.5(12) -76.85(93) ε20 / MHz -8.98(85) -11.00(68) ε30 / MHz -3.87(64) -2.00(47) [A-(B+C)/2]10 / MHz -0.095(15) 0.201(32) [(B+C)/2]10 / MHz -0.0414(21) -0.0944(50) [(B-C)/4]10 / MHz -0.0282(20) -0.0365(50) 8 other parameters IR frequencies fit to isolated ν8 state with ERHAM (no interactions with other vibrational states) Ground state constants from B. J. Drouin, et al., J. Mol. Spectrosc. 240 (2006) 227–237 International Symposium on Molecular Spectroscopy, June 20-24, 2016

Last year: 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, ν14 & ν27 [4] ν14 + 3ν27, ν21 FR 2ν14 + 2ν27, ν8 FR 3ν14 + ν27 4ν14 [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. International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Perturbations 1 * Fermi resonance possible between ν8 and 2ν14 + 2ν27, both levels have A1 symmetry * Local resonances observed for some torsional substates, particularly for 01 (EE) International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Perturbations 1 * Fermi resonance possible between ν8 and 2ν14 + 2ν27, both levels have A1 symmetry * Local resonances observed for some torsional substates, particularly for 01 (EE) * New Work: ν8 Energy levels from combination differences (residuals to one early fit) International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Perturbations 2 * More ν8 Energy levels from combination differences International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Reduced energy plots ν8 parameters from "best" isolated fit, no interaction! 2ν14 + 2ν27, 1 cm-1 below ν8, ε parameters estimated from torsional prediction, ABC from extrapolation of constants in GS, ν14, ν27 (Drouin et al.) International Symposium on Molecular Spectroscopy, June 20-24, 2016

Modifications to ERHAM First trials with ERHAM modified to treat Fermi resonance and Coriolis interactions were not successful * Original labeling scheme did not work sufficiently well with interacting states * Reorganize labeling code making full use of molecular symmetry * Generate new input file according to new labeling scheme Test calculations Plots of ν' - ν0, where ν' = calculated frequency with interaction ν0 = calculated frequency without interaction Key for interactions F Fermi term Px, Py, Pz regular Coriolis term Pxt, Pyt, Pzt tunneling Coriolis term International Symposium on Molecular Spectroscopy, June 20-24, 2016

Modifications to ERHAM Test calculations Qr - Series J1,J-1 ← J0J Observed upper state energy International Symposium on Molecular Spectroscopy, June 20-24, 2016

Modifications to ERHAM Test calculations Qr - Series J2,J-1 ← J1J Observed upper state energy International Symposium on Molecular Spectroscopy, June 20-24, 2016

Modifications to ERHAM * Effective Hamiltonian vs. Interaction Hamiltonian Test calculations Qr - Series J2,J-2 ← J1,J-1 Observed upper state energy International Symposium on Molecular Spectroscopy, June 20-24, 2016

Perturbations in reduced energy plots ν8 parameters from "best" isolated fit 2ν14 + 2ν27, 1 cm-1 below ν8, ε parameters estimated from torsional prediction, ABC from extrapolation of constants in GS, ν14, ν27 (Drouin et al.) International Symposium on Molecular Spectroscopy, June 20-24, 2016

Effective rotational Hamiltonian (isolated vibrational state) or The expressions for Sl and S0 depend on the exact symmetry of the problem. International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Interacting states * and The coefficients Tlqq' and T'lqq' are in this version the sums or differences of the original coefficients Tlv'v,q,q' and Tlv'v,-q-,q' . Luckily, program did not have to be changed except for one little test Insufficient time to try this out. International Symposium on Molecular Spectroscopy, June 20-24, 2016

Where are we now? (Conclusions) * The LS fit still is elusive (shots-into-the-dark trials have not worked) * We don’t know Of the perturbing dark state Identity, energy, A, B, C, tunneling coefficients / splittings Of the interaction operators Kinds and magnitudes Based on experimental results, some (like Px) can be ruled out * Other potential perturber: ν9 + 2ν27 (A1) about 20 cm-1 higher (does not solve the problem of identifying the dark state) International Symposium on Molecular Spectroscopy, June 20-24, 2016

International Symposium on Molecular Spectroscopy, June 20-24, 2016 Thank you International Symposium on Molecular Spectroscopy, June 20-24, 2016