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

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

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)

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) 49-60. 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

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 » 0.1 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

Dt-Ladders Universal Free Rotor Spectral Predictor m 5 4 -10 1 -13 -2 K = 0 1 2 3 4 5 6 7 8 9 10 11 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

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!

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

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

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.

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

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.

In-plane CD3-Rocking Sub-Band Origins

– 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) = 0.0000 cm-1 d(A+ ri) = 0.0005 cm-1 3A vt=0 ri 3A vt=3 gd 3A vt=0 gd + – 20 21 19 J 834.5867 834.6882 888.0540 888.0942 831.8157 831.9300 885.2830 885.3365 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) = 1.31 cm-1 Substantial Fermi perturbation!

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 199.2095 0-1 238.0296 10-9 267.0720 14-15 169.4983 5-6 E2 201.4189 1-0 236.8650 11-10 265.7069 15-16 171.1530 6-7 E1 202.9654 2-1 235.4742 12-11 264.3121 16-17 172.6504 7-8 204.4224 3-2 234.0495 13-12 262.8700 8-9 205.8388 4-3 232.5633 14-13 261.3096 9-10 207.2274 5-4 230.8483 258.1301 vt=4¬3 t-Families t = 2¬3 10-11 208.5997 238.4208 278.8873 306.5296 11-12 209.9518 1-2 239.5820 277.4353 305.2949 12-13 211.2900 2-3 240.9142 276.1777 304.0521 13-14 212.6157 3-4 242.2330 274.9118 302.8001 213.9303 243.5398 273.6365 15-14 301.5380 215.2348 244.8359 6-5 272.3507 16-15 300.2645 216.5303 246.1223 7-6 271.0533 17-16 298.9782 247.4000 8-7 269.7429 248.6707 9-8 268.4184

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