Torsion-Rotation Program for Six-Fold Barrier Molecules Toluene MW Fit Vadim V. Ilyushin 1, Zbigniew Kisiel 2, Lech Pszczolkowski 2, Heinrich Mäder 3, Jon T. Hougen 4 1 Institute of Radio Astronomy of NASU, Kharkov, Ukraine 2 Institute of Physics, Polish Acad. of Sci., Warsaw, Poland 3 Institute for Phys. Chem., Kiel University, Kiel, Germany 4 Optical Technology Division, NIST, Gaithersburg, MD
H1 H2 H3 H4 H6 H5 H7 H8 Cf Cg Ca Cb CeCc Cd z x Toluene PI Group Operations Toluene C3 top C2 frame (23)* (123) (ab)(cd)x (45)(67) G12 C6v A1, A2, B1, B2, E1, E2 Methanol C3 top C2 frame (23)* (123) none G6 C3v A1, A2, E
Transformation properties of the torsional and rotational variables under various operations of the PI group G12 for toluene torsional rotational E , , (123) + 2 /3 , , (ab)()()() + , , (ab)()()()(123) 2 /6 + , , (23)* , , +
Symmetry species in G12 and time reversal symmetry (+) or ( ) Torsional Momenta |JKaKc A1cos6 (+) ee A2 sin6 (+)Jz ( ), p ( )eo B1 cos3 (+)Jy ( ) oe B2 sin3 (+)Jx ( ) oo E1exp( i ) E2 exp( 2i )
Character table for the subgroup G6 of G12 needed to understand basis set construction in the two-step diagonalization procedure basis functions: exp(6k+ )i |JKM> E (ab)(123) (ab)(123) 2 (123) (123) 2 (ab) K A even B odd E - * * E1 1 - * - * E2+ 2 * * 1 +2 E2 2 * * 1 -2 = exp(2 i/3)
Where are we in the fitting procedure? Answer: In the middle of it. 234 transitions for m = 0, 1, 2, +3, parameters standard deviation = 5.9 kHz J 25 for m = 0, but J 8 for m = 1,2,+3,-3 Ka, Kc labels are problematic (next slides)
Current understanding of the toluene spectrum: J = 2 ← 1 region Observed (waveguide FTMW) Calculated = |m|≤3 in fit = |m|>3 assigned, not yet fitted
Specimen fit:
Conclusions: 1.Our 6 kHz fit is excellent, but: 2.Assignments need to be extended into higher J and K problem regions (see Zbigniew Kisiel at this meeting). 3. Measure J = 1 0 region (see Heinrich Mäder at this meeting). 4 Labeling algorithm in program needs to be able to deal with Ka,Kc (high-barrier) and K (low barrier) labels.