Gas-phase structure and vibrational properties of trifluoromethyl trifluoromethanesulfonate, CF3SO2OCF3

Article abstract of DOI:10.1002/ejic.200600940

Trifluoromethyl trifluoromethanesulfonate, CF₃SO ₂OCF₃, has been synthesised and its gas-phase structure determined from electron-diffraction data. This structural study was supported by HF, MP2 and DFT (B3LYP and B1B95) calculations, which revealed a strong dependence of the theoretical structure on the polarisation of the basis set. Infrared spectra for the gas and solid and a Raman spectrum for the liquid were obtained, and the observed bands were assigned. The experimental vibrational data, along with theoretical (B3LYP) force constants, were used to define a scaled quantum mechanical force field, which enabled reproduction of the measured frequencies with a final root-mean-square deviation of 6 cm ^-1. Wiley-VCH Verlag GmbH & Co. KGaA, 2007.

Full text of DOI:10.1002/ejic.200600940

FULL PAPER
DOI: 10.1002/ejic.200600940
Gas-Phase Structure and Vibrational Properties of Trifluoromethyl
Trifluoromethanesulfonate, CF3SO2OCF3
María E. Tuttolomondo,[a] Pablo E. Argañaraz,[a] Eduardo L. Varetti,[b][‡] Stuart A. Hayes,[c]
Derek A. Wann,[c] Heather E. Robertson,[c] David W. H. Rankin,[c] and
Aida Ben Altabef*[a][‡]
Keywords: Electron diffraction / IR spectroscopy / Raman spectroscopy / Structure elucidation / Ab initio calculations
Trifluoromethyl trifluoromethanesulfonate, CF3SO2OCF3,
has been synthesised and its gas-phase structure determined
from electron-diffraction data. This structural study was sup-
ported by HF, MP2 and DFT (B3LYP and B1B95) calculations,
which revealed a strong dependence of the theoretical struc-
ture on the polarisation of the basis set. Infrared spectra for
the gas and solid and a Raman spectrum for the liquid were
obtained, and the observed bands were assigned. The exper-
imental vibrational data, along with theoretical (B3LYP) force
constants, were used to define a scaled quantum mechanical
force field, which enabled reproduction of the measured fre-
quencies with a final root-mean-square deviation of 6 cm–1
.
(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim,
Germany, 2007)
the experimental results previously obtained for
Introduction
[5]
CF3SO2OCH3 and ClSO2OCF3,[9] and with those calcu-
The synthesis of trifluoromethyl trifluoromethanesulfon-
ate, CF3SO2OCF3, was first reported by Noftle and Cady[1]
as a product of the thermal decomposition of (CF3SO2)2O.
Different synthetic routes were later proposed by Olah and
Ohyama,[2] Kobayashi et al.[3] and Hassani et al.,[4] but no
structural or vibrational studies have been reported.
lated for several CF3SO2X[6] and CF3SO2OX[7,8] molecules,
which shows that covalent sulfonates prefer a gauche con-
formation (Figure 1).[5]
Our previous studies on derivatives of trifluoromethane-
sulfonic acid[5–8] have been extended to CF3SO2OCF3 in or-
der to investigate further the characteristic conformations
and force constants for such molecules. For that purpose,
the substance has been synthesised and its gas-phase struc-
ture determined by electron diffraction. Additionally, infra-
red and Raman spectra were recorded for different physical
states. These experimental measurements were comple-
mented by quantum chemical calculations to obtain an op-
timised molecular structure and frequencies corresponding
to the normal modes of vibration. Of particular interest is
the comparison of the experimental and theoretical molecu-
lar geometric parameters and conformational isomers with
Figure 1. Molecular structure of CF3SO2OCF3, showing atom
numbering.
Results and Discussion
[a] Instituto de Química Física, Facultad de Bioquímica, Química
y Farmacia, Universidad Nacional de Tucumán,
San Lorenzo 456, 4000 Tucumán, R. Argentina
E-mail: altabef@fbqf.unt.edu.ar
Theoretical Study
A starting geometry for CF3SO2OCF3 was obtained by
using RHF theory with a 3-21G(d) basis set[10–12] followed
by a 6-31G(d) basis set.[13–15] Electron correlation was then
accounted for by using the MP2,[16] B3LYP[17] and
B1B95[18] methods before increasing the basis set sequen-
tially from 6-31G(d) to 6-311+G(d).[19,20] In addition, the
6-31G(3df) basis set,[21] the Dunning correlation-consistent
basis sets, cc-pVDZ and cc-pVTZ[22] and Ahlrichs’
TZVP[23] and TZVPP[24] basis sets were used to gauge the
[b] Centro de Química Inorgánica (CEQUINOR, CONICET-
UNLP), Departamento de Química, Facultad de Ciencias Ex-
actas, Universidad Nacional de La Plata,
C. Correo 962, 1900 La Plata, R. Argentina
[c] School of Chemistry, University of Edinburgh,
West Mains Road, Edinburgh, EH9 3JJ, UK
E-mail: d.w.h.rankin@ed.ac.uk
[‡] Members of the Carrera del Investigador Científico, CON-
ICET, R. Argentina
Supporting information for this article is available on the
WWW under http://www.eurjic.org or from the author.
Eur. J. Inorg. Chem. 2007, 1381–1389
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1381

A. Ben Altabef et al.
FULL PAPER
effect of including further polarisation functions. The re-
sults of the geometry optimisations are available in
Tables S1 and S2 in the Supporting Information. In all
cases, a molecular structure with C1 symmetry was pre-
dicted, as shown in Figure 1. The force field obtained at
the RHF/6-31G(d) level was then used with the program
SHRINK[25] to obtain estimates of the amplitudes of vi-
bration (uh1) and perpendicular vibrational correction
terms (kh1) used in the gas electron diffraction (GED) re-
finement.
Scans of the potential energy with respect to the C–S–
O–C torsion were performed at the RHF/6-31G(d) and
MP2/6-31G(d) levels and a third scan at the MP2/6-31G(d)
level with the 6-31G(3df) basis set on sulfur (Figure 2).
These reveal two symmetrically equivalent minima, corre-
sponding to enantiomers, and O–C(5) eclipses one or other
of the S=O bonds when viewed down the S–O(4) bond. As
enantiomers are indistinguishable by GED, the subsequent
refinement was performed with the eclipsing of the S=O(3)
bond by O–C as in the calculated structures. The shallow
barrier between the two equivalent conformers is ca. 5–
10 kJmol–1, easily surmountable at the experimental tem-
peratures. The quantum chemical calculations predict the
existence of two stable, asymmetric (point group C1) and
structurally equivalent conformers for CF3SO2OCF3, both
with a gauche conformation with a C–S–O–C dihedral an-
gle of about 110°. As shown in Table 1, this angle is rela-
tively sensitive to changes in method and basis set and has a
Figure 2. Torsional potential around the S–O(4) bond for
CF3SO2OCF3, stepped in 5° increments. Calculations were per-
formed at the HF (light grey) and MP2 (dark grey) levels by using
a 6-31G(d) basis set and by using MP2/6-31G(d) with 3df polarisa-
tion on sulfur (black).
this in mind, the MP2/6-31G(3df) geometry appeared to be
the best as both a starting point for the GED refinement
and the basis for geometrical restraints.
GED Model
The molecular model for the GED refinement assumed
larger value than that calculated for CF3SO2OCH3 (93°).[5] overall C1 symmetry (Figure 1), as predicted by the calcula-
Similar molecules that were previously studied by us were tions. The structure of CF3SO2OCF3 was defined in terms
also calculated to have gauche conformations, with C–S–O– of 25 independent parameters, comprising 11 bond lengths
[7]
C dihedral angles of 114.8° in CF3SO2OCH2CF3 and and differences, 10 bond angles and differences, one tilt an-
[8]
91.5° in CF3SO2OCH2CH3 [B3LYP/6-31G(d) values in gle and three torsional angles, listed in Table 2. The bonded
both cases].
distances S–O(4), O(4)–C(5) and S–C(9) were each defined
The calculated C–O and C–F bond lengths converged individually (p7, p10 and p11, respectively), whilst simple
reasonably well with increasing basis set size and showed averages were taken of the six C–F bond lengths (p1) and
fairly good agreement between different post-Hartree–Fock of the two S=O bond lengths (p8). The difference between
methods, as shown in Table 1. Bond lengths to sulfur, how- the average C–F distance in the CF3 group bonded to O(4)
ever, are extremely sensitive to both method and basis set. (group 1) and the average C–F distance in the CF3 group
Particularly interesting was the result of adding additional bonded directly to the sulfur atom (group 2) was defined
polarisation functions to the basis set, which resulted in (p2). For CF3 in group 1, the C–F(6) distance was then
shortening of the bond lengths, the most significant is a found by defining the difference between this distance and
reduction of 5.5 pm for the S–O bond [MP2/6-31G(d) to the average of the C–F(7) and C–F(8) bond lengths (p3).
MP2/6-31G(3df)].
The difference between the latter two bond lengths was then
defined (p5). Similarly, in group 2, the difference between
[5]
With reference to structural studies on CF3SO2OCH3
and ClSO2OCF3,[9] the bond lengths to sulfur were overesti- the C–F(11) distance and an average of the other two bond
mated by B3LYP relative to those obtained by GED and lengths (p4) and the difference between the C–F(12) bond
X-ray crystal values (the latter for ClSO2OCF3 only). With length and the C–F(10) bond length (p6) were defined. The
Table 1. Selected calculated and GED geometrical parameters for CF3SO2OCF3 (distances in pm, angles in º).
GED
HF/
6-31G(d)
MP2/
6-31G(d)
B3LYP/
6-31G(3df) 6-31G(3df)
B1B95/
6-311+G(d)
6-31G(3df)
cc-pVTZ
TZVPP
rC–F average
rS–O
rS=O average
rC–O
rC–S
φC–S–O–C
133.3(2)
161.5(4)
141.9(3)
139.3(7)
181.3(4)
119.5(18)
130.2
160.3
140.9
137.4
182.1
111.2
133.3
167.7
144.7
139.3
184.5
108.4
132.5
167.1
143.4
138.5
186.3
110.7
131.9
162.2
141.9
139.0
183.8
105.6
132.1
163.9
143.1
139.1
185.4
108.2
132.1
163.8
143.1
139.0
185.6
108.6
132.6
163.6
142.0
139.5
187.4
105.8
131.8
161.8
141.4
138.9
185.1
107.5
1382
www.eurjic.org
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Inorg. Chem. 2007, 1381–1389

Gas-Phase Structure and Vibrational Properties of CF3SO2OCF3
FULL PAPER
difference between the two S=O double bond lengths (p9) are equal. This group was also allowed to rotate around the
allowed these bond lengths to be defined.
S–C bond, defined by the torsional angle O(4)–S–C–F(11)
(p25). In this case, an angle of 180° corresponds to a stag-
gered conformation and a larger angle brings F(11) closer
to O(3).
Table 2. GED refined parameters (rh1 structure) for CF3SO2OCF3
(distances in pm, angles in degrees).
Description
Value
MP2/
Restraint
6-31G(3df) uncertainty[a]
Independent parameters
p1 rC–F average
Electron Diffraction Refinement
133.3(2)
–0.4(1)
0.4(1)
0.2(1)
0.2(1)
131.9
–0.4
0.4
0.2
0.2
p2 rC–F difference 1
p3 rC–F difference 2
p4 rC–F difference 3
p5 rC–F difference 4
p6 rC–F difference 5
p7 rS–O
p8 rS=O average
p9 rS–O difference
p10 rC–O
0.1
0.1
0.1
0.1
0.1
The GED refinement (Table 3) was carried out with the
SARACEN method,[26] which allows parameters that are
poorly defined by GED data alone to be restrained to cal-
culated values with specified uncertainties, on the basis of
the degree of convergence of the calculations. Distances
were corrected for curvilinear perpendicular motion (kh1)
and yielded rh1 parameters.[25] All 25 independent param-
eters were refined, along with two individual and eight
groups of amplitudes of vibration, to produce an RG factor
of 0.067 (RD = 0.029). The refined parameters are displayed
in Table 2 along with the corresponding values predicted by
MP2/6-31G(3df) calculations. The radial-distribution curve
is shown in Figure 3, and the molecular-scattering intensity
curve is provided as Supporting Information (Figure S1).
0.0(1)
0.0
161.5(4)
141.9(3)
0.4(1)
139.3(7)
181.3(4)
96.9(10)
108.0(2)
3.8(4)
107.9(3)
1.3(2)
121.8(4)
104.6(4)
108.0(2)
162.2
141.9
0.4
139.0
183.8
97.0
108.0
4.4
107.6
1.3
121.3
105.8
109.3
0.4
0.1
p11 rC–S
p12 ЄO(4)–S–C
1.0
0.5
p13 ЄO–S–O(4) average
p14 ЄO–S–O(4) difference
p15 ЄC–S–O average
p16 ЄC–S–O difference
p17 ЄS–O–C
p18 ЄO–C–F(6)
p19 ЄF–C–F group 1 average
p20 ЄF–C–F group 1 difference 0.3(2)
p21 ЄS–C–F tilt
0.2
0.5
0.2
0.5
1.6(5)
1.6
p22 ЄF–C–F group 2
p23 φC–S–O–C
p24 φS–O–C–F(6)
p25 φO–S–C–F(11)
Dependent parameter
d1 ЄO(2)=S=O(3)
108.6(2)
109.8
119.5(18) 105.6
195.2(9) 182.6
177.2(10) 178.5
2.0
1.0
124.6(8)
125.1
[a] Restraint values are given by the corresponding MP2/6-
31G(3df) values.
The geometry around sulfur was described using three
angles and two differences: the O(4)–S–C(9) angle (p12), the
average of the O(2)–S–O(4) and O(3)–S–O(4) angles (p13)
and their difference (p14), and the average of the O(2)–S–
C(9) and O(3)–S–C(9) angles (p15) and their difference (p16).
Fluorine atom positions in CF3 in group 1 were de-
scribed by using the average of the three internal F–C–F
angles (p19) and the difference between the F(7)–C–F(8) an-
gle and the angles F(6)–C–F(7) and F(6)–C–F(8) (p20), the
latter two angles are assumed to be identical. The orienta-
tion of this CF3 group with respect to sulfur was defined
by using the angles S–O–C (p17) and O–C–F(6) (p18), and
Figure 3. Experimental and difference (experimental – theoretical)
radial-distribution curves, P(r)/r, for CF3SO2OCF3. Before Fourier
inversion, the data were multiplied by sϫexp[(–0.00002s2)/(ZS
fS)(ZF – fF)].
–
Where required, restraints on geometrical parameters
the torsional angles C–S–O–C (p23) and S–O–C–F(6) (p24). were derived from the MP2/6-31G(3df) calculated values.
CF3 in group 2 was described by using a single F–C–F Those applied directly to independent or dependent param-
angle (p22) and orientated by using a tilt angle (p21). A posi- eters are given in Table 2, whilst restraints on the differences
tive tilt was defined as a reduction in the S–C–F(11) angle, between independent parameters are provided in Table 3.
with the zero point occurring when the three S–C–F angles The only group of amplitudes of vibration allowed to refine
Table 3. Restraints on differences between pairs of independent parameters (distances in pm, angles in degrees).
Difference
GED[a]
MP2/6-31G(3df)
Uncertainty[b]
p10 – p1
p13 – p15
p22 – p19
p19 – p18
[rC–O] – [rC–F average]
6.1(8)
0.1(2)
0.5(2)
3.5(5)
7.0
0.3
0.5
3.5
1.0
0.2
0.2
0.5
[ЄO–S–O(4) average] – [ЄC–S–O average]
[ЄF–C–F group 2] – [ЄF–C–F group 1 average]
[ЄF–C–F group 1 average] – [ЄO–C–F(6)]
[a] Refined value. [b] Restraint values are given by the corresponding MP2/6-31G(3df) values.
Eur. J. Inorg. Chem. 2007, 1381–1389
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjic.org
1383

A. Ben Altabef et al.
FULL PAPER
unrestrained was that containing the bonded distances of mate the S–O bond length by just 2.4 and 2.3 pm, respec-
less than 150 pm. The remaining amplitudes for bonded tively, relative to the GED determined value of 161.5(4) pm.
atom pairs were restrained with uncertainties of 10% of Similar observations can also be made for the S=O and S–
their calculated values, whilst the groups of non-bonded C bond lengths, albeit to a lesser extent.
amplitudes were restrained with uncertainties of 20%. A
The C–S–O–C torsional angle was found to be 119.5(18)°
full list of interatomic distances and corresponding calcu- by GED relative to between 105 and 112° by various theo-
lated and refined amplitudes of vibration are provided in retical methods. However, the estimated standard deviation
Table S3 (Supporting Information), and the least-squares of this value does not give a good estimate of its uncer-
correlation matrix in Table S4.
tainty, as the refinement can be performed by fixing this
angle at any arbitrary value between 100 and 150° without
significantly affecting the remaining parameters or the RG
factor. It would, in principle, be possible to replace the rigid
model adopted in the refinement by a dynamic model based
GED and Calculated Structures
Two large discrepancies can be seen between the GED on the potential function of the C–S–O–C torsion. How-
and calculated structures: the S–C bond length and the tor- ever, it can be seen from the theoretical potential energy
sional angles, particularly C–S–O–C. The S–C distance is scan (Figure 2) that this potential energy curve is not a sim-
2.5 pm shorter than that predicted by MP2/6-31G(3df) cal- ple function, and several parameters would be required to
culations. However, the S–O bond length, which for similar model it. In such cases, the uncertainties of the extra pa-
compounds is generally poorly defined by theory, is only rameters are extremely large, and so the refined values are
0.7 pm shorter experimentally. The MP2/6-31G(3df) calcu- of little physical significance. We therefore did not use such
lation is thus significantly more accurate for predicting a dynamic model in this case.
these bond lengths than other methods or basis sets requir-
ing similar computational resources. For instance, the MP2/
6-311+G(d) calculation overestimates the S–O and S–C dis- Vibrational Study
tances by 5.6 and 3.0 pm, respectively, and B3LYP/6-
CF3SO2OCF3 has C1 symmetry, and therefore its 30 nor-
31G(3df) underestimates the same bond lengths by 2.0 and
mal modes of vibration are active in the IR and Raman
6.1 pm, respectively. The B1B95/6-31G(3df) calculation pre-
spectra. Representative spectra appear in Figures 4 (IR
spectra of the gas and solid) and 5 (Raman spectrum of the
liquid), and the frequencies for the observed spectral fea-
tures are collated in Table 4.
dicts parameter values that are similar to those predicted
by MP2, overestimating the respective S–O and S–C dis-
tances by 0.3 and 3.8 pm, respectively, relative to the GED
values. MP2 and B1B95 are therefore marginally better
than B3LYP at describing the geometry of CF3SO2OCF3,
and for this type of compound, B1B95 is likely be the best
compromise between accuracy and computational cost.
Comparison of these results with parameters for similar
[5]
compounds CF3SO2OCH3 and FSO2OSF5,[27] studied by
GED and B3LYP/6-31G(d) calculations, shows that in these
cases, despite the reasonably close agreement between dif-
ferent theoretical methods, the experimental S–O bonds are
5–7 pm shorter. In the case of CF3SO2OCH3,[5] the experi-
mentally determined S–C bond is 3.3 pm shorter. The study
on ClSO2OCF3[9] also shows that B3LYP/6-311G(d) under-
estimates the S–O bond length by 6 to 7 pm, but the
B3LYP/6-311+G(3df) calculation reduces this difference to
ca. 3 pm. These GED and theoretical results are therefore
consistent with the more general observation that distances
Figure 4. Infrared spectra for CF3SO2OCF3 in the gas phase (upper
between sulfur and oxygen are poorly predicted with stan-
trace; resolution 2 cm–1, path length 10 cm, pressure ca. 1.0 Torr)
dard methods [such as MP2/6-31G(d)], and indicate that
and in the solid phase (lower trace; film on cooled KBr window,
resolution 2 cm–1). Asterisks indicate solid SO2 bands.
this may be due primarily to insufficient polarisation func-
tions in the basis set. This conclusion is also consistent with
the molecular structures calculated at the MP2 level by
The B3LYP calculations reproduced the normal fre-
using Dunning’s cc-pVDZ and cc-pVTZ, and Ahlrichs’ quencies of vibration with the following root-mean-square-
TZVP and TZVPP basis sets (Table S2). As was the case deviation (RMSD) values for each basis set: 19.8 cm–1 for
for the Pople 6-31G(d) basis set, the cc-pVDZ and TZVP 6-31G(d), 21.6 cm–1 for 6-311G(d) and 27.1 cm–1 for 6-
bases contain only a single d-type Gaussian and underesti- 311+G(d). The first and second basis sets reproduce the
mate the S–O bond length by 8.9 and 6.6 pm, respectively. experimental frequencies somewhat better, and the results
In contrast, the cc-pVTZ and TZVPP bases, which both obtained with the 6-31G(d) basis set were used for the vi-
incorporate two d-type and one f-type Gaussian, underesti- brational analysis, in order to allow direct comparison with
1384
www.eurjic.org
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Inorg. Chem. 2007, 1381–1389

Gas-Phase Structure and Vibrational Properties of CF3SO2OCF3
FULL PAPER
The proposed assignments of spectral features to the dif-
ferent modes of vibration given in Table 4 are based on the
calculated frequencies and on the infrared and Raman in-
tensities and also on comparisons with known data for re-
lated molecules.
SO2 Group Modes
The SO2 antisymmetric and symmetric stretching modes
appear in the regions 1357–1467 cm–1 and 1140–1157 cm–1,
respectively, in the molecules CF3SO2X (X = F, OH, NH2,
CH3, OCH2CH3, OCH2CF3).[6–8] The intense bands ob-
served at 1469 and 1139 cm–1 in the spectrum of the gas
can therefore immediately be assigned to these modes. The
last mode, however, is a complex mix of several simple vi-
brations, as discussed below. The medium intensity band at
586 cm–1 in the gas infrared spectrum is assigned to the SO2
bend. This frequency is somewhat higher than usual, as this
mode appears in the region 488–538 cm–1 in the compounds
listed above. The bands for the three modes corresponding
to the movements of the whole SO2 group appear at rela-
tively low frequencies. The following assignments are pro-
posed, with the corresponding frequency ranges for the
molecules mentioned above in parentheses: SO2 wagging,
606 cm–1 (611–628 cm–1); SO2 rocking, 394 cm–1 (382–
463 cm–1); SO2 twisting, 300 cm–1 (310–351 cm–1). These as-
signments are also supported by the calculations.
Figure 5. Raman spectrum for liquid CF3SO2OCF3 (resolution
4 cm–1).
Table 4. Frequencies of observed bands in the infrared and Raman
spectra of CF3SO2OCF3 (units are cm–1).[a]
Infrared
Raman[b]
Mode assignment
Gas
1469 (s)
Solid
1458 (s)
Liquid
1458 (3)
1342 (3)
ν1
?
1327 (vs)
1277 (s)
1268 (vs)
1266 (vs)
1246 (vs)
1228 (s)
1221 (vs)
1144 (vs)
1140 (vs)
1119 (s)
952 (s)
SO2
ν2
ν3
ν4
ν5, ν6
1282 (s)
1268 (vs)
1268 (20)
Trifluoromethyl Group Modes
1236 (vs)
Inspection of the atomic displacements for the vi-
brational modes calculated in the 1100–1300 cm–1 region
shows that the stretching vibrations, especially the symmet-
ric stretches, of the two CF3 groups are strongly coupled.
For this reason it is not possible to discuss the assignments
of bands for these two groups separately.
1150 (sh.)
1139 (vs)
1146 (100)
952 (2)
ν7
ν8
SO2
ν9
?
956 (s)
816 (m)
792 (m)
766 (w)
796 (m)
767 (m)
695 (vw)
628 (m)
606 (m)
584 (m)
794 (2)
766 (60)
ν10
ν11
ν12
ν13
ν14
ν15
ν16
ν17
?
ν18
ν19
ν20
ν21
ν22
ν23
ν24
ν25
ν26
ν27
The two CF3 symmetric modes are predicted to have
large Raman intensities. One mode includes the symmetric
stretches of the two CF3 groups, coupled with contributions
from the CS and CO stretches and the SO2 symmetric
stretch; the latter is out of phase in relation to the other
four. The second mode mixes the same five simple vi-
brations, but with the SO2 symmetric stretch now in phase.
These two complex modes are assigned to the strong Ra-
man bands located at 1268 and 1146 cm–1. The 1146 cm–1
band exhibits a shoulder at ca. 1120 cm–1, best defined in
the infrared spectrum of the solid, and is assigned to a third
mode, which also mixes the two CF3 symmetric stretching
vibrations and the CO and CS stretches in an out-of-phase
fashion, but with almost no participation of the SO2 sym-
metric stretch. Four bands should still be assigned to the
CF3 antisymmetric stretching vibrations. As not enough ar-
guments are available for precise assignments, those appear-
ing in Table 4 and Table 5 are tentative.
627 (m)
606 (m)
586 (w)
603 (vvw)
584 (6)
560 (3)
542 (5)
520 (3)
509 (3)
445 (vvw)
394 (9)
345 (19)
320 (15)
300 (11)
280 (23)
200 (1, br.)
172 (4)
540 (vw)
508 (w)
542 (w)
522 (m)
508 (w)
444 (vvw)
150 (sh.
[a] s = strong, m = medium, w = weak, v = very, sh. = shoulder,
br. = broad. [b] For the Raman spectrum, relative band heights are
given in parentheses.
Symmetric deformation modes are observed at 792 cm–1
(CF3S group) and 695 cm–1 (CF3O group) in the gas infra-
calculations performed previously for related molecules. red spectra. The two antisymmetric deformation modes of
The calculated frequencies of vibration appear in Table 5, the SCF3 group appear at 540 and 560 cm–1, i.e. about
together with the experimental values.
10 cm–1 higher than the calculated values. The antisymmet-
Eur. J. Inorg. Chem. 2007, 1381–1389
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjic.org
1385

A. Ben Altabef et al.
Table 5. Observed and calculated frequencies, infrared and Raman intensities and potential-energy distribution for CF3SO2OCF3.
FULL PAPER
Mode
Observed
Calculated[a]
Calculated SQM[b] IR intensity[c] Raman activity[d]
Potential-energy distribution[e]
1
2
3
4
5
6
7
8
1469
1282
1268
1266
1236
1236
1150
1139
956
792
766
695
627
606
586
560
540
508
444
394
345
320
300
280
200
172
150
–
1414
1304
1242
1293
1283
1264
1116
1144
933
777
737
682
613
588
567
549
526
487
430
380
325
304
275
263
185
158
145
66
1461
1283
1272
1263
1247
1233
1152
1142
937
795
756
696
634
610
589
559
536
502
453
397
341
319
289
277
195
170
154
67
287
48
3.6
9.1
0.86
0.52
0.64
2.1
6.4
2.2
1.0
1.5
16.0
0.53
0.47
0.60
3.0
2.2
2.9
1.3
0.17
2.2
4.8
3.6
2.6
3.8
0.25
0.44
0.26
0.04
0.01
0.01
96S1
54S2 + 20S8 + 11S21
31S2 + 10S7 + 25S8
30S4 + 10S5 + 51S6 + 12S13 + 11S19
51S4 + 40S5
308
212
334
515
238
280
137
26
105
3.87
66
114
38
16S4 + 46S5 + 31S6
21S3 + 31S7 + 29S9 + 22S10 + 24S12 + 13S22
15S3 + 12S7 + 44S8 + 36S9 + 20S12
28S3 + 31S9 + 23S11
37S7 + 17S10 + 14S22
21S3 + 39S11 + 12S21
12S3 + 24S12 + 15S26
12S6 + 12S13 + 19S14 + 19S19
12S10 + 12S12 + 16S13 + 30S14
38S15 + 10S17
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
RMSD
0.37
29
20
54S16
45S17 + 17S18
19S15 + 12S17 + 49S18
49S13 + 57S19
21S16 + 36S20 + 21S25
18S11 + 28S15 + 25S21 + 14S27
10S11 + 12S14 + 14S21 + 17S22 + 16S24
39S23 + 17S25
23S22 + 36S24
34S20 + 49S23 + 56S25
56S56 + 23S27
1.90
3.94
1.05
1.05
1.37
5.50
2.03
1.07
1.31
0.15
0.15
0.03
28S24 + 19S26 + 86S27 + 12S28 + 15S29
–
–
–
–
51
36
19.8
51
36
6.04
–
[a] B3LYP/6-31G* calculation. Observed and calculated values in cm–1. [b] From scaled quantum mechanics force field (see text for
further definition). [c] Units are kmmol–1. [d] Units are Å4 (amu)–1. [e] See Table 6 for definitions of natural symmetry coordinates.
ric deformation modes of the CF3O group show a larger Torsional Modes
splitting, appearing at 508 and 627 cm–1.
Very weak spectral features were expected for the three
The CF3 rocking modes were assigned by taking into ac-
torsional modes and, in fact, no bands could be identified
count the theoretically predicted frequencies and with
to be assigned to these modes.
knowledge of modes in related molecules. In this way, the
weak bands located at 200 and 280 cm–1 are assigned to the
rocking modes of the CF3S group, which appear at around
200 and 340 cm–1 in CF3SO2X molecules.[6] Higher fre-
quencies, with values of 340 and 440 cm–1, were reported
for the CF3O rocking motions in CF3OX molecules,[28] and
consequently the bands observed at 345 and 444 cm–1 for
CF3SO2OCF3 are assigned to these modes.
Calculation of Force Constants
The Cartesian force field for CF3SO2OCF3, as calcu-
lated, was transformed into the set of non-redundant, natu-
ral coordinates defined in Table 6 through the B-matrix[30]
obtained with a standard program. Such coordinates take
into account the local symmetry around the C and S atoms
and are in accordance with the proposals of Fogarasi et
Skeletal Modes
The O–S stretching mode appears as a strong Raman al.[31] The resulting force field was subsequently scaled by
band located at 766 cm–1. The strong 956 cm–1 infrared using the scheme proposed by Pulay et al.,[32] in which the
band in the gas spectrum is well predicted by calculations, diagonal force constants are multiplied by scale factors kf,i,
in terms of both position and intensity, to be due to the C– kf,j, etc., and the corresponding interaction constants are
O stretch, although the mode is best described as the out- multiplied by (kf,i ϫkf,j)1/2. A set of initial scale factors was
of-phase coupling of the C–O and O–S stretches, as can be defined by using values recommended by Kalincsák and
observed from the calculated atomic displacements when Pongor[33] where available and by using unity for the rest.
displayed with the program GaussView.[29]
These scale factors were subsequently adjusted by a least-
The 320 cm–1 mode shows a strong contribution from the squares procedure in order to obtain the best fit to the ex-
C–S stretch. The CSO bend appears as the main component perimental frequencies.(initial and final scale factors are
of the 150 cm–1 mode, and is also strongly coupled with the available in Table S5, Supporting Information). All vi-
COS bend in the 172 cm–1 mode. These last two modes ap- brational bands were assigned the same weight in the ad-
pear as very weak, ill-defined Raman bands.
justment except for those missing or showing uncertain fre-
1386
www.eurjic.org
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Inorg. Chem. 2007, 1381–1389

Gas-Phase Structure and Vibrational Properties of CF3SO2OCF3
FULL PAPER
Table 6. Definitions of natural symmetry coordinates for CF3SO2OCF3.[a]
Label Definition
Description
S1
S2
S3
S4
S5
S6
S7
S8
r(1–2) – r(1–3)
2m(6–5) – m(8–5) – m(7–5)
m(8–5) + m(6–5) + m(7–5)
d(9–10) – d(9–12)
2d(9–11) – d(9–10) – d(9–12)
m(8–5) – m(7–5)
d(9–10) + d(9–11) + d(9–12)
r(1–2) + r(1–3)
SO2 antisymmetric stretch
OCF3 antisymmetric stretch
OCF3 symmetric stretch
SCF3 antisymmetric stretch
SCF3 antisymmetric stretch
OCF3 antisymmetric stretch
SCF3 symmetric stretch
SO2 symmetric stretch
C–O stretch
S9
p(4–5)
S10
S11
S12
S13
S14
S15
S16
S17
S18
S19
S20
S21
S22
S23
S24
S25
S26
S27
S28
S29
S30
ε(10–9–11) + ε(10–9–12) + ε(11–9–12) – β(10–9–1) – β(11–9–1) – β(12–9–1)
l(1–4)
µ(6–5–7) + µ(6–5–8) + µ(7–5–8) – Ω(6–5–4) – Ω(7–5–4) – Ω(8–5–4)
µ(8–5–6) – µ(7–5–6)
ψ(9–1–2) + ψ(9–1–3) – γ(4–1–2) – γ(4–1–3)
4φ(2–1–3) – ψ(9–1–2) – ψ(9–1–3) – γ(4–1–2) – γ(4–1–3)
ε(10–9–11) – ε(12–9–11)
2ε(10–9–12) – ε(10–9–11) – ε(12–9–11)
2µ(8–5–7) – µ(8–5–6) – µ(7–5–6)
Ω(8–5–4) – Ω(7–5–4)
ψ(9–1–2) – ψ(9–1–3) + γ(4–1–2) – γ(4–1–3)
2Ω(6–5–4) – Ω(8–5–4) – Ω(7–5–4)
t(1–9)
ψ(9–1–2) – ψ(9–1–3) – γ(4–1–2) + γ(4–1–3)
2β(11–9–1) – β(10–9–1) – β(12–9–1)
β(10–9–1) – β(12–9–1)
SCF3 symmetric bend
S–O stretch
OCF3 symmetric bend
OCF3 antisymmetric bend
SO2 wag
SO2 bend
SCF3 antisymmetric bend
SCF3 antisymmetric bend
OCF3 antisymmetric bend
CF3 rock
SO2 rock
OCF3 rock
C–S stretch
SO2 twist
SCF3 rock
SCF3 rock
SOC bend
CSO bend
S–O torsion
OCF3 torsion
α(1–4–5)
4θ(9–1–4) – ψ(9–1–2) – ψ(9–1–3) – γ(4–1–2) – γ(4–1–3)
τ(9–1–4–5) + τ(2–1–4–5) + τ(3–1–4–5)
τ(8–5–4–1) + τ(6–5–4–1) + τ(7–5–4–1)
τ(10–9–1–2) + τ(11–9–1–2) + τ(12–9–1–2) + τ(10–9–1–3) + τ(11–9–1–3)
+ τ(12–9–1–3) + τ(10–9–1–4) + τ(11–9–1–4) + τ(12–9–1–4)
SCF3 torsion
[a] Latin letters denote changes in bonds between the atoms whose numbers appear in parentheses. Greek letters denote changes in angles
defined by the atoms that are also indicated with numbers.
quencies, for which zero weights were used. No empirical the adjacent O–C bond length increases (from 139.3 to
correction of the theoretical geometry was used. The poten- 145.5 pm), and its force constant decreases (from 5.50 to
tial-energy distribution, which shows the relative contri- 4.60 mdynÅ–1). The highly electronegative CF3 group
bution of the diagonal force constants to each vibrational seems to enhance the participation of the oxygen electronic
mode, was subsequently calculated with the resulting scaled charge in the O–C bond of CF3SO2OCF3, strengthening
quantum mechanics (SQM) force field. The resulting fre- that bond to the detriment of the S–O bond.
quencies, final RMSD value and potential-energy distribu-
tion are presented in Table 5. It can be seen that only about
one half of the modes have a participation of Ն50% of
one definite coordinate, whereas the other modes represent
complex vibrations where several coordinates are involved.
The force-field transformation, scaling and potential-en-
ergy distribution calculations were performed with the pro-
gram FCARTP.[34] The atomic displacements, given by the
calculations for each vibrational mode, served as a tool to
help understand qualitatively the nature of the molecular
vibrations. The program GaussView was used along with
the corresponding data to represent this graphically.[29]
The SQM force field (Table S6, Supporting Information)
was used to calculate the internal force constants for
CF3SO2OCF3 (Table 7), and these are compared to the
equivalent values for some related molecules. It can be seen
that on moving from CF3SO2OCF3 to CF3SO2OCH3, the
calculated S–O bond becomes shorter (from 168.2 to
162.2 pm), and, consequently, the corresponding force con-
Table 7. Force constants in internal (valence) coordinates for
CF3SO2OCF3 and related molecules.
[b]
[c]
Force constants[a] CF3SO2OCF3 CF3SO2OCH3
CF3SO2OCH2CF3
kf [C(1)–F]
kf [C(9)–F]
kf [C–S]
kf [S–O]
kf [S=O]
6.50
6.13
3.00
3.82
11.05
5.50
1.14
1.26
1.16
1.00
1.24
1.36
0.94
–0.093
5.94
5.85
6.15
3.18
4.62
10.90
5.01
1.10
1.25
1.0
3.10
4.96
10.70
4.60
1.19
1.26
1.16
1.00
1.29
kf [O–C]
kf [O = S=O]
kf [O–S=O]
kf [C–S–O]
kf [C–S=O]
kf [F–C(1)–F]
kf [F–C(9)–F]
kf [C–F/C–F]
kf [S=O/S=O]
1.0
1.29
1.35
0.71
–0.076
0.71
–0.076
[a] Units are mdynÅ–1 for stretches and stretch–stretch interac-
tions, and mdynÅrad–2 for angular deformations. [b] Ref.[5] [c]
stant increases (from 3.82 to 4.96 mdynÅ–1). In contrast, Ref.[7]
Eur. J. Inorg. Chem. 2007, 1381–1389
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjic.org
1387

A. Ben Altabef et al.
FULL PAPER
a Perkin–Elmer 1600 FTIR instrument. The spectrum for
the solid was obtained after depositing the compound from
the vacuum line onto a KBr window, maintained at about
197 K, in a variable temperature RIIC (VLT-2) cell. The
Raman spectrum for the liquid at room temperature was
obtained with the FRA-106 accessory mounted on a Bruker
IFS66 FTIR instrument, by using 1064-nm light from a Nd/
YAG laser for excitation.
Conclusions
CF3SO2OCF3 was synthesised in good yields by using a
published technique. A complete investigation of its gas-
phase molecular structure was carried out by using electron
diffraction techniques complemented by theoretical meth-
ods. The experimental and theoretical structures both show
this molecule as a single gauche conformer having a C–S–
O–C dihedral angle of 119.5(18)° determined by GED, rela-
tive to 105 to 112° calculated by quantum chemistry calcu-
lations. A comparison of the bond lengths obtained by
GED and those predicted by various ab initio and DFT
methods shows that CF3SO2OCF3 is a particularly chal-
lenging case for theoretical geometry optimisation. The in-
clusion of multiple polarisation functions in the basis set
plays a crucial role, but the choice of method is also signifi-
cant. These results are consistent with what seem to be com-
mon structural characteristics of covalent sulfonates.
Infrared and Raman spectra were obtained for
CF3SO2OCF3, and bands assignable to 27 out of the ex-
pected 30 normal modes of vibration were observed. The
vibrational data were used as a basis to define the symmetry
(SQM force field) and internal force constants of the mole-
cule.
Computational Resources
The majority of the calculations described in this paper were per-
formed with a Linux 10-processor Parallel Quantum Solutions
(PQS) workstation[39] running the Gaussian 03 suite of pro-
grams.[40] The scans of the potential-energy surface and all calcula-
tions using the 6-31G(3df), cc-pVTZ, TZVP and TZVPP basis sets
were performed with the resources of the EPSRC National Service
for Computational Chemistry Software[41] on a cluster of 22 Linux
Opteron nodes, where each Opteron server has twin 2.4 GHz Op-
teron 250 CPUs and 8 GB of memory connected with a high-speed,
low-latency Myrinet network.
Supporting Information (see footnote on the first page of this arti-
cle): Details of GED data analysis parameters, interatomic dis-
tances, amplitudes of vibrations, distance corrections for perpen-
dicular motion, the least-squares correlation matrix and the molec-
ular-scattering intensity curves used in the GED refinement are
presented. Geometric molecular parameters for all ab initio and
DFT calculations are also given. GED atomic coordinates and
those obtained from MP2/6-31G(3df), MP2/cc-pVTZ, MP2/
TZVPP, B3LYP/6-31G(3df) and B1B95/6-31G(3df) calculations are
provided, as well as the force field scaling factors.
Synthesis
CF3SO2OCF3 was synthesised by reaction between
CF3SO2OH and its anhydride, (CF3SO2)2O, according to
the method reported by Hassani et al.[4] The reactants were
heated in a sealed tube for 1 h at approximately 450 K, and
after the reaction had occurred, the product was purified
by distillation on a vacuum line.
Acknowledgments
Research grants from the following Argentine institutions are
gratefully acknowledged: CONICET (Consejo Nacional de Invest-
igaciones Científicas y Técnicas), ANPCYT (Agencia Nacional de
Promoción Científica y Tecnológica) (PICT 11127), CIUNT (Con-
sejo de Investigaciones de la Universidad Nacional de Tucumán)
and UNLP (Universidad Nacional de La Plata). D. A. W. and
H. E. R. thank the EPSRC (grant EP/C513649) and S. A. H.
thanks the School of Chemistry, University of Edinburgh for fund-
ing.
Gas Electron Diffraction (GED)
Data were collected by using the Edinburgh gas electron
diffraction apparatus[35] with an accelerating voltage of ca.
40 kV (ca. 6 pm electron wavelength) on Kodak Electron
Image film. Nozzle-to-film distances were determined by
using benzene vapour as a standard, immediately after re-
cording the diffraction patterns for CF3SO2OCF3. Sample
and nozzle temperatures of 195 and 298 K, respectively,
were used for both the short and long nozzle-to-camera dis-
tances (130.5 and 291.5 mm). The electron scattering
pattern was converted into digital form by using an Epson
Expression 1680 Pro flatbed scanner with a scanning pro-
gram that was described elsewhere.[36] Data reduction and
least-squares refinements were carried out with the ed@ed
program[37] employing the scattering factors of Ross et
al.[38] The scale factors, s limits, weighting points, corre-
lation parameters and electron wavelengths are given in
Table S7 (Supporting Information).
[1] R. E. Noftle, G. Cady, Inorg. Chem. 1965, 4, 1010.
[2] G. A. Olah, T. Ohyama, Synthesis 1976, 319.
[3] Y. Kobayashi, T. Yoshida, I. Kumadaki, Tetrahedron Lett.
1979, 20, 3865.
[4] M. O. Hassani, A. Germain, D. Brunel, A. Commeyras, Tetra-
hedron Lett. 1981, 22, 65.
[5] F. Trautner, A. Ben Altabef, L. E. Fernández, E. L. Varetti, H.
Oberhammer, Inorg. Chem. 1999, 38, 3051.
[6] L. E. Fernández, A. Ben Altabef, E. L. Varetti, J. Mol. Struct.
2002, 612, 1.
[7] M. E. Tuttolomondo, L. E. Fernández, A. Navarro, E. L. Var-
etti, A. Ben Altabef, Spectrochim. Acta Part A 2004, 60, 611.
[8] M. E. Tuttolomondo, A. Navarro, E. L. Varetti, A. Ben Alta-
bef, J. Raman Spectrosc. 2005, 36, 427.
[9] M. F. Erben, C. O. Della Vedova, R. Boese, H. Willner, C. Lei-
bold, H. Oberhammer, Inorg. Chem. 2003, 42, 7297.
[10] J. S. Binkley, J. A. Pople, W. J. Hehre, J. Am. Chem. Soc. 1980,
102, 939.
Infrared and Raman Spectra
Infrared spectra for CF3SO2OCF3 in the gas and solid
phases were recorded in the 400–4000 cm–1 range by using
1388
www.eurjic.org
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Inorg. Chem. 2007, 1381–1389

Gas-Phase Structure and Vibrational Properties of CF3SO2OCF3
FULL PAPER
[11] M. S. Gordon, J. S. Binkley, J. A. Pople, W. J. Pietro, W. J.
Hehre, J. Am. Chem. Soc. 1982, 104, 2797.
[12] W. J. Pietro, M. M. Francl, W. J. Hehre, D. J. DeFrees, J. A. Po-
ple, J. S. Binkley, J. Am. Chem. Soc. 1982, 104, 5039.
[13] W. J. Hehre, R. Ditchfield, J. A. Pople, J. Chem. Phys. 1972, 56,
2257.
[14] P. C. Hariharan, J. A. Pople, Theor. Chim. Acta 1973, 28, 213.
[15] M. S. Gordon, Chem. Phys. Lett. 1980, 76, 163.
[16] C. Møller, M. S. Plesset, Phys. Rev. 1934, 46, 618.
[17] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785; A. D.
Becke, J. Chem. Phys. 1993, 98, 5648.
[33]
[34]
[35]
[36]
F. Kalincsák, G. Pongor, Spectrochim. Acta Part A 2002, 58,
999.
W. B. Collier, Program FCARTP (QCPE # 631), Department
of Chemistry, Oral Roberts University, Tulsa OK, USA, 1992.
C. M. Huntley, G. S. Laurenson, D. W. H. Rankin, J. Chem.
Soc., Dalton Trans. 1980, 954.
H. Fleischer, D. A. Wann, S. L. Hinchley, K. B. Borisenko,
J. R. Lewis, R. J. Mawhorter, H. E. Robertson, D. W. H. Ran-
kin, Dalton Trans. 2005, 3221.
S. L. Hinchley, H. E. Robertson, K. B. Borisenko, A. R.
Turner, B. F. Johnston, D. W. H. Rankin, M. Ahmadian, J. N.
Jones, A. H. Cowley, Dalton Trans. 2004, 2469.
[37]
[18] A. D. Becke, J. Chem. Phys. 1996, 104, 1040.
[19] A. D. McLean, G. S. Chandler, J. Chem. Phys. 1980, 72, 5639.
[20] R. Krishnan, J. S. Binkley, R. Seeger, J. A. Pople, J. Chem.
Phys. 1980, 72, 650.
[38] A. W. Ross, M. Fink, R. Hilderbrandt, International Tables for
Crystallography Vol. C (Ed.: A. J. C. Wilson), Kluwer Aca-
demic Publishers, Dordrecht, Boston and London, 1992, p.
245.
[21] M. J. Frisch, J. A. Pople, J. S. Binkley, J. Chem. Phys. 1984, 80,
3265.
[22] T. H. Dunning Jr, J. Chem. Phys. 1989, 90, 1007.
[23] A. Schaefer, H. Huber, R. Ahlrichs, J. Chem. Phys. 1994, 100,
5829.
[24] F. Weigend, M. Haeser, H. Patzelt, R. Ahlrichs, Chem. Phys.
Lett. 1998, 294, 143.
[25] V. A. Sipachev, J. Mol. Struct. (THEOCHEM) 1985, 121, 143.
[26] a) N. W. Mitzel, B. A. Smart, A. J. Blake, H. E. Robertson,
D. W. H. Rankin, J. Phys. Chem. 1996, 100, 9339; b) A. J.
Blake, P. T. Brain, H. McNab, J. Miller, C. A. Morrison, S. Par-
sons, D. W. H. Rankin, H. E. Robertson, B. A. Smart, J. Phys.
Chem. 1996, 100, 12280; c) N. W. Mitzel, D. W. H. Rankin,
Dalton Trans. 2003, 3650.
[27] C. Leibold, H. Oberhammer, T. D. Thomas, L. J. Saethre, R.
Winter, G. L. Gard, Inorg. Chem. 2004, 43, 3942.
[28] L. E. Fernández, E. L. Varetti, J. Mol. Struct. (THEOCHEM)
2003, 629, 175.
[39] Parallel Quantum Solutions, Fayetteville AR, USA.
[40] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
M. A. Robb, J. R. Cheeseman, J. A. Montgomery Jr, T. Vreven,
K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tom-
asi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega,
G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota,
R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda,
O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratch-
ian, J. B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R. E.
Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli,
J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Sal-
vador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D.
Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck,
K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Ba-
boul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Lia-
shenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T.
Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M.
Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W.
Wong, C. Gonzalez, J. A. Pople, Gaussian 03, Revision B.02,
Gaussian Inc., Pittsburgh PA, 2003.
[29] A. B. Nielsen, A. J. Holder, GaussView, User’s Reference,
Gaussian, Inc., Pittsburgh PA, 1997–1998.
[30] E. B. Wilson, J. C. Decius, P. C. Cross, Molecular Vibrations,
McGraw-Hill, New York, 1955.
[31] G. Fogarasi, X. Zhou, P. W. Taylor, P. Pulay, J. Am. Chem. Soc.
1992, 114, 8191.
[32] P. Pulay, G. Fogarasi, G. Pongor, J. E. Boggs, A. Vargha, J. Am.
Chem. Soc. 1983, 105, 7037.
[41] EPSRC National Service for Computational Chemistry Soft-
ware. URL: http://www.nsccs.ac.uk.
Received: October 4, 2006
Published Online: February 21, 2007
Eur. J. Inorg. Chem. 2007, 1381–1389
© 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjic.org
1389