Transcript IlyushinColumbus2009.ppt

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
Two step diagonalization procedure
I. step
Dr. Isabelle Kleiner
BELGI
(available at PROSPE)
1
H tor  F ( p  J z ) 2  V6 (1  cos 6 )
2
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
Km i ( 3t  )
are kept for the second stage
9 lowest eigenfunctions Km   At e
t
II. step
1
1
1
2
2
H rottor  ( B  C ) J  [ A  ( B  C )] J z  ( B  C )( J x2  J y2 ) 
2
2
2
 higher order rotation, torsion - rotation distortion terms
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 JKM Km A1 and A2 as well as B1 and
B2 species are not separated in our calculations.
Parameter space of the new program
H 1
B
2 knpqrst
[ J J J J p cos(3s ) sin( 3t )
2k
knpqrst
n
z
p
x
q
y
r
 sin( 3t ) cos(3s ) pr J yq J xp J zn J 2 k ]
k n p q
r s t
_________________________________________________________________________________________________
muz
,
V6
,
V6
,
A-0.5(B+C),
0.5(B+C) ,
0.5(B-C) ,
0.5(B-C) ,
F
,
RHO
,
FJ
,
FK
,
Fbc
,
Fbc
,
0,
0,
0,
0,
1,
0,
0,
0,
0,
1,
0,
0,
0,
1,
0,
0,
2,
0,
0,
0,
0,
1,
0,
2,
0,
0,
0,
0,
0,
0,
0,
2,
0,
0,
0,
0,
0,
2,
0,
0,
0,
0,
0,
0,
0,
2,
0,
0,
0,
0,
0,
2,
0,
0,
0,
0,
0,
0,
0,
2,
1,
2,
2,
2,
2,
...
0,
0,
2,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.375E+00
0.241E+01
0.100E+01
0.113E+00
0.711E-01
0.128E-01
-0.100E+01
0.529E-01
0.358E-01
-0.372E-06
-0.466E-05
0.747E-07
-0.100E+01
,
,
,
,
,
,
,
,
,
,
,
,
,
0, 0,
1, 1,
1, -1,
2, 1,
2, 1,
2, 1,
2, -1,
1, 1,
1, 1,
2, 1,
2, 1,
2, 1,
2, -1,
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
Determination of the sign of V6
G. O. Sørensen, T. Pedersen, “Symmetry and Microwave Spectrum
of Nitro-methane” in Studies in Physical and Theoretical Chemistry,
23 (1983) 219-236.
½V6(1cos6)
-
+
a minimum energy at  = (2n+1)/6
a minimum energy at =2n/6
sin3=(-1)n; cos3=0
sin3=0; cos3=(-1)n
Terms that discriminate
sin3(JzJy+ JyJz)
cos3(JzJx+ JxJz)
Jx{p,cos3}
Jy{p,sin3}
G. O. Sørensen, T. Pedersen, in Studies in Physical and Theoretical
Chemistry, 23 (1983) 219-236.
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) 6787-6805.
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) 3658-3669.
Reduced energy level diagrams for m=1 and m=2 states of
toluene and nitromethane-d3
Nitromethane-d3
Toluene
m=2
m=2
m=1
m=1
J
J
Reduced energy level diagrams for m=1 and m=2 states of
toluene and nitromethane-d3
Nitromethane-d3
Toluene
m=2
m=2
m=1
m=1
J
J
New measurements in the millimeter wave range
measurement
prediction
92690.
m=5
m=1
m=2
m=2
m=+3
m=1
m=0
m=0
m=1
m=2
m=0
m=4
m=0
m=2
m=5
0
R-type, J=24,25,26, Ka<9
92710.
92730.
92750. MHz
m=2
E-1/2(B+C)J(J+1)
cm-1
Reduced energy level diagrams for m=1 and m=2 states of
toluene
m=1
J
1
1 2
2
2
2
2
 9F  V6  ( A   F ) J z  BJ x  CJ y 
V6  36F 2  2 J z2
2
16
cm-1
H
eff
3
E-1/2(B+C)J(J+1)
m= -3
m= +3
J




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.
Acknowledgements



Dr. Isabelle Kleiner (details BELGI)
Dr. Sergei Tashkun (banded matrices)
National Institute of Standards and Technology,
USA (financial support)
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”