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Following the first successful high-resolution of the far-infrared spectrum of DMSO recorded with the AILES
beamline, Arnaud Cuisset and Dmitrii Sadovskii, from the Laboratory of Physical Chemistry of the Atmosphere in
Dunkerque, discovered a sequence of fourfold clusters of rotational levels. This unusual system of localized states
corresponds to classical rotations about a pair of tilted axes, which become stationary at high angular momenta.
These results were recently published in Physical Review Letters (A. Cuisset et al. Phys. Rev. Lett. Vol. 109, 094101,
(2012)).
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Many of us have enjoyed the spectacle of a spinning top influenced
by friction: rotating rapidly about a stable stationary axis, the top
loses slowly its angular momentum j (and energy), slows down
gradually, and then, suddenly, its axis becomes unstable, the top
wobbles, and an abrupt change of the top’s position follows. In
other words, the system undergoes a bifurcation. In the case of the
tippe top, rotation about its lower point is stable at low values of
angular momentum j and becomes unstable at large j. Something
quite similar occurs in a freely rotating dimethylsulfoxyde (DMSO,
(CH3)2SO) molecule. For the first time in such large polyatomic
molecule a quantum bifurcation induced by a gyroscopic
destabilization was observed. This unusual phenomenon in
rotational dynamics was discovered in the rovibrational states of the
bending fundamental !23 band of DMSO whose high-resolution gas
phase absorption spectrum was observed along with that of !11 by
Cuisset et al. (Chem. Phys. Lett. 492, 30, (2010)) using the
exceptional properties of AILES in the Far-Infrared domain.
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!23
!11
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306
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theory J<50
experiment
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Frequency cm-1
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DMSOFIRnu11SReduction.cat
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DMSO/DMSOexp.dat
Absorbance intensity (arb. units)
DMSO
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(!"#$%&( F()( GH9&%"I&/7.,( JK,$&L( ./1( 75&+%&7"8.,( JK,.8ML( 39&87%.( +-( NA@OE( !23 and !11
bands are associated respectively to the symmetric and asymmetric bending vibrations.(
Rotational structure of i11 and i23
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In order to observe this phenomenon, it was necessary to
assign a large number of spectral lines. The analysis was
complicated by a large number and high density of spectral
lines and had to account for the specific spectral structures
reflecting the accidental closeness of DMSO to the
symmetric top. 4500 rovibrational transitions of the !11
band were firstly assigned using a common procedure in
rovibrational spectroscopy to adjust the molecular
parameters. For the !23 band, a computer aided assignment
procedure based on a systematic search of all combination
frequencies was necessary to assign more than 7500
transitions and to reproduce the spectrum at the
experimental accuracy. By analyzing the obtained
spectroscopic constants, the interesting classical rotational
dynamics with additional stationary axes of rotation was
uncovered for !23.
X
DMSO
2-cluster 2
axis A
axis B
axis C
axis X
4
4-cluster
i23
i11
5
4
A
2
2
i23
0
4
B
files: DMSOFIRnu11SReduction.egy Jan-18-15:52 on 2012-01-20 by dima
Reduced rotational energy in cm-1
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ground state (bottom)!
50
Angular momentum J
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Figure 3 presents the observed and predicted doublet
energy levels of !23 (respectively short and long
dashed) and the energies of classical rotations (solid
lines) around the stationary axes. The low-J structure
of !23 resembles that of a rigid oblate asymmetric top:
sequences of C and A-type rotational levels ascend
and descend from the respective minimum and
maximum energies towards the transition region B.
For J>27, a classical pitchfork bifurcation takes place
at A creating a pair of new stationary rotation axes X.
A-type doublets crossing into the X domain and
merging into quadruplets. These 4-fold clusters were
actually observed in about 20 out of the 7500
transitions! The far infrared synchrotron radiation
made a great number of complex molecular systems
such as DMSO accessible. The interesting rotational
dynamics uncovered in DMSO, and the way this
dynamics was observed has many analogs in different
areas of modern nonlinear physics.