Microwave, millimeter-wave, and high-resolution FTIR study of SO2F2: The v3, v7, v9 triad at 550 cm-1

Article abstract of DOI:10.1016/S0022-2860(02)00084-4

The high-resolution infrared spectrum of the v₃ (A₁), v₇ (B₁), and v₉ (B₂) bands of SO₂F₂ at 551.6, 544.1, and 539.1 cm^-1, respectively, has been recorded with a resolution of 0.0026 cm^-1. Ca. 5500 transitions of this triad with ΔK_a = 0, ±1 have been assigned. Microwave and millimeter-wave spectra up to 450 GHz of the v₃ = 1, v₇ = 1, and v₉ = 1 states have been recorded and 499 pure rotational transitions in the triad states have been measured. Rotational and rovibrational data have been analyzed simultaneously with a model taking into account Coriolis interactions within the triad. In the fit the first order Coriolis resonance parameters were constrained to values from a scaled ab initio force field calculated in this work. Excited state parameters for the triad states up to octic centrifugal distortion constants have been obtained using the Watson Hamiltonian in S-reduction.

Full text of DOI:10.1016/S0022-2860(02)00084-4

Journal of Molecular Structure 612 (2002) 133±141
www.elsevier.com/locate/molstruc
Microwave, millimeter-wave, and high-resolution FTIR study of
SO F : the n , n , n triad at 550 cm
21q
2
2
3
7
9
a
H. B uÈ rger , J. Demaison , F. Hegelund , L. Margul eÁ s , I. Merke
b
c,
b
d
*
a
FB9, Anorganische Chemie, Universit aÈ t-GH Wuppertal, D-42097 Wuppertal, Germany
Laboratoire de Physique des Lasers, Atomes et Mol e cules, UMR CNRS 8253, Universit e de Lille 1, F-59655 Villeneuve d'Ascq, France
b
c
Department of Chemistry, University of Aarhus, DK-8000 Aarhus C, Denmark
d
Institut f uÈ r Physikalische Chemie, RWTH Aachen, D-52056 Aachen, Germany
Dedicated to Professors Helmut Dreizler and Paolo Favero
Received 14 May 2001; accepted 24 July 2001
Abstract
The high-resolution infrared spectrum of the n (A ), n (B ), and n (B ) bands of SO F at 551.6, 544.1, and 539.1 cm
2
1
,
3
1
7
1
9
2
2 2
2
respectively, has been recorded with a resolution of 0.0026 cm . Ca. 5500 transitions of this triad with DK
1
a
ˆ 0, ^1 have been
assigned. Microwave and millimeter-wave spectra up to 450 GHz of the n
3
ˆ 1, n
7
ˆ 1, and n
9
ˆ 1 states have been recorded
and 499 pure rotational transitions in the triad states have been measured. Rotational and rovibrational data have been analyzed
simultaneously with a model taking into account Coriolis interactions within the triad. In the ®t the ®rst order Coriolis resonance
parameters were constrained to values from a scaled ab initio force ®eld calculated in this work. Excited state parameters for the
triad states up to octic centrifugal distortion constants have been obtained using the Watson Hamiltonian in S-reduction.
q 2002 Elsevier Science B.V. All rights reserved.
Keywords: Sulfuryl ¯uoride; Microwave; Millimeter-wave; Infrared; Coriolis resonance
1
. Introduction
B uÈ rger et al. [2] performed the ®rst detailed rovibra-
tional analysis of a fundamental state of SO2F2
combining microwave, millimeter-wave, and high-
resolution FTIR data for n8.
Sulfuryl ¯uoride, SO F , has recently attracted our
2
2
interest since this asymmetric top molecule (point
group C ) is close to an accidentally spherical
Despite numerous microwave [3,4], low and
medium resolution infrared [5±7], and solid state
Raman [8] studies over the years, the vibrational
assignment of the bending modes of SO F is still
2
v
rotor. In Ref. [1] Sarka et al. showed that either S-
reduction or 6-reduction, in which all six quartic
centrifugal distortion constants are determinable, has
to be used, and complete sets of ground state constants
up to sextic order were obtained. Simultaneously,
2
2
subject to some doubt. These modes fall into two
21
groups, a diad around 380 cm and a triad around
21
5
50 cm . The present work was initiated in order
to establish the assignment of the individual modes
q
This paper is dedicated to Professor Paolo G. Favero and
21
Professor Helmut Dreizler in appreciation of their signi®cant contri-
butions to the ®eld of microwave spectroscopy.
of the 550 cm triad from microwave, millimeter-
wave, and high resolution infrared spectra of SO2F2
in gas phase, and to determine a set of spectroscopic
parameters for the vibrational states of the triad.
*
Corresponding author. Tel.: 145-8942-3333; fax: 145-8619-
1999.
E-mail address: heg@chem.au.dk (F. Hegelund).
6
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.
PII: S0022-2860(02)00084-4

134
H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
3 7 9 2 2
Fig. 1. Survey spectrum of the n , n , n triad of SO F . The ®gure shows the assignment of the Q-branches in the triad. Some fringing occurs as
may be seen in the wings of the spectrum.
2
The three modes clustered in the 550 cm wave-
1
by low resolution IR spectroscopy) had been
converted to SO F . Puri®cation of SO F was
number region are n (A , OSO bend), n (B , SO
3
1
7
1
2
2
2
2 2
rock), and n (B , SO wag) which give rise to a-, b-
9
achieved by fractional condensation using a standard
greaseless vacuum line.
2
2
,
and c-type fundamental bands in the IR, respectively.
In the present paper these bands are assigned using
microwave and high-resolution infrared spectra. The
fundamental levels n , n , and n form a triad which is
perturbed by mutual a-, b-, and c-Coriolis resonances.
We report a set of spectroscopic constants for these
levels from a global ®t taking into account these inter-
actions, and using assigned microwave, millimeter-
wave, and high-resolution FTIR data. In the ®t the
2
.2. FTIR spectrum
3
7
9
The infrared spectrum of SO F was recorded in the
2
2
21
375±825 cm region using the Bruker 120 HR inter-
ferometer in Wuppertal. This was equipped with a
Globarsource, a 3.5 mm Mylar beamsplitterand a liquid
He-cooled Cu:Ge detector. The resolution was set to
23
21
2
.6 £ 10 cm (1/maximum optical path difference),
®
rst order Coriolis resonance parameters for the
and trapezoidal apodization applied. In total 57scans
were coadded. A glass cell of 28 cm length equipped
with CsBr windows was used, and a pressure of 500 Pa
triad are constrained to values calculated from an ab
initio predicted harmonic force ®eld of the molecule.
In our global ®t the Watson model, S-reduction, has
been employed for each of the triad levels.
adjusted. Calibration was done using residual H O lines
2
2
1
in the 450±510 cm range as reported in Ref. [9].
Wavenumber precision of isolated, medium intensity
2
4
21
lines is ca. 1 £ 10 cm . Wavenumber accuracy is
2
. Experimental section
23
21
estimated better than 1 £ 10 cm .
2
.1. Material
2.3. Microwave and millimeter-wave spectrum
SO2F2 was prepared by passing in a dynamic
vacuum SO Cl at 400 8C over dried KF. Since the
In Aachen Fourier transform measurements in the
frequency region 10±40 GHz were performed with a
supersonic molecular beam spectrometer [10,11]. The
sample was introduced as a mixture of approximately
2
2
¯uorination proceeds stepwise this procedure was
repeated several times until all SO FCl (monitored
2

H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
135
P
P
Fig. 2. Assignment of a small part of the P-wing of the c-type band n
9
of SO
2 2 a
F . Individual K -components of the P(43)± P(45) clusters are
assigned. Transitions with K odd are stronger by a factor of three than K
a
a
even transitions due to nuclear spin statistical weights.
21
1
% SO F in helium at a stagnation pressure of about
2
SO F in the region 500±600 cm is shown. Three Q-
2 2
2
1
00 kPa. Because of just partly resolved spin±spin and
branches can be clearly distinguished. They are
21
spin±rotation splittings the accuracy for the center
frequency is estimated to be limited to 2 kHz. Transi-
tions in the frequency region 50±110 GHz were
recorded using an absorption-type spectrometer [12]
under free-space cell conditions with source modulation
and 2f phase-sensitive detection. Schottky diodes were
usedasdetectors. Thepressureinthe cell wasabout2 Pa
throughout. Under these conditions the line centers
could be determined with an accuracy of about 10±
observed at 539.1, 544.1, and 551.6 cm . In the
present work they are assigned to n , n , and n ,
9
7
3
respectively. The Q-branch due to n is symmetrical.
9
The Q-branch of n degrades towards lower wave-
7
numbers, while that of n degrades oppositely.
3
The line density in this band system is very high, in
particular in the Q-branch region where intense P- and
R-branch lines due to all three bands blend. Our
assignment was initiated by the observation of a series
of P-clusters in the low wavenumber region of the
spectrum. These clusters show the same appearance
3
0 kHzforunblended linesdependingontheir intensity.
In Lille, the spectrum was measured with a source-
modulation spectrometer using as a source either
harmonics of a Gunn diode between 150 and
as observed for the n band, e.g. a characteristic varia-
8
tion in the intensity of the K -components of a P(J)-
a
2
50 GHz or a Thomson backward-wave oscillator
cluster corresponding to nuclear spin statistical
weights, o=e ˆ 3 : 1: See Ref. [2] for further details.
between 420 and 450 GHz. In both cases a He-cooled
InSb bolometer was used as a detector. The accuracy
of the measurement varies between 50 and 300 kHz
depending on the frequency region and the frequency
step chosen to record the spectrum.
P
This means that this series of clusters being P(J)
transitions, belongs to a- b- or c-type band. From
ground state combination differences, GSCDs, based
R
on the ground state constants [2], a series of R(J)
P
clusters related to the P(J) series was easily found,
and the J and K assignments of individual lines were
a
P
established. A part of our assignment of the P-branch
3. Description of the IR spectrum and assignment
of bands
is shown in Fig. 2. Extending the assignment to lower
K , asymmetry splitting was observed. From GSCDs
the splittings proved to be consistent with c-type
a
In Fig. 1 a survey spectrum of the IR spectrum of

136
H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
R
R
7 2 2 a
Fig. 3. Assignment of a small part of the R-wing of the b-type band n of SO F . Individual K -components of the R(40)± R(42) clusters are
assigned.
selection rules. Thus the series belong to n . The Q-
9
were ®tted using the standard model of Watson, S-
reduction. Comparing the rotational constants
obtained with those obtained from microwave
analyses of series in excited states showed a good
agreement which made possible the identi®cation
of excited state microwave line series belonging to
the vibrational states n and n . The microwave lines
2
branch of this band is located at 539.1 cm . Ca. 2400
1
P-and R-branch transitions with DK ˆ ^1 were
a
®
nally assigned in n . Our assignment reaches
9
J ˆ 86 and K ˆ 84. Asymmetry splitting is observed
a
for K , 11.
a
During the assignment of the R-wing of n we iden-
9
7
9
R
ti®ed an additional series of R-clusters. Using
GSCDs as described earlier a corresponding series
are of a-type, and the identi®cation was further
con®rmed by the observation that microwave lines
with K even are stronger than lines with K odd. This
P
of P-clusters was found and assignment to J and K
established. This P- and R-branch system belongs to
a
a
a
is to be expected for lines in excited vibrational
states of B or B symmetry from nuclear spin statis-
tical weights.
21
the Q-branch at 544.1 cm . Extending the K -assign-
a
1
2
ment to lower K , asymmetry splitting consistent with
a
b-type selection rules was observed. Thus, the
Clearly, the Q-branch observed in the IR at
21
21
5
con®rmation that this band is of b-type comes from
44.1 cm band may be assigned to n . A further
551.6 cm
belongs to n . However, it was not
3
7
possible by simple inspection to ®nd any P- and R-
branch series since the region is too congested with
lines. Furthermore, in contrast to b- and c-type bands
the cluster structure for a-type bands does not show
the observation of long P- and R-branch series for low
K . The series show systematic overlap since
rotational energy levels JJ±K;K and JJ±K;K11 with the
a
same K ˆ J±K become systematically degenerate for
any marked series onset since lines with K close to J
a
a
low K. A small part of the assignment of the R-wing is
shown in Fig. 3. P- and R-branch transitions with
DK ˆ ^1 up to J ˆ 84 K ˆ 80 have been assigned.
are weak. However, in the microwave spectrum a
relatively strong series of lines could be assigned
with con®dence to transitions in the n state. From
a
a
3
Asymmetry splitting is observed for K , 7. Ca. 2400
this series rotational constants were determined, and
using these constants together with a band center
a
lines were assigned for this band.
The assigned transitions in both bands n and n
21
value of 551.6 cm the IR spectrum of n3 was
9
7

H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
137
Table 1
21
2 2
Symmetry coordinates and experimental vibrational frequencies (cm ) for sulfuryl ¯uoride, SO F
a
b
Species
Coordinate
Description
Frequency
2
2
1=2
c
A
1
S ˆ ꢀ2†
ꢀR 1 R †
SO sym. stretch
SF sym. stretch
OSO bend
1269
1
1
2
1=2
S ˆ ꢀ2†
ꢀr 1 r †
849.5
551.6
386.2
2
1
2
S ˆ /ꢀOSO†
3
S ˆ /ꢀFSF†
FSF bend
4
A
2
S ˆ ꢀ1=2†ꢀa 2 a 2 a 1 a †
Torsion
384
5
1
2
3
4
2
1=2
c
B
1
2
S ˆ ꢀ2†
ꢀR 2 R †
SO asym. stretch
1502
6
1
2
S ˆ ꢀ1=2†ꢀa 1 a 2 a 2 a †
SO
2
rock
544.1
7
1
2
3
4
2
1=2
d
B
S ˆ ꢀ2†
ꢀr 2 r †
SF asym. stretch
SO wag
887.2
8
1
2
S ˆ ꢀ1=2†ꢀa 2 a 1 a 2 a †
2
539.1
9
1
2
3
4
a
b
c
d
R
1
is SO bond length; r
1
is SF bond length; a ˆ /ꢀOSF†:
This work, unless otherwise stated.
Ref. [7].
Ref. [2].
predicted. From this prediction P- and R-branch
clusters of n corresponding to DK ˆ 0 were easily
non-negligible errors, but they are mainly systematic
and can be corrected by an empirical scaling.
3
a
assigned in the IR spectrum. Series of P- and R-branch
lines in n are considerably weaker than for n and n .
The quantum mechanical force ®eld was calculated
by using the gaussian 94 program [15]. Two different
methods were used: the second-order Mùller±Plesset
perturbation theory (MP2) [16] and the density func-
tional theory (DFT) approximation in the Kohn±
Sham formulation [17] and using the hybrid Becke's
three-parameter exchange functional [18] in combina-
tion with the Lee, Yang and Parr (LYP) correlation
functional [19]. Different basis sets were also tried:
the 6-31111G(3df,2pd) basis set as implemented in
gaussian 94 and the correlation consistent triple zeta
basis set of Dunning [20] supplemented by a single set
of d functions for sulfur whose exponent equals the
highest d exponent in the corresponding quintuple-
zeta basis set [21]. This basis set is denoted
VTZ 1 1. The best results were obtained at the
MP2/VTZ 1 1 level and were used for the subsequent
scaling.
The molecular potentials expressed in Cartesian
coordinates were transformed into non-redundant
local symmetry coordinates using the asym20
program [22]. The de®nitions of the internal coordi-
nates and the local symmetry coordinate set are
collected in Table 1. The geometric mean method of
Pulay et al. [13,14] was used to scale the theoretical
force constants to the experimental vibrational
frequencies given in Table 1. In the particular case
3
7
9
In total we assigned only 770 lines in n . Maximum
3
value of J is 53, and transitions with K in the interval
a
5±46 were observed. No asymmetry splitted lines
were found.
4
. Harmonic force ®eld
The Coriolis interaction between two vibrational
states is de®ned by the energy difference DE between
these two states and the Coriolis constant z (plus
higher order terms, if necessary). It is dif®cult to
determine experimentally these two parameters
because they are usually highly correlated. Fortu-
nately, the Coriolis constant only depends on the
harmonic force ®eld and thus can be accurately calcu-
lated provided that the force ®eld is known. There are
indeed several determinations of the force ®eld
available [7] but, as the number of experimental
data was small, they were obtained with many
assumptions, so that they are not accurate.
On the other hand, it is well established that ab
initio quantum mechanical methods may calculate
reliable harmonic force ®elds (even at the Hartree±
Fock level of theory) for fairly complex molecules
[
13,14]. With basis sets of modest size, there are
of SO F , a scale factor may be assigned to each
2 2

138
H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
Table 2
Experimental and calculated ground state quartic centrifugal distor-
tion constants (kHz) in S-reduction
number of fundamental vibrations, the scaled frequen-
cies are equal to the experimental ones. There is
however a way to check the accuracy of the force
®eld in comparing the experimental and calculated
quartic centrifugal distortion constants. These are
given in Table 2 and they are in almost perfect agree-
ment indicating that the scaled force ®eld given in
Table 3 is likely to be accurate.
a
Parameter
Experimental
Calculated
Difference (%)
DJ
1.4783
2 1.5293
1.85071.8264
2 0.0302
0.1372
1.4792
2 1.5032
1.31
2 0.06
1.71
DJK
DK
d
d
1
2 0.0302
0.1364
0.00
0.58
2
a
Ref. [1].
5. Simultaneous ®t of the n , n , n triad
3 7 9
frequency, and the diagonal force constants F and F
ii
Infrared transitions from each of the bands n , n ,
3 7
jj
are multiplied by c and c ; respectively; the geometric
i
j
and n ®t well using the standard Watson Hamiltonian
9
1=2
mean ꢀc c † is used for the coupling term F : This
in S-reduction. The standard deviation of individual
i
j
ij
21
method neglects the anharmonicity of the vibrations
but, in the particular case of SO F , their effect is
expected to be small.
®ts was typically around 0.00060 cm . No local
crossings seem to be present. For n the upper state
2
2
9
constants obtained were quite close to the ground state
values [2]. However, for n and n the quartic centri-
The choice of the reference geometry is important
for a correct scaling. The MP2/VTZ 1 1 geometry is
not expected to be reliable because the basis set is too
small and, furthermore, the MP2 method not
accurate enough. As reference geometry, we have
3
7
fugal distortion constant DJK and most of the sextic
constants deviate rather unacceptably much from the
ground state constants. For n , the difference DD is
3
JK
large and negative; for n its value is large and posi-
7
used the experimental r structure calculated from
0
tive. Together with the different sense of Q-branch
degradation observed for n and n , see Fig. 1, this
the rotational constants of the parent species and the
3
3
7
4
18 16
SO2F2 and S O OF :
two isotopic species
indicates a J-dependent perturbation, i.e. a Coriolis
resonance. From symmetry considerations c-Coriolis
interaction is possible between n and n .
2
r(SO) ˆ 140.0 pm, r(SF) ˆ 153.7pm, /(OSO) ˆ
1
25.138, and /(FSF) ˆ 95.368 [23]. This empirical
3
7
structure is believed to be a good approximation of
the equilibrium structure because the least-squares ®t
is well conditioned and SO F is a rigid molecule
The triad levels n , n , and n are rather isolated
3 7 9
from neighboring levels. The closest are the n , n
4
5
2
dyad at ca. 380 cm , and the triad consisting of
1
2
2
21
without light atoms. This assumption is con®rmed
by the determination of the average structure as well
as by high level ab initio calculations [23].
binary overtones from those levels at ca. 760 cm .
Thus, the triad n , n , n may be treated as an isolated
3
7
9
system to a good approximation. The Coriolis reso-
nances within this triad are shown in Fig. 4. For a
simultaneous analysis of n , n , and n we decided
As the number of scale factors is equal to the
3
7
9
to use a model including the ®rst order a-, b-, and c-
Coriolis interactions as depicted in Fig. 4. For each of
the triad levels we use the Watson Hamiltonian in S-
Table 3
2 2
Scaled ab initio MP2/VTZ 1 1 harmonic force ®eld of SO F (units
Ê
are consistent with aJ for energy, A for distances, and radians for
angles)
r
reduction and I -representation. In the ®t the Coriolis
coupling constants were ®xed to the values calculated
from our ab initio predicted harmonic force ®eld of
SO F as described in Section 4. The values of the
Coriolis coupling constants are given in Fig. 4. In
the model the following Coriolis resonance para-
meters appear
A
1
block
1.903
A
2
block
1.132
1
0
0
.228
.108
5.851
2 0.385
0.393
2 2
1.708
2
0.072
block
1.769
0.361
2 0.069
1.876
B
1
B
2
block
5.266
1
2
1.620
2 0.613
2.181
ꢀ
a†
ꢀa†
1=2
Z
ˆ z ꢀv 1 v †=ꢀv v †
:
r;s
r;s
r
s
r
s

H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
139
2
around 550 cm . The ®gure shows the situation and the symmetry of the levels in the n
1
Fig. 4. Vibrational energy levels of SO
2
F
2
3
, n
7
, n
Symmetry allowed Coriolis resonances around the a-, b-, and c-axis are indicated together with the band type in IR. Values of Coriolis coupling
9
triad.
constants calculated from an ab initio force ®eld are given in the ®gure.
2
1
The values of the Coriolis resonance parameters used
in the ®t are given in Table 4. The largest resonance
parameter is for the n ,n c-Coriolis interaction. This
perturbation is therefore the most important within the
triad as also indicated by our single band analyses.
Table 4 also includes the spectroscopic constants
obtained from our ®nal ®t. In the ®t we included
diagonal distortion constants up to octic order and
non-diagonal distortion constants up to sextic order,
was 0.000553 cm which seems to be reasonable as
compared to our estimated precision of 0.00010 cm
21
for selected and unblended high quality lines. For the
microwave and millimeter-wave lines a standard
deviation of 0.155 MHz was obtained which is ca.
three times higher than expected from the quality of
lines. For rotational lines with low J, i.e. J , 25;
deviations are small while the high-J millimeter-
wave lines show larger, systematic deviations. We
tried to introduce additional parameters to overcome
this but we have not been able to improve the ®t of
high J rotational lines in this way.
3
7
except for n where the addition of a single octic non-
7
diagonal constant improved the ®t further. For n we
7
included all ®ve diagonal octic constants, for the other
triad levels only some of them could be determined
with signi®cance.
The quartic centrifugal distortion constants
obtained are close to their ground state values for
most of the triad levels. The largest difference is for
the constant d for n and n which is ca. 10, respec-
In the ®t we used microwave, millimeter-wave, and
high resolution FTIR data for the triad. The IR data
were transformed to upper state energies by the
addition of the proper ground state energies calculated
from the ground state constants [2] to the observed
wavenumbers. The ®t was weighted. IR data were
1
7
3
tively, 50 times larger than the ground state value.
However, the sextic constants differ considerably
more from ground state values, up to a factor of
thousand. Together with the necessity to introduce
octic constants this indicates the presence of small
additional contributions due to Coriolis resonance.
Lists of observed and calculated microwave and
millimeter-wave frequencies and infrared transition
wavenumbers have been deposited as supplementary
material. This list may be obtained from Fachinfor-
mationszentrum Karlsruhe, D-76344 Eggenstein±
Leopoldshafen, Germany, on submission of the
26
uniformly weighted and given a weight of 10 as
compared to a typical microwave weight corre-
sponding to the higher precision of microwave data
3
of a factor of ca. 10 as compared to infrared data.
Microwave and millimeter-wave data were given indi-
vidual weights re¯ecting line quality. The ®t was
performed using the program system of Pickett [24].
For the IR transitions the standard deviation of ®t

140
H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
Table 4
Vibrational, rotational, centrifugal distortion, Coriolis coupling parameters (cm ), and statistical data for the n
2
1
3
7 9 2 2
, n , n triad of SO F . S-
r
reduction, I -representation (one standard error in parentheses; these errors do not account for systematic errors, which may be signi®cantly
larger)
GS
n
3
n
7
n
9
A
B
C
D
D
0.171281099
0.171480543(87)
0.169388249(14)
0.168394400(14)
5.7456(45)
2 7.292(15)
7.457(19)
0.171215234(31)
0.1692879566(94)
0.1688481105(96)
4.6899(30)
2 4.5154(91)
5.8729(64)
2 0.9752(25)
1.1571(21)
2 359.5(39)
800(13)
0.171359923(22)
0.169452113(11)
0.168744956(11)
4.7269(18)
0.169219650
0.168685233
8
J
£ 10
4.93029
2 5.0958
6.1723
2 0.10039
0.45750
0.99
8
£ 10
2 5.0292(45)
6.3259(33)
JK
8
DK £ 10
8
d
d
1
£ 10
£ 10
2 4.9201(78)
0.1403(78)
557.0(67)
2 0.2673(24)
0.17860(88)
50.3(11)
8
2
1
4
H £ 10
J
1
4
H
JK
£ 10
3.16
1.20
2 1882(25)
1417(32)
21.8(26)
2 149.0(29)
78.9(97)
1
4
HKJ £ 10
2 535(16)
99.4(70)
1
4
HK £ 10
2 2.88
1.77
2 225(11)
628(13)
1
1
1
4
4
4
h
1
h
2
h
3
£ 10
£ 10
£ 10
308.7(31)
23.46(97)
a
0.368
0.368
2 2.187
±
72(13)
2 2.187
2 91.0(24)
2 21.91(66)
443(13)
a
9.86(25)
15.6(26)
2 130.8(41)
±
1
8
L
JJJJ
£ 10
2 1082(17)
3836(60)
2 2465(61)
1
8
L
JJJK £ 10
±
2 1478(53)
1666(92)
1
8
LJJKK £ 10
±
1
8
LJKKK £ 10
LKKKK £ 10
±
±
2 806(70)
176(20)
319.9(41)
2 204.7(24)
2
1
8
±
±
1
8
l
1
£ 10
±
0.0
±
551.642805(12)
2 237.6(65)
544.1379225(94)
n
0
c
539.1413440(54)
b
Z
Z
Z
K
N
s
s
3,7
b
3,9
a
0.0891
b
0.0577
b
0.028
7,9
max max
/J
c
c
c
a
46/53
80/84
84/86
c
c
c
IR/NMW
IR £ 10
770/146
1575/200
2461/153
3
0.553
d
155
MW
a
Constrained to ground state values.
b
c
d
Constrained to values from ab initio calculations.
Dimensionless.
Value in kHz.
names of the authors, the literature reference, and the
registry number 10099.
places correctly n as the highest member of the triad.
3
However, our investigation shows that the assignment
of n and n [8] has to be interchanged with n being
the lowest fundamental of the triad.
7
9
9
6
. Discussion
The spectroscopic constants obtained from our
present triad analysis are given in Table 4. For all
three levels the order A . B . C is maintained in
spite of the closeness of rotational constants, particu-
larly of B and C. Some of the higher order constants
are effective parameters in the sense that they may
compensate de®ciencies of our present Coriolis
model essentially based on the ab initio harmonic
force ®eld. In our present study microwave,
An unambiguous vibrational assignment of the
21
triad around 550 cm of SO F has been established
2
2
from high-resolution IR spectra. In Ref. [6] a tentative
vibrational assignment was proposed which was used
to determine the force ®eld of SO F in Ref. [7]. Our
2
2
present study shows that the assignment [6] of n and
3
n7 has to be inverted. The solid state Raman work [8]

H. B uÈ rger et al. / Journal of Molecular Structure 612 (2002) 133±141
141
Table 5
Vibrational band centers and a-constants for the n
References
3
7 9
, n , n triad of
21
SO
2
F
2
. (cm )
[
1] K. Sarka, J. Demaison, L. Margul eÁ s, I. Merke, N. Heineking,
H. B uÈ rger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55.
2] H. B uÈ rger, H. Ruland, I. Merke, K. Sarka, L. Margul eÁ s,
J. Demaison, J. Mol. Spectrosc. 203 (2000) 268.
n
3
n
7
n
9
[
a
n
0
551.6428(10
544.1379(10)
0.65865(31)
539.1413(10)
2 0.78824(22)
2 2.32463(11)
2 0.59723(11)
A
B
C
4
b
[3] R.M. Fristrom, J. Chem. Phys. 20 (1952) 1.
[4] D.R. Lide, D.E. Mann, R.M. Fristrom, J. Chem. Phys. 26
(1957) 734.
a
a
a
£ 10
£ 10
£ 10
2 1.99444(87)
2 1.68599(14)
2.90833(14)
4
4
2 0.68307(9)
2 1.62878(10)
[
5] W.D. Perkin, M.K. Wilson, J. Chem. Phys. 20 (1952) 1791.
a
Error quoted for n
Errors quoted for the as are standard errors.
0
is estimated wavenumber accuracy.
[6] D.R. Lide, D.E. Mann, J.J. Comeford, Spectrochim. Acta 21
(1965) 497.
b
[
7] R.A. Suthers, T. Henshall, Z. Anorg, Allg. Chem. 388 (1972)
57.
[8] A. Kornath, J. Mol. Spectrosc. 188 (1998) 63.
9] R. Paso, V.-M. Horneman, J. Opt. Soc. Am. B12 (1995) 1813.
2
millimeter-wave and infrared data are analyzed simul-
taneously. Such an analysis results in highly precise
rotation and centrifugal distortion constants for the
triad levels. These constants are useful for our
ongoing analysis of other fundamental bands of
SO F .
[
[
[
10] U. Andresen, H. Dreizler, J.-U. Grabow, W. Stahl, Rev. Sci.
Instrum. 61 (1990) 3694.
11] I. Merke, W. Stahl, H. Dreizler, Z. Naturforsch A: Phys. Sci.
4
9 (1994) 490.
2
2
[12] I. Merke, to be published.
[
13] G. Fogarasi, P. Pulay, in: J.R. Durig (Ed.), Vibrational Spectra
and Structure, vol. 14, Elsevier, Amsterdam, 1985, p. 125.
14] P. Pulay, Adv. Chem. Phys. 69 (1987) 241.
Table 5 summarizes the vibrational band centers of
the triad together with the vibrational dependence of
the rotational constants. These data are useful for
future comparisons with spectroscopic constants
calculated from ab initio anharmonic force ®elds,
and for the determination of the structure of SO F .
Since we have used a model accounting for the ®rst
order Coriolis interactions within the triad to obtain
spectroscopic constants, most resonance contributions
are absent from the rovibrational parameters given in
Tables 4 and 5.
[
[
15] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G.
Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A.
Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-
Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman,
J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challa-
combe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L.
Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox,
J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-
Gordon, C. Gonzalez, J.A. Pople, gaussian 94, Revision E.2,
Gaussian, Inc., Pittsburgh PA, 1995.
2
2
[
[
16] C. Mùller, M.S. Plesset, Phys. Rev. 46 (1934) 618.
17] J.M. Seminario, P. Polizer (Eds.), Modern Density Functional
Theory. A Tool for Chemistry Elsevier, Ansterdam, 1995.
18] D. Becke, J. Chem. Phys. 98 (1993) 5648.
Acknowledgements
[
[
[
[
[
19] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B41 (1988) 785.
20] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.
21] D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358.
22] L. Hedberg, I.M. Mills, J. Mol. Spectrosc. 203 (2000) 82.
This work has been supported by the French/
German PICS program (599). We thank the Fonds
der Chemie and the Deutsche Forschungsge-
meinschaft for ®nancial support. Dr H. Ruland is
thanked for help in obtaining the IR spectrum. F.H.
thanks Mrs G. Nathansen for assistance in the assign-
ment procedure for IR spectra.
[23] I. Merke, N. Heineking, J. Demaison, to be published.
[24] H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371.