1. Canadian Light Source, University of Saskatchewan
FTIR Synchrotron Spectroscopy of High Torsional Levels of CD3OH: the Tau of Methanol
R.M. Lees, Li-Hong Xu
Centre for Laser, Atomic and Molecular Sciences (CLAMS) Department of Physics, University of New Brunswick
B.E. Billinghurst
Canadian Light Source, University of Saskatchewan

2. The Yin and Yang of Molecular Symmetry
The Way of Tauism
A/E t

3. t Duality for Methanol Internal Rotation s [A/E] Yin Yang CD3 OH
(0, ±1) t
(1, 2, 3)
Ds = 0
Dt = ±1
r = Itop/Ia = ICD3/Ia
r = IOH/Ia = (r – 1)

4. E = F<Pg2> + V3/2 <1- cos3g>
CD3OH Torsional Manifold
Free Rotor m-states
E ~ F<Pg2> » F(m + rK)2 -7
m = s + 3N 6
vt = 4 -6
Eigenfunctions: Y ~ eimg 5
vt = 3 -5
M.A. Mekhtiev and J.T. Hougen,
J. Mol. Spectrosc. 187 (1998) 4 -4
vt = 2 3
Torsional
Barrier V3 -3
vt = 1
vt = 0
Hindered Rotor States
E = F<Pg2> + V3/2 <1- cos3g>
0.5
1.0
1.5

5. The Tau of Methanol
The axis scale factor for A and E torsional energy curves is rK, where r = Imeth/Ia. As r=0.895 for CD3OH, (K+1)¬K transitions involve large steps along the rK axis and large erratic changes in torsional energy.
Dennison’s symmetry label t (1,2,3) has a scale factor of (1 – r)K » The smaller steps mean that many spectral features group closely in terms of t. Thus, t labeling can serve as a useful clue to understanding of the spectrum.
For given t, the torsional symmetry cycles with K from A (red circle) to E2 (triangle) to E1 (black circle), etc.
t = 2
t = 1
t = 3
(1 – r)K Axis

6. Dt-Ladders Universal Free Rotor Spectral Predictor m 5 4 -10 1 -13 -2
K = 5 4 m
-10 1
-13 -2 -3
vt = 4 3 -1 -7 -9 2
-12
Dt-Ladders
vt = 3
vt = 2
vt = 1
vt = 0

7. Some initial rR-Lines of the t = 3 ¬ 1 sub-band ladder
0.3 cm-1
Q(13)
01-10 A
R(12)
44-33 A
Q-branch
K-doublets!

8. Vibrational Bands of CD3OH Methanol
Asymmetric Bends?
Out-of-plane Rock?
OH Bend
cm-1
CO Stretch
16A
4E2
3E2
10E2
3E1
5E2
14A
8E1 4A
10A
7E2 9A 7A
5E1
Dense Q-branch shading to blue
In-plane CD3-Rock
CD3 Symmetric Bend
Two significantly different Q-branch patterns,
indicating different upper-state energy structures

9. CD3OH Torsional Interaction Regions
Small-amplitude vibrations, vt = 0
OH Bend
Asymmetric CD3 Bends
C-O Stretch
Out-of-plane CD3 Rock
In-plane CD3 Rock
Symmetric CD3 Bend
vt = 4
CD3OH Torsional Manifold
t = 3
vt = 3 3A
6E1
t = 2
t = 1
vt = 2

10. CD3OH (o – c) Level Shifts due to Rock/vt=3 Coupling
Deviations between observed and calculated sub-state origins indicate sizeable anharmonic interactions between the vt = 3 and CD3-rocking modes, giving possible clues to the location of the out-of-plane rocking dark state.

11. CD3OH (o – c) Level Shifts due to vt = 4 Coupling
Weber 82 sb sb oh co oh ab co sb ab ab

12. Summary
FIR sub-bands accessing a further 28 vt = 3 and 17 vt = 4 substates of CD3OH methanol have been assigned, better characterizing the vt = 3,4 torsional energy manifold in the regions overlapping the CD3-rocking, CO-stretching, CD3-bending and OH-stretching modes where strong torsion-mediated interactions abound.
For high torsional states in the free rotor region, spectral features fall in close groupings related by Dennison’s torsional symmetry label t, rather than the A/E symmetries, giving useful predictive power. Strong Dm = 0 sub-bands fall along systematic Dt-ladders in a free-rotor energy plot
Interactions between vt = 3,4 and the small-amplitude vibrational states induce large Fermi shifts for numerous near-resonant levels, as well as J-localized level- crossing perturbations. The extensive coupling provides copious doorways for energy and population transfer between torsional and vibrational manifolds.
The intensity of high-vt Dm = 0 transitions is comparable to that of low-vt lines, permitting radiative transfer throughout the whole vt-manifold in astrophysical environments. FIR pumping via the torsional bands is believed to be an important mechanism for the excitation of interstellar methanol in warm, dense regions of star formation.

13. In-plane CD3-Rocking Sub-Band Origins

14. – Fermi Mixing of 3A vt=0 ri and vt=3 gd Levels 20 + J 21 19
Combination Loop Defects
Pri(21) – Rri(19) + Rgd(19) – Pgd (21)
d(A– ri) = cm-1
d(A+ ri) = cm-1
3A vt=0 ri
3A vt=3 gd
3A vt=0 gd + – 20 21 19 J
Inverted! W
Interaction Parameter W
Est. origin pertbn dE » 1.06 cm-1
Obs. origin sep’n DE = 2.69 cm-1
\ Unpert. sep’n DEo » 0.57 cm-1
DE = Ö(DEo2 + 4W2)
W = 0.5 Ö(2.692 – 0.572) = cm-1
Substantial Fermi perturbation!

15. Spectral t-Grouping of Sub-band Origins
Torsional energy changes for K – (K+1) transitions vary smoothly for given t connections, compensating the changes in K-rotational energy. Calculated high-vt sub-band origins fall together in compact t-groups.
Green - known previously. Blue – observed in present work.
vt=3 t-Families
K'¬K"
t = 3¬2
t = 1¬3
t = 3¬1
t = 2¬1
4-5 A
0-1
10-9
14-15
5-6 E2
1-0
11-10
15-16
6-7 E1
2-1
12-11
16-17
7-8
3-2
13-12
8-9
4-3
14-13
9-10
5-4
vt=4¬3 t-Families
t = 2¬3
10-11
11-12
1-2
12-13
2-3
13-14
3-4
15-14
6-5
16-15
7-6
17-16
8-7
9-8

16. CD3OH Level-Crossing Interactions
J-Localized Level-crossing Resonances
Strong Asymmetry Mixing (DK=2)