1. Analysis of torsional splitting in the ν8 band of propane near 870
Analysis of torsional splitting in the ν8 band of propane near 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

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

3. 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 cm-1 ν21 (in-plane CH3 rock)
b-type band at 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: /j.jms
“First high resolution analysis of the ν21 band of propane CH3CH2CH3 at  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) ; J. Mol. Spectrosc. 278 (2012) 52-67
International Symposium on Molecular Spectroscopy, June 20-24, 2016

4. 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
# parameters 17 25 ρ
β / deg
8.68
A / MHz
(78)
(57)
B / MHz
(34)
(30)
C / MHz
(29)
(26)
ΔJ / kHz
7.359(23)
7.413(18)
ΔJK / kHz
-20.85(15)
-22.04(12)
ΔK / kHz
155.71(43)
161.02(36)
δJ / kHz
1.431(19)
1.408(18)
δK / kHz
12.4(13)
16.89(109)
ε00 / cm-1
(94)
(71)
ε1-1 / MHz
-44.00(82)
-50.63(59)
ε10 / MHz
-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
(21)
(50)
[(B-C)/4]10 / MHz
(20)
(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

5. 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) ; 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

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

13. 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

14. 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

15. 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

16. 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

17. 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

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