1. MOLECULES WITH A SIX-FOLD BARRIER: MICROWAVE SPECTRUM OF TOLUENE
Vadim V. Ilyushin1, Zbigniew Kisiel2, Lech Pszczolkowski2,
Heinrich Mäder3, Jon T. Hougen4
1Institute of Radio Astronomy of NASU, Kharkov, Ukraine
2Institute of Physics, Polish Acad. of Sci., Warsaw, Poland
3Institute for Phys. Chem., Kiel University, Kiel, Germany
4Optical Technology Division, NIST, Gaithersburg, MD

2. Two step diagonalization procedure
I. step
Dr. Isabelle Kleiner
BELGI (available at PROSPE)
For =0,1,2,3 and each K in the range –Jmax  K  Jmax a matrix of order 2121 is diagonalized in the basis set e[i(3t+)] with t=-10 to +10
9 lowest eigenfunctions
are kept for the second stage
II. step
For each J in the range 0  J  Jmax a matrix of order (2J+1) 9(2J+1)9 is diagonalized in the basis set A1 and A2 as well as B1 and B2 species are not separated in our calculations.

3. Parameter space of the new program
k n p q r s t
_________________________________________________________________________________________________
muz , 0, 1, 0, 0, 0, 0, 0, E+00 , 0, 0,
V , 0, 0, 0, 0, 0, 0, 0, E+01 , 1, 1,
V , 0, 0, 0, 0, 0, 2, 0, E+01 , 1, -1,
A-0.5(B+C), 0, 2, 0, 0, 0, 0, 0, E+00 , 2, 1,
0.5(B+C) , 1, 0, 0, 0, 0, 0, 0, E-01 , 2, 1,
0.5(B-C) , 0, 0, 2, 0, 0, 0, 0, E-01 , 2, 1,
0.5(B-C) , 0, 0, 0, 2, 0, 0, 0, E+01 , 2, -1,
F , 0, 0, 0, 0, 2, 0, 0, E-01 , 1, 1,
RHO , 0, 1, 0, 0, 1, 0, 0, E-01 , 1, 1,
FJ , 1, 0, 0, 0, 2, 0, 0, E-06 , 2, 1,
FK , 0, 2, 0, 0, 2, 0, 0, E-05 , 2, 1,
Fbc , 0, 0, 2, 0, 2, 0, 0, E-07 , 2, 1,
Fbc , 0, 0, 0, 2, 2, 0, 0, E+01 , 2, -1,
...

4. General features of the new program
Simultaneous treatment of all torsion-rotation states associated with large-amplitude torsional motion using one set of parameters
Any symmetry allowed term is allowed
Weighted least-squares procedure with special treatment of blended lines
Calculation of the spectral predictions with no Ka,Kc selection rules imposed

5. Terms that discriminate
G. O. Sørensen, T. Pedersen, “Symmetry and Microwave Spectrum of Nitro-methane” in Studies in Physical and Theoretical Chemistry, 23 (1983)
½V6(1cos6)
Determination of the sign of V6 + -
a minimum energy at =2n/6
sin3=0; cos3=(-1)n
a minimum energy at  = (2n+1)/6
sin3=(-1)n; cos3=0
Terms that discriminate
sin3(JzJy+ JyJz)
cos3(JzJx+ JxJz)
Jx{p,cos3}
Jy{p,sin3}

6. rms=6.8 kHz (‘+’ sign) rms=9.6kHz (‘-’ sign)
G. O. Sørensen, T. Pedersen, in Studies in Physical and Theoretical Chemistry, 23 (1983)
CD3NO2
J≤10, 67 lines rms=0.04MHz (‘+’ sign) rms=0.20MHz (‘-’ sign)
J ≤20, 74 lines rms=0.05MHz (‘+’ sign) rms=6 MHz (‘-’ sign)
Toluene
J ≤ 30, 363 lines
rms=6.8 kHz (‘+’ sign) rms=9.6kHz (‘-’ sign)
Kueih-Tzu Lu, Frank Weinhold, James C. Weisshaar “Understanding barriers to internal rotation in substituted toluenes and their cations” J. Chem. Phys. 102 (1995)
David R. Borst and David W. Pratt “Toluene: structure, dynamics, and barrier to methyl group rotation in its electronically excited state. A route to IVR” J. Chem. Phys. 113 (2000)

7. Reduced energy level diagrams for m=1 and m=2 states of toluene and nitromethane-d3J
m=1
m=2

8. Reduced energy level diagrams for m=1 and m=2 states of toluene and nitromethane-d3J
m=1
m=2

9. New measurements in the millimeter wave range
92690.
92710.
92730.
92750.
MHz
prediction
m=5
m=2
m=2
m=0
m=2
m=0
m=1
m=5
m=2
m=4
m=+3
m=0
m=1
R-type, J=24,25,26, Ka<9
m=0
m=1

10. Reduced energy level diagrams for m=1 and m=2 states of toluene
E-1/2(B+C)J(J+1)
m=1
m=2
cm-1 J

11. m= -3
m= +3
cm-1
E-1/2(B+C)J(J+1) J

12. Conclusions:
A new program was written for molecules with six-fold barriers.
The sign of the V6 potential can not be determined with confidence from the current fit.
m=2 lines give clear indication of significant intertorsional interactions
Assignments need to be extended into the problem regions.

13. Acknowledgements Dr. Isabelle Kleiner (details BELGI)
Dr. Sergei Tashkun (banded matrices)
National Institute of Standards and Technology, USA (financial support)

14. Acknowledgements Dr. Isabelle Kleiner (details BELGI)
Dr. Sergei Tashkun (banded matrices)
National Institute of Standards and Technology, USA (financial support)
Unknown person or persons who told Jon Hougen last year at this meeting to go back and check some old reprints in his collection, because nobody would like to be a coauthor of a paper on “reinvention of the wheel”