Molecular structure of 3,4-difluorofuran-2,5-dione (difluoromaleic anhydride) as determined by electron diffraction and microwave spectroscopy in the gas phase and by theoretical computations

Article abstract of DOI:10.1021/jp984554o

The structure of 3,4-difluorofuran-2,5-dione has been determined experimentally in the gas phase by microwave spectroscopy using rotation constants derived from five isotopomers and by a combined analysis of electrondiffraction and microwave data. The geometry is planar with C_2v symmetry. Structural parameters [distances (rα^o)/pm, angles _a/deg, (1α errors)] for the combined analysis are: r(C=O) = 119.0(1); r(C-F) = 130.9(2); r(C=C) = 133.2(3); r(O-C) = 139.3(1); KC-C) = 148.5(2); C-C=C = 108.3(1); ZC=C-F = 129.9-(1); C-C=O = 129.3(1); C-O-C = 108.9(1); O-C-C = 107.2(1). These values are in excellent agreement with those obtained in an ab initio study of the molecular geometry at the MP2/6-311+G (2df) level of theory. The dipole moment of difluoromaleic anhydride has been determined experimentally by Starkeffect measurements to be 1.867(3) D.

Full text of DOI:10.1021/jp984554o

1758
J. Phys. Chem. A 1999, 103, 1758-1767
Molecular Structure of 3,4-Difluorofuran-2,5-dione (Difluoromaleic Anhydride) As
Determined by Electron Diffraction and Microwave Spectroscopy in the Gas Phase and by
Theoretical Computations
Basil T. Abdo,† Halima Amer,‡ R. Eric Banks,† Paul T. Brain,‡ A. Peter Cox,§
Oliver J. Dunning,§ Vincent Murtagh,† David W. H. Rankin,*,‡ Heather E. Robertson,‡ and
Bruce A. Smart‡
Department of Chemistry, U.M.I.S.T., P.O. Box 88, Manchester, M60 1QD, U.K., Department of Chemistry,
UniVersity of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, U.K., and School of Chemistry,
The UniVersity, Cantock’s Close, Bristol, BS8 1TS, U.K.
ReceiVed: NoVember 30, 1998; In Final Form: January 15, 1999
The structure of 3,4-difluorofuran-2,5-dione has been determined experimentally in the gas phase by microwave
spectroscopy using rotation constants derived from five isotopomers and by a combined analysis of electron-
diffraction and microwave data. The geometry is planar with C2V symmetry. Structural parameters [distances
(rR°)/pm, angles R/deg, (1σ errors)] for the combined analysis are: r(CdO) ) 119.0(1); r(C-F) ) 130.9(2);
r(CdC) ) 133.2(3); r(O-C) ) 139.3(1); r(C-C) ) 148.5(2); C-CdC ) 108.3(1); CdC-F ) 129.9-
(1); C-CdO ) 129.3(1); C-O-C ) 108.9(1); O-C-C ) 107.2(1). These values are in excellent
agreement with those obtained in an ab initio study of the molecular geometry at the MP2/6-311+G*(2df)
level of theory. The dipole moment of difluoromaleic anhydride has been determined experimentally by Stark-
effect measurements to be 1.867(3) D.
Introduction
anhydride in the gas phase by microwave spectroscopy and
electron diffraction. In addition, theoretical computations for
maleic anhydride and its dihalo derivatives (X ) F, Cl, and
Br) are reported in support of our experimental conclusions.
Saturation of the CdC double bond in 3,4-difluorofuran-2,5-
dione (difluoromaleic anhydride) (1) with bis(trifluoromethyl)-
amino-oxyl, (CF3)2NO, occurs smoothly at 60 °C during 24 h
to give the corresponding 1:2 adduct virtually quantitatively.1
This adduct is under investigation as a precursor (via reactions
involving the anhydride function) of surfactants suitable, for
example, as a means of preparing emulsions from “blood
substitutes” (oxygen carriers), synthesized via saturation of Cd
C bonds in perfluoro-alkanes and -cycloalkanes with (CF3)2-
NO.1,2 The need to prepare difluoromaleic anhydride for this
project enabled a structural investigation of this potentially
important compound to be carried out.
Although all four dihalomaleic anhydrides are known3-6
(dichloromaleic anhydride having been first reported in 18834),
it has been the parent compound, maleic anhydride itself, that
has received greatest attention, in terms of both its physical
properties and characterization, including a study of its gas-
phase structure by electron diffraction (GED)7 and microwave
(MW) spectroscopy,8 and its chemical reactivity.9 Of the dihalo
derivatives, structural parameters are available only for dichlo-
romaleic anhydride as refined from its electron-diffraction
pattern.10 Considering the difference in size and electronegativity
between chlorine and hydrogen,11 it was surprising to discover
from the gas-phase studies that there is very little difference
between the structures of the parent and its dichloro deriva-
tive.7,10 To investigate this further, and as part of a wider study
of small fluorocarbons and fluorinated organometallic com-
pounds,12,13 we have determined the structure of difluoromaleic
Experimental Section
Preparation of Difluoromaleic Anhydride (1). Although
shorter routes are known, e.g., the oxidation of commercially
available pentafluorophenol with peracetic acid,14 followed by
dehydration of the difluoromaleic acid thus formed, the classical
multi-stage DuPont route3 outlined in Scheme 1 was chosen.
This approach provides trifluorosuccinic acid (3) and also can
be modified to give 2,2-difluorosuccinic acid and monofluoro-
maleic anhydride, all products needed for associated studies
involving (CF3)2NO.
The key intermediate in the DuPont synthetic scheme is 1,1,2-
trichloro-2,3,3-trifluorocyclobutane (4), prepared by a thermal
[2 + 2] cycloaddition reaction between the commercial olefins
chlorotrifluoroethene (bp -28.5 °C; Fluorochem, U.K.) and 1,1-
dichloroethene (bp 30-32 °C; Aldrich). Only this first stage
requires special equipment (a 1-liter stainless steel Magnedrive
autoclave was used, providing ca. 300 g of analytically pure
redistilled 4 per run) and techniques (high pressure and gas
handling). Extensive polymer formation (despite the use of
hydroquinone as an inhibitor)3 is responsible for the moderate
yield of 4 (lit.3 48%; this work, 52%) and also creates autoclave-
cleaning problems, not mentioned previously.3 The polymeric
material formed in our work tended to adhere strongly to the
inner wall of the autoclave; it was easily removed by pouring
hot water into the cup, the differential expansion (steel vs
polymer) causing the organic material to peel off, leaving a clean
metal surface. (Note: This cleaning operation must be carried
out in an efficient fume cupboard so that any volatile organic
material released is not inhaled by the operator.)
* Author to whom correspondence should be addressed.
† Department of chemistry, U.M.I.S.T.
‡ Department of Chemistry, University of Edinburgh.
§ School of Chemistry, The University.
10.1021/jp984554o CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/05/1999

Molecular Structure of 3,4-Difluorofuran-2,5-dione
J. Phys. Chem. A, Vol. 103, No. 12, 1999 1759
SCHEME 1
was initially made by measurement of strong, high J transitions
(J ) 18-27) thrown down by asymmetry into the 8-12 GHz
region. The two singly substituted 18O species were measured
using Stark spectroscopy on enriched samples. The assignment
of the exo-substituted species was confirmed by radio frequency-
microwave double resonance using the small µa component of
the dipole generated by the rotation of the principal axes. This
method was not available for the C2V species since it possesses
only a µb component of the dipole. Carbon-13 lines were
measured in natural abundance at Exeter University in col-
laboration with Professor A. C. Legon using Fourier transform
microwave spectroscopy on the sample in free jet expansion.
Transition frequencies and their assignments for the five
isotopomers are given in Table 2 and the spectroscopic constants
in Table 3.
Vibrational and NMR Spectroscopy. Infrared spectra in the
range 4000-400 cm-1 were recorded using a Mattson “Galaxy”
FT spectrometer employing a standard 10-cm gas cell equipped
with CsI windows. For Raman spectroscopy, the sample was
presented as a liquid at room temperature sealed in an evacuated,
Pyrex-glass ampule. Spectra were recorded in the range 2000-
50 cm-1 using a Dilor “LabRam” Raman microscope. The
observed frequencies are reported in the Supporting Information.
NMR spectra were recorded at room temperature for a solution
in CFCl3 on Bruker AC-300 (13C, 75.5 MHz, external TMS
reference) and AC-200 (19F, 188.8 MHz, external CF3CO2H
reference) spectrometers.
Ab Initio Calculations. All ab initio molecular orbital
calculations were carried out on a DEC Alpha APX 1000
workstation using the Gaussian 94 program.19 Geometry opti-
mizations on difluoromaleic anhydride were undertaken at the
SCF and MP2 levels using the standard 6-31G(d)20-22 and
6-311G(d)23,24 basis sets. To investigate the effects of diffuse
functions and larger polarization sets, geometry optimizations
were undertaken also at the MP2 level using the 6-311G(2df)
and 6-311+G(2df) basis sets (Table 4). Harmonic force-field
calculations were undertaken at the SCF/6-31G(d) and MP2/
6-31G(d) levels; fundamental frequencies from the latter are
listed in Table 5. Subsequently, frequency calculations using
the larger 6-311G(d) basis set were performed at the MP2 and
B3LYP levels to verify the ordering of the lowest two modes.
Force-Field Calculations. The program ASYM4025 was used
to convert the theoretical (MP2/6-31G(d) level) Cartesian force
field to one described by symmetry coordinates. An optimum
fit of the theoretical to the experimental frequencies was
achieved by a refinement of the ab initio force constants using
eight scaling factors. Details, including a list of the internal and
symmetry coordinates, are given as part of the Supporting
Information. Root-mean-square amplitudes of vibration (u),
perpendicular amplitudes of vibration (K), harmonic vibrational
corrections (R/2) to the observed rotation constants (B0), and
corrections to bond lengths upon isotopic substitution were then
calculated from the scaled force constants using ASYM40.
In the present work, only the yield reported for the final step
in Scheme 1 (89% of 1)3 was not matched. The best yield of 1
was achieved by heating an intimate mixture of phosphorus
pentoxide (14.2 g, 100 mmol) with the mixed difluoromaleic
and difluorofumaric acids (2) (15.0 g, 98 mmol) at 70 °C (oil-
bath temperature) in vacuo in the stillpot (100 cm3; equipped
with a PTFE-coated stirrer bar) of a Vigreux distillation unit.
The crude difluoromaleic anhydride was collected, as it formed,
in a cooled (ice) receiver and redistilled to give 7.3 g (54.5
mmol, 56%) of a clear, colorless, viscous liquid (bp 127-129
°C; lit.3 128 °C) which was identified as difluoromaleic
anhydride (1) by 13C and 19F NMR spectroscopy [δC 138.2 (d,
1JCF 302 Hz), 155.3 (m) ppm; δF -61.5 (s) ppm (CF3CO2H
ref)].
For microwave spectroscopy (see below), samples were
enriched with 18O on a millimolar scale by hydrolysis of
difluoromaleic anhydride with excess water enriched 40% in
18O. After equilibration, the mixture was distilled to remove
the excess water from the maleic acid product. The acid was
then mixed with P2O5 and the enriched maleic anhydride
sublimed from the mixture by gentle heating in vacuo. The
proportion H218O/H216O taken optimized the yield of the single-
substituted 18O isotopomers in order to simplify measurement
of the spectra.
Electron Diffraction. Electron scattering intensities were
recorded on Kodak Electron Image plates using the Edinburgh
gas diffraction apparatus.15 The sample and nozzle were
maintained at ca. 293 K during the exposure of three and two
plates, respectively, at the long (286 mm) and short (128 mm)
camera distances. Scattering intensities for benzene were also
recorded, to provide calibration of the camera distances and the
electron wavelength. The plates were traced using a computer-
controlled Joyce Loebl MDM6 microdensitometer at the EPSRC
Daresbury Laboratory.16 Analysis of the data made use of
standard data reduction16 and least-squares refinement17 pro-
grams and scattering factors.18 The s ranges, weighting points,
and other experimental details are listed in Table 1.
Rotational Spectroscopy. Microwave spectra were measured
using a conventional Stark modulation spectrometer operating
at 100 kHz. Gas samples at 3-10 Pa were introduced into a
3-m stainless steel X-band absorption cell, cooled to ca. 243
K. Under these conditions the sample was stable, no degradation
in the spectrum being visible after ca. 8 h. For assignment
purposes, low-resolution spectra were taken using backward-
wave oscillator sources in the 8-40 GHz region. Assignment
Structural Analysis
Microwave Spectroscopy. Difluoromaleic anhydride shows
a rich b-type asymmetric-rotor spectrum (κ ) +0.08) with many
vibrational satellites. Both the ground- and excited-state spectral
intensities show the 3:1 nuclear spin statistical weightings
associated with the exchange of two equivalent fluorine atoms
1
(I ) /2). Taken together with the ground-state inertial defect
values (∆ ) Ic - Ia - Ib) for the main species, ∆ ) 0.0202(2)
u Å2, and the isotopic species, these observed spin statistics
establish unequivocally the molecule to be planar with C2V

1760 J. Phys. Chem. A, Vol. 103, No. 12, 1999
Abdo et al.
TABLE 1: Nozzle-to-Plate Distances, Weighting Functions, Correlation Parameters, Scale Factors, and Electron Wavelengths
for the Combined GED/MW Study
nozzle-to-plate
distance, mm
correlation
parameter
scale
electron
a
a
a
a
∆sa
smin
sw1
sw2
smax
factor kb
wavelength,c pm
285.94
128.22
2
4
20
60
40
80
122
304
144
356
0.490
0.453
0.804(8)
0.667(11)
5.672
5.675
a In nm-1 b Figures in parentheses are the estimated standard deviations (1σ). c Determined by reference to the scattering pattern of benzene.
.
symmetry. The inertial defect is accounted for satisfactorily by
the harmonic force-field calculations. The ring structure can be
calculated directly by isotopic substitution and the C-F bonds
placed from the moment equations. The fluorine coordinates
were derived using the first- and second-moment equations for
the substitution structure, but the second-moment equations were
preferred for the rz structure. Planar moments were used in
Kraitchman’s equations26 for both the substitution and average
structures. In adopting isotopic shrinkage corrections in the
calculation of the rz parameters, it was necessary to estimate
changes in ring angles commensurate with bond length changes
derived from ASYM40. Table 6 gives the rs (substitution) and
rz structures calculated from the experimental microwave data.
The permanent dipole moment lies along the C2 symmetry
axis (Figure 1) such that µtotal ) µb, and µa ) µc ) 0. The
dipole moment has been determined from high-resolution Stark
measurements on several transitions for the vibrational ground-
state including the J ) 6 r 5 as detailed in Table 7. In deriving
the experimental second-order Stark coefficients, it was neces-
sary to make corrections for fourth-order effects. The experi-
mental dipole moment of 1.867(3) D obtained for DFMA agrees
well with the vector sum (1.76 D) of maleic anhydride (3.95
D),8 and the C-F bond moment obtained from cis-1,2 difluo-
roethene (µtotal ) 2.43 D).27
Figure 2 shows a typical transition from the spectrum in which
the ground-state line is clearly accompanied by two vibrational
series. The series to low-frequency belongs to a vibration with
torsional (a2) symmetry at 154(10) cm-1, with the same spin
statistics as the ground state, and the other to an out-of-plane
ring-bending (b1) vibration at 102(12) cm-1 showing 1:3
alternation. The wavenumber values have been determined by
relative intensity measurements averaged over 10 and 5 transi-
tions for the torsional and bending modes, respectively. These
values correspond to those of maleic anhydride at 266(20) and
168(15) cm-1, respectively.28 Table 8 gives the rotation constants
and inertial defects of these modes in difluoromaleic anhydride
versus vibrational quantum number. The values for the inertial
defects agree well with the values (cm-1) determined from
relative intensity measurements, the large negative values being
typical of low-frequency out-of-plane modes.
Electron Diffraction. Assuming that difluoromaleic anhy-
dride has C2V symmetry, eight independent parameters are
required to define the structure. As the radial-distribution curve
(Figure 3) contains only five distinct peaks, it was expected
that strong correlation between parameters would make it
difficult to refine all of the geometrical parameters simulta-
neously; in particular, the CdC and C-F bond lengths would
be very similar to one another. The independent parameters
(Table 9) needed to represent the five different bonded distances
were chosen to be their weighted mean (p1), the difference
between the mean of r(C-C) and r(O-C) and the weighted
mean of the CdC, C-F, and CdO bond lengths (p2), the
difference between r(C-C) and r(O-C) (p3), the difference
between the weighted mean of the C-F and CdC bond lengths
and r(CdO) (p4), and the difference between r(CdC) and r(C-
F) (p5). The other three parameters were defined to be the
internal ring angle CdC-C (p6), and the external ring angles
CdC-F (p7) and C-CdO (p8).
The radial-distribution curve (Figure 3) shows all the
interatomic bonded distances lying under the broad peak
centered at ca. 135 pm, with the two-bond nonbonded distances
associated uniquely with the feature at ca. 220 pm. The three-
bond O‚‚‚F and F‚‚‚F distances account for the peak near 300
pm, the remaining three-bond nonbonded distances all lying
under the peak at ca. 350 pm. The two four-bond distances lie
under the feature at r > 400 pm, the O‚‚‚O distance represented
by a shoulder at ca. 450 pm.
Two rR° refinements of the structure were undertaken, one
using the ED data alone (ED), while in the latter the ED data
and the rotation constants (Bz) were fitted simultaneously (ED/
MW). Starting values for the refinements were taken from the
theoretical geometry and vibrational force-field computations
at the MP2/6-31G(d) level. The results are compared in Table
9.
Using the ED data alone, it was possible to refine simulta-
neously seven of the eight independent geometrical parameters.
Allowing p5, the difference between the CdC and C-F bond
lengths, to refine freely returned a value of 4.8(19) pm, the large
uncertainty reflecting the high degree of correlation between it
and other refining parameters. Consequently, the CdC bond
distance, at 135.3(16) pm, was poorly defined and appeared
unreasonably long compared to the value determined experi-
mentally from the MW data [rz ) 132.5(4) pm)] and predicted
ab initio [re ) 133.6 pm at MP2/6-311+G(2df)]. Since fixing
the value of p5 in the final refinement undoubtedly leads to an
underestimate of the errors for other refining parameters with
which it is correlated, it was refined using a flexible restraint.29
Flexible restraints may allow the refinement of parameters
which would otherwise have to be fixed.29 Estimates of the
values of these restrained quantities and their uncertainties are
used as additional observations in a combined analysis similar
to those routinely carried out for electron-diffraction data
combined with rotation constants and/or dipolar coupling
constants.12 The values and uncertainties for the extra observa-
tions are derived from another method such as X-ray diffraction
or theoretical computations. All geometrical parameters are then
included in the refinements. In cases where a restrained
parameter is also a refinable parameter, if the intensity pattern
contains useful information concerning the parameter, it will
refine with an esd less than the uncertainty in the corresponding
additional observation. However, if there is essentially no
relevant information, the parameter will refine with an esd
approximately equal to the uncertainty of the extra observation
and its refined value will equal that of the restraint. In this case,
if the correlation matrix also shows no correlation with other
refining parameters, the parameter can simply be fixed, in the
knowledge that doing this does not influence either the
magnitudes or the esd’s of other parameters. In some cases,
because increasing the number of refining parameters allows
all effects of correlation to be considered, some esd’s may
increase. Overall, this approach utilizes all available data as fully
as possible and returns more realistic esd’s for refining

Molecular Structure of 3,4-Difluorofuran-2,5-dione
J. Phys. Chem. A, Vol. 103, No. 12, 1999 1761
TABLE 2: Measured and Calculateda Ground-State Rotational Transition Frequencies (MHz)
(a) Normal Species
J′
Ka′
Kc′
J′′
Ka′′
Kc′′
νobs
ν(obs-calc)
J′
Ka′
Kc′
J′′
Ka′′
Kc′′
νobs
ν(obs-calc)
2
2
2
4
0
1
5
5
1
0
5
5
4
4
6
6
5
6
2
5
5
7
7
4
8
5
6
5
7
7
2
3
5
1
2
3
4
6
6
3
9
9
5
7
6
1
0
1
4
4
1
0
5
5
1
2
3
3
0
1
2
1
5
2
3
0
1
5
1
3
2
4
2
2
7
6
5
8
8
6
6
4
3
7
0
1
6
4
5
1
1
3
3
3
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
8
7
8
9
8
8
8
8
8
8
8
8
8
8
9
10
9
1
1
3
1
0
4
4
0
1
4
4
1
3
5
5
4
5
3
4
4
6
6
3
7
4
5
4
6
6
3
2
4
2
1
4
3
5
5
2
8
8
4
6
5
0
1
0
3
3
0
1
4
4
2
1
4
2
1
0
1
2
4
3
2
1
0
4
0
4
3
3
3
1
6
7
4
7
7
5
5
3
4
6
1
0
5
5
4
8147.351b
9267.348b
18011.69
9034.503b
9129.894b
22836.57
22890.82
11108.959b
11086.593b
25964.14
25516.30
31964.78
22235.92
27631.44
27616.80
25516.30
30583.92
18806.99
29524.71
27682.37
32385.55
32381.94
24623.92
37142.67
34072.46
33744.36
29162.71
11650.35
35252.19
23193.74
12340.18
30136.20
21186.74
21189.40
24824.53
25892.66
34862.19
37504.73
23273.34
41902.41
41902.21
30980.09
11453.09
36020.98
0.006
0.000
-0.08
-0.001
0.003
-0.06
-0.06
-0.001
-0.001
0.07
-0.09
-0.10
-0.13
-0.01
-0.05
-0.09
-0.08
-0.12
0.00
-0.10
-0.13
-0.05
0.04
-0.04
-0.04
-0.08
-0.02
-0.03
-0.05
0.04
10
10
10
10
10
1
2
9
9
9
2
1
8
8
4
7
9
23203.75
23204.29
41534.53
25250.57
21182.78
0.03
0.01
2
4
4
4
5
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
9
9
9
9
7
3
6
-0.07
3
1,0
8
10
2
0,1
0.09
0.06
10
10
10
11
11
11
11
11
11
11
11
11
11
12
2
3
8
7
7
3
11
8
7
7
10
6
10
9
11
12
9
9
9
3
4
3
7
0
4
5
4
2
5
1
2
1
1
7
6
6
4
25230.23
27151.42
27512.73
11916.73
23199.98
29264.29
30871.97
32106.68
25220.36
36689.80
25220.48
27253.97
23199.98
25217.31
0.07
0.13
0.03
4
8
11
10
10
10
10
10
10
10
10
10
11,0
-0.14
-0.03
0.04
1
10
7
3
4
6
0.05
5
6
0.17
1
9
0.01
6
5
0.11
2
9
0.02
3
8
0.06
0
10
11
-0.03
0,1
-0.01
12
1,2
11
11
2,1
10
27237.13
0.04
13
13
13
13
6
5
4
7
9
9
13
13
13
12
5
4
3
8
10
10
12
11949.57
18418.13
18390.34
27234.63
-0.06
-0.13
-0.06
-0.01
0,1
13
1,0
13
13
13
14
14
14
14
14
2
8
12
5
12
13
12
14
14
13
14
13
1
7
11
6
29254.01
9021.830
29254.01
20469.88
27124.03
29251.94
27124.03
33294.98
0.03
0.00
0.11
0.08
-0.03
-0.03
0.01
0.08
0.01
1
12
10
13
14
13
12
2
11
11
14
13
14
11
0.03
4
3
0.00
1
0
0.12
0
1
-0.03
2
1
0.12
2,3
3,2
0.05
-0.07
14
14
15
15
23
1
6
5
9
14
9
10
6
8
13
13
14
15
23
0
5
6
8
13
8
29251.94
39801.09
41437.89
9915.610
22825.71
-0.02
-0.03
-0.07
0.16
0.09
0.04
9
0.05
7
0.08
15
14
9
0.06
0.04
-0.15
(b) Isotopic Species
18O6
18O1
J′
Ka′
Kc′
J′′
Ka′′
Kc′′
νobs
ν(obs-calc)
νobs
ν(obs-calc)
6
5
6
2
1
5
5
4
5
1
0
25180.81
0.10
6
7
27045.87
30038.76
0.02
0.03
6
1
6
5
2
7
6
2
6
5
1
30017.93
31992.03
31994.54
34769.86
34800.64
0.07
-0.02
0.01
-0.10
-0.06
7
7
1
6
6
0
31709.12
31714.28
34572.15
0.03
-0.03
-0.03
7
7
0
6
6
1
8
7
2
7
6
1
8
7
1
7
6
2
8
8
1
7
7
0
36366.81
-0.02
9
2
8
8
1
7
20671.70
20663.46
24642.19
30668.56
22631.15
24602.42
24602.64
28526.70
29873.75
31622.18
24598.99
26569.68
26566.86
-0.01
0.08
0.08
0.01
-0.04
-0.01
-0.01
0.02
-0.01
0.01
10
10
10
11
11
11
11
11
11
12
12
13
1,0
3
10
8
9
0,1
2
9
20985.47
25007.71
30313.31
0.07
0.03
0.01
9
7
5
6
9
4
5
0,1
1
11
10
10
8
10
10
10
10
10
10
11
11
12
1,0
2
10
9
24984.97
24985.03
29001.68
30748.13
-0.03
-0.02
0.07
2
1
9
3
4
7
4
7
7
12
11
13
5
6
-0.02
5
4
6
0,1
1,2
0,1
1,0
2,1
1,0
11
10
12
-0.04
0.03
-0.02
24982.44
26982.97
26980.97
0.00
-0.07
-0.01
b
b
13C2
13C3
J′
Ka′
Kc′
J′′
Ka′′
Kc′′
νobs
ν(obs-calc)
νobs
ν(obs-calc)
4
4
5
5
1
0
0
1
4
4
5
5
3
3
4
4
0
1
1
0
3
3
4
4
9098.080
9001.161
11046.516
11069.382
0.000
0.001
9019.020
11067.358
11089.520
0.000
0.000
0.000
0.001
-0.001
a Derived rotational constants (B) are given in Table 3 (Fitted in the IIIrrepresentation). b Fourier-transform measurements.

1762 J. Phys. Chem. A, Vol. 103, No. 12, 1999
Abdo et al.
TABLE 3: Ground-State Spectroscopic Constantsa from the MW Study (B/MHz, ∆/u Å2)
isotopomer/substitution
constant
[1] parent
[2] 13C2
[3] 13C3
[4] 18O6
[5] 18O1
b
A0b
2379.5563(6)
1750.9848(8)
1008.6812(2)
2379.1129
1751.0408
1008.6228
0.0202(2)
2373.688(9)
1743.248(4)
1005.0585(8)
2373.247
2374.628(6)
1748.339(2)
1006.9260(4)
2374.193
2353.3685(16)
1691.0397(30)
983.9487(6)
2352.936
2327.7705(14)
1751.0467(36)
999.2885(7)
2327.350
B0b
C0
Az
Bz
Cz
∆
∆
1743.303
1748.399
1691.086
1751.113
1005.002
1006.8681
0.0160(4)
0.0158
983.8921
0.0193(10)
0.0175
999.2310
0.0149(5)
0.0157
0.0201(11)
0.0188
0
0.0188
z
a Figures in parentheses are the estimated standard deviations (1σ). b Conversion factor of 505379.1 MHz u Å2.
TABLE 4: Theoretical (re) Geometrical Parameters (distances/pm, angles/deg)a
level of theory/basis set
parameter
SCF/6-31G(d)
MP2/6-31G(d)
SCF/6-311G(d)
MP2/6-311G(d)
MP2/6-311G(2df)
MP2/6-311+G(2df)
r(C2dO6)
r(C3-F8)
r(C3dC4)
r(O1-C2)
r(C2-C3)
C2C3dC4
C4dC3F8
C3C2dO6
C2O1C5
116.8
129.6
131.2
136.0
148.8
108.1
130.7
129.0
110.5
106.7
120.3
132.4
134.1
140.0
148.5
108.4
130.3
129.2
108.8
107.2
116.1
129.1
131.0
135.7
148.8
108.0
130.7
128.8
110.4
106.8
119.3
131.3
134.0
139.1
149.9
108.1
130.6
128.8
108.8
107.5
119.1
130.6
133.6
138.8
148.2
108.1
130.4
128.9
108.8
107.5
119.2
130.6
133.6
138.9
148.2
108.2
130.1
129.1
108.9
107.4
O1C2C3
a For atom-numbering scheme, see Figure 1.
TABLE 5: Observed (anharmonic) and Calculated
TABLE 6: Geometrical Parameters Refined from the MW
Data (distances/pm, angles/deg)a
(harmonic) Fundamental Vibrational Frequencies (cm-1
)
theoreticala
structure type
symmetry
mode
unscaled
scaledb
exptc
parameter
rs
rzb
a1
ν1
ν2
1914
1821
1330
1156
678
624
377
248
656
470
110
706
312
159
1860
1438
1088
948
733
517
297
2.7
1881
1765
1297
1131
671
630
382
258
683
490
115
735
325
166
1823
1404
1057
934
761
525
303
0.6
1885 (IR)
1763 (IR)
1280 (IR)
1141 (IR)
676 (IR)
r(C2dO6)
r(C3-F8)
r(C3dC4)
r(O1-C2)
r(C2-C3)
C2C3dC4
C4dC3F8
C3C2dO6
C2O1C5
119.2
118.3(4)
132.1
131.3(4)
ν3
131.8
132.5(4)
ν4
139.3
139.7(2)
ν5
147.5
148.7(6)
ν6
630 (R)
108.64
130.27
129.93
108.47
107.13
108.65(1)
130.09(9)
129.92(1)
109.09(31)
106.81(16)
ν7
385 (R)
257 (R)
ν8
a2
b1
b2
ν9
not observed
not observed
[154 (MW)]d
735 (IR)
ν10
ν11
ν12
ν13
ν14
ν15
ν16
ν17
ν18
ν19
ν20
ν21
O1C2C3
a For atom-numbering scheme, see Figure 1. b Estimated errors (1σ)
in parentheses calculated as absolute /2(rz - rs).
1
325 (R)
[102 (MW)]d
1820 (IR)
1392 (IR)
1062 (IR)
933 (IR)
756 (R)
523 (R)
305 (R)
rms % error (excluding a2
modes and ν14)
a Calculated at the MP2/6-31G(d) level. b Details of scaling are given
in the Supporting Information. c Key: IR ) infrared of gas; R ) Raman
of liquid; MW ) microwave. d Frequency not included when scaling
force constants.
parameters; the unknown effects of correlation with otherwise
fixed parameters are revealed and included.30
Figure 1. Molecular structure of difluoromaleic anhydride as refined
from the ED/MW study. Principal rotation axes (a and b) and the
direction of the dipole moment are shown.
For p5, a restraint of 2.3 pm with an uncertainty of (0.7 pm
was employed, these values being derived from the results of
the ab initio computations reported in Table 5. Subsequently,
p5 refined to 2.6(6) pm with all other parameters returning
realistic values and esd’s. In particular, the esd for the CdC
bond length increased by a factor of 2.5, i.e., r(CdC) ) 133.6-
(5) pm compared to 133.3(2) pm when p5 was fixed.
All amplitudes of vibration pertaining to nonbonded distances
could be refined freely. However, it was necessary to apply
restraints to the ratios of refining amplitudes tied together in
pairs. The values of these ratio restraints were taken from the
scaled MP2/6-31G(d) force field with uncertainties of 2.5% of
the absolute values. Attempts to refine the amplitudes for the
five bonded distances using a similar approach were unsuc-
cessful. Instead u(C-F) and the four ratios of u(C-F) with the
other amplitudes for bonded distances were restrained. For the
final cycle, RG ) 0.0903 (RD ) 0.0503).
In the combined ED/MW refinements, 15 rotation constants
determined from the microwave spectra of five different
16
19
isotopomers, viz. the parent [1] (12C2-5
,
O
,
F ) with
8,9
1,6,7

Molecular Structure of 3,4-Difluorofuran-2,5-dione
J. Phys. Chem. A, Vol. 103, No. 12, 1999 1763
TABLE 7: Stark Measurements and Dipole Momenta
four, only the calculated value for A[1] - A[4] lay outwith 2×
the uncertainty range, corresponding to Bz(obs - calc) ) 0.06
MHz. Although such slight incompatibilities may be assigned
to small changes in the ring angles on isotopic substitution which
are not allowed for in our model, the scatter of differences is
consistent with the expected pattern for the quoted uncertainties.
Relative to the ED-only refinement, there was a slight increase
(0.001) in RG accompanied by a significant reduction in the
estimated uncertainties of all geometrical parameters.
The success of the final ED/MW refinement, for which RG
) 0.091 (RD ) 0.059), may be assessed on the basis of the
difference between the experimental and calculated radial-
distribution curves (Figure 3). The interatomic distances and
vibrational amplitudes (and restraints) of the optimum refine-
ment are listed in Table 11. The least-squares correlation matrix
is given as part of the Supporting Information together with
the experimental molecular-scattering intensity curves.
∆νcorrb/E2 (MHz kV-2 cm-2
)
J′ Ka′ Kc′
J′′ Ka′′ Kc′′
M
expt
calcd
6
6
6
5
5
4
2
2
3
r
r
r
5
5
5
4
4
3
1
1
2
2
3
2
-14.059(44)
-34.959(44)
-23.092(83)
-14.052
-35.001
-23.123
µb ) µtotal ) 1.8665(33) D
a Figures in parentheses are the standard deviations (1σ); calibration
b
µ(OCS) ) 0.7152(2) D; 1D ) 3.33564 × 10-30 C m. ∆νcorr ) ∆ν
corrected for fourth-order effects.
Discussion
The experimental measurements described herein provide the
first structural information for 3,4-difluorofuran-2,5-dione. The
analyses of both the microwave (Table 6) and the electron-
diffraction (Table 9) data are consistent with the spectroscopic
evidence that the molecule consists of a planar five-membered
ring incorporating a CdC double bond with C2V symmetry in
the gas phase. Studies of the structure in the solid phase by
single-crystal X-ray crystallography (not detailed here) have
been frustrated to date by the growth of crystals of inadequate
quality for high-resolution measurements. However, preliminary
data suggest strongly that the structure in the solid phase is also
molecular with C2V, or near C2V, symmetry.31
The geometrical parameters refined experimentally from the
microwave data alone and from the combined microwave/
electron-diffraction data agree well (Table 12); at the 3σ (99.7%
probability) level, the only significant differences lie with the
angles C2C3dC4 [MW: 108.65(1)°; GED/MW: 108.3(1)°] and
C3C2dO6 [MW: 129.92(1)°; GED/MW: 129.3(1)°]. In the
GED/MW combined analysis, all correlation between refining
parameters is included in the error estimates by the use of
flexible restraints. There are effectively no systematic errors in
the electron wavelength and camera distances since the data
for the benzene calibrant are treated identically to that of the
compound. Systematic errors must result from not allowing for
changes in bond angles on isotopic substitution and from
excluding the two lowest-frequency modes from the vibrational
analysis (underestimation of K corrections). However, it is not
possible to say which esd’s are affected explicitly and, moreover,
ignoring such deficiencies is not expected to give rise to
significantly underestimated errors. We therefore quote the
estimated standard deviations, 1σ, with the proviso that one or
two parameters may be defined slightly less precisely than this
would indicate.
Figure 2. Part of the microwave spectrum recorded between 9.6 and
10.1 GHz using a 1000 Vcm-1 Stark field. This is the 1596 r 1587
transition showing vibrational satellites associated with the low-
frequency torsional mode (Vt) and the out-of-plane bending mode (Vb).
substitution 13C2 [2], 13C3 [3], 18O6 [4], and 18O1 [5], were
combined with the GED data. The corrected rotational data Bz
were presented in the refinements as the three absolute values
for the parent isotopomer, A[1], B[1], and C[1], and the
differences of the other isotopomers for each axis from these
values, i.e., A[1] - A[2], B[1] - B[2], C[1] - C[2], etc. (Table
10).
The vibrational corrections to the microwave constants (B0
f Bz) for each isotopomer are summations of the corrections
for each mode.25 These sums were small, ca. 0.44 MHz for the
A axis and ca. 0.06 MHz for the B and C axes, but contributions
from some individual modes were of the order of 5 MHz. The
10% error in the absolute value of the vibrational correction
normally assumed was deemed inappropriately small. Instead,
the uncertainty in the absolute correction was computed from a
summation of an assumed 10% error in the correction for each
mode, according to eq 1 below, where c(m)i is the vibrational
correction of the ith mode of the main isotopomer, i.e., A[1],
B[1], or C[1]. The uncertainty in the correction for a difference
between the rotation constants for two isotopomers was
calculated similarly, as in eq 2, where c(n)i is the vibrational
correction of the ith mode of isotopomer n, i.e., A[1] - A[n],
B[1] - B[n], and C[1] - C[n], (n ) 2-5).
2
c(m)i
The structural parameters predicted at the MP2 level of theory
are in very good quantitative agreement with those obtained
experimentally (Tables 4 and 12). From the graded series of ab
initio calculations detailed in Table 4, it is clear that an account
of the correlated motion of electrons is essential if such good
quantitative agreement between theory and experiment is to be
obtained. The inclusion of electron correlation at the MP2 level
leads to a marked increase in all bond lengths of double-bond
character and of bonds to the highly electronegative O and F
atoms, relative to the uncorrelated SCF computations, e.g., SCF/
6-31G(d) vs MP2/6-31G(d); this is as expected for electron
precise molecules.32 Optimum agreement with experimental
(1)
∑
[
]
x
10
i
2
c(m)i - c(n)i
(2)
∑
[
]
x
10
i
Simultaneous refinement of the ED and MW data permitted
p5 to be refined freely. The data from the two methods
demonstrated a good degree of compatibility, with 11 of the 15
rotation constants fitting within the estimated uncertainties of
the corrected experimental values (see Table 10). Of the other

1764 J. Phys. Chem. A, Vol. 103, No. 12, 1999
Abdo et al.
TABLE 8: Excited-State Spectroscopic Constantsa from the MW Study (B/MHz, ∆/(u Å2), D,d,σ/kHz)
constant
V ) 0
1 (bend)
2 (bend)
1 (torsion)
2 (torsion)
A
B
C
2379.5563(6)
1750.9847(8)
1008.6812(2)
0.1706(50)
-0.2814(60)
0.11176b
-0.0416(46)
-0.0272(33)
6
2375.506(6)
1752.458(4)
1009.613(4)
2371.470(3)
1753.913(2)
1010.586(4)
2373.743(1)
1747.332(4)
1007.187(4)
2368.138(4)
1743.882(4)
1005.878(22)
DJ
DJK
DK
d1
d2
σ
ω(bend) ) 102(12) cm-1
ω(torsion) ) 154(10) cm-1
n
∆
84
0.0202(2)
c
-0.562(2)
-1.167(2)
-0.361(2)
-0.783(11)
a Figures in parentheses are the estimated standard deviations (1σ). b Fixed at MP2/6-31G(d) force-field value. c ∆ ) Ic - Ib - Ia, conversion
factor of 505379.1 MHz u Å2.
TABLE 10: Microwave Rotation Constants (B/MHz) Used
in the GED Refinements
constanta
BZ(obs)b
BZ(calc)c BZ(obs - calc) uncertaintyd
A[1]
B[1]
C[1]
2379.1125 2379.8913
1751.0413 1750.5843
1008.6231 1008.6491
-0.7788
0.4570
-0.0260
0.008
-0.004
-0.0006
0.004
1.0058
0.4476
0.1087
0.018
0.121
0.0052
0.020
A[1] - A[2]
B[1] - B[2]
C[1] - C[2]
A[1] - A[3]
B[1] - B[3]
C[1] - C[3]
A[1] - A[4]
B[1] - B[4]
C[1] - C[4]
A[1] - A[5]
B[1] - B[5]
C[1] - C[5]
5.866
7.738
3.6226
4.920
5.858
7.742
3.6232
4.916
2.642
2.630
0.012
0.053
1.7550
26.1767
59.9549
24.7309
51.7628
-0.0720
9.3921
1.7564
26.1178
59.9469
24.7289
51.7006
0.0001
9.4057
-0.0014
0.0589
0.0080
0.0020
0.0552
-0.0721
-0.0136
0.0054
0.0181
0.0631
0.0072
0.0400
0.0969
0.0083
Figure 3. Observed and final weighted difference radial-distribution
curves. Before Fourier inversion the data were multiplied by s exp-
[(-0.000 02s2)/(ZC - fC)(ZF - fF)].
a Isotopomer numbering: [1] ) parent (12C, 16O, 19F); [2] ) 13C2;
[3] ) 13C3; [4] ) 18O6; [5] ) 18O1. b From microwave spectroscopy.
B0 f BZ corrections were derived from the MP2/6-31G(d) force field
using ASYM40. c From the GED/MW refinement. d For details of the
derivation of uncertainty estimates, see the text.
TABLE 9: Geometrical Parameters (rr°/ r) for the
Electron-Diffraction Study (r/pm, angle/deg)a,b
no.
parameter
EDc
ED/MWc
TABLE 11: Interatomic Distances and Amplitudes of
(a) Independent
Vibration for the Combined GED/MW Study (ra, u/pm)a,b
p1 1/9[2r(O1-C2) + 2r(C2-C3) + 2r(C3-F8) + 134.3(1) 134.29(1)
r(C3dC4) + 2r(C2dO6)]
no. atom pair distance (ra) amplitude (u)
restraint
p2 1/2[r(C2-C3) + r(O1-C2)] - 1/5[2r(C3-F8) + 17.6(4)
r(C3dC4) + 2r(C2dO6)]
17.3(2)
r1
r2
r3
r4
r5
r6
r7
r8
C2dO6
C3-F8
C3dC4
O1-C2
C2-C3
C2‚‚‚C5
O1‚‚‚O6
C2‚‚‚C4
O1‚‚‚C3
C3‚‚‚F9
C3‚‚‚O6
C2‚‚‚F8
O6‚‚‚F8
F8‚‚‚F9
C2‚‚‚O7
C3‚‚‚O7
O1‚‚‚F8
C2‚‚‚F9
O6‚‚‚O7
O6‚‚‚F9
119.6(1)
131.4(2)
133.6(3)
139.6(1)
148.7(3)
226.7(2)
228.3(2)
228.6(2)
232.0(2)
239.7(2)
242.6(1)
244.5(1)
293.7(2)
301.3(2)
340.5(2)
344.1(2)
355.9(1)
357.6(1)
448.9(2)
470.2(1)
3.6(1)
4.1(1)
3.9(1)
4.9(2)
4.8(1)
5.6(2)
5.7(2)
5.4(2)
5.6(2)
5.1(2)
5.2(3)
5.9(3)
10.8(5)
10.8(5)
8.7(4)
8.5(4)
9.8(4)
9.4(4)
10.4(7)
10.5(7)
u2 ) 4.2 ( 0.1
u2/u1 ) 1.149 ( 0.029
u2/u3 ) 1.017 ( 0.025
u2/u4 ) 0.841 ( 0.021
u2/u5 ) 0.855 ( 0.021
u7/u6 ) 1.022 ( 0.026
u7/u8 ) 1.048 ( 0.026
u7/u9 ) 1.015 ( 0.025
p3 r(C2-C3) - r(O1-C2)
9.9(6)
13.3(4)
2.6(6)
9.2(3)
12.7(1)
2.3(4)
p4 1/3[2r(C3-F8) + r(C3dC4)] - r(C2dO6)
p5 r(C3dC4) - r(C3-F8)
p6
p7
p8
C2C3dC4
C4dC3F8
C3C2dO6
108.0(2) 108.3(1)
130.0(11) 129.9(1)
128.2(5) 129.3(1)
(b) Dependent
r9
d1 r(C2dO6)
d2 r(C3-F8)
d3 r(C3dC4)
d4 r(O1-C2)
d5 r(C2-C3)
118.5(3) 119.0(1)
130.9(3) 130.9(2)
133.6(5) 133.2(3)
139.1(4) 139.3(1)
149.0(3) 148.5(2)
108.3(7) 108.9(1)
107.9(5) 107.2(1)
r10
r11
r12
r13
r14
r15
r16
r17
r18
r19
r20
u10/u11 ) 0.975 ( 0.024
u10/u12 ) 0.874 ( 0.022
u13/u14 ) 1.006 ( 0.025
u15/u16 ) 1.029 ( 0.026
u17/u18 ) 1.041 ( 0.026
d6
d7
C2O1C5
O1C2C3
a For atom-numbering scheme, see Figure 1. b Figures in parentheses
are the estimated standard deviations (1σ). c For details of the refine-
ments, see the text.
u20/u19 ) 1.015 ( 0.025
a For atom-numbering scheme, see Figure 1. b Figures in parentheses
are the estimated standard deviations (1σ).
parameters is found when the basis set is extended to triple-ú
quality including additional d- and f-type polarization functions,
as has been observed elsewhere for wave functions which
account for electron correlation.32 Diffuse functions were not
found to offer any significant improvement. Thus, at the MP2
level with the 6-311G(2df) basis set, theoretical parameters offer
excellent support for those derived experimentally.33
The observed experimental vibrational frequencies for liquid-
phase (Raman) and vapor-phase (IR) samples of difluoromaleic
anhydride are listed as part of the Supporting Information.
Harmonic frequencies calculated at the MP2/6-31G(d) level are
given in Table 5. An assignment of the experimental funda-
mental frequencies has been made (Table 5), on the basis of a

Molecular Structure of 3,4-Difluorofuran-2,5-dione
J. Phys. Chem. A, Vol. 103, No. 12, 1999 1765
TABLE 12: Geometrical Parameters of 3,4-Disubstituted Maleic Anhydrides (distances/pm, angles/deg)a,b
H
F
Cl
Br
parameter
MW (rs)
GED (ra) ab initio (re)c
MW (rz)
GED/MW (rR°) ab initio (re)c GED (ra) ab initio (re)c ab initio (re)c
r(C2dO6)
r(C3-X8)
r(C3dC4)
r(O1-C2)
r(C2-C3)
119.62(1) 119.5(3)
107.91(3) 109.1(21)
133.31(4) 133.0(30)
138.76(1) 139.4(11)
148.49(3) 150.0(5)
120.6
108.3
134.0
139.9
148.8
142.3
108.2
129.5
129.7
108.3
107.7
0.6
118.3(4)
131.3(4)
132.5(4)
139.7(2)
148.7(6)
141.9(10)
108.65(1)
130.09(9)
129.92(1)
109.09(31)
106.81(16)
2.3(4)
119.0(1)
130.9(2)
133.2(3)
139.3(1)
148.5(2)
141.8(4)
108.3(1)
129.9(1)
129.3(1)
108.9(1)
107.2(2)
1.7(1)
120.3
132.4
134.1
140.0
148.5
142.2
108.4
130.3
129.2
108.8
107.2
1.6
118.8(2)
168.5(2)
133.2(5)
138.9(3)
149.5(3)
142.0(8)
107.9(2)
129.4(4)
128.5(4)
108.2(6)
108.1(4)
0.3(6)
120.3
168.9
134.8
139.7
149.2
142.5
108.1
129.8
129.4
109.0
107.4
1.6
120.3
184.7
134.7
139.9
149.1
142.5
108.2
129.2
129.6
109.1
107.3
1.8
r
ring(mean)d 141.56(6) 142.4(35)
C2C3dC4 107.90(1) 107.7(10)
C4dC3X8 129.99(0) 128.9(33)
C3C2dO6 129.61(1) 129.3(20)
C2O1C5
O1C2C3
108.06(1) 107.0(11)
108.07(0) 108.8(12)
e
∆
0.17(1)
8
1.8(16)
7
int. ring
ref
this work
this work
this work
this work
10
this work
this work
a For atom-numbering scheme, see Figure 1. b Estimated errors given in parentheses are as quoted in the original work. c MP2/6-31(d) level.
d rring(mean) ) 1/5[r(C3dC4) + 2 r(O1-C2) + 2 r(C2-C3)]. e Maximum difference of internal ring angles.
careful comparison of both the experimental and theoretical
frequencies and their intensities.34 In general, the theoretical
values are found to differ by no more than 4% of the assigned
experimental frequency. The exceptions are the two lowest-
frequency modes, ν11 and ν14, corresponding to a ring torsional
(a2) mode and an out-of-plane ring bending (b1) mode, which
have not been observed directly. From the MP2/6-31G(d) level
force field (scaled or unscaled), the a2 mode is predicted to lie
at lower frequency than the b1 mode, ∆ν ) (ν14 - ν11) ) 49
cm-1. However, microwave vibrational satellite intensities
(Figure 2) show that the b1 mode has the lowest fundamental
frequency in the molecule, ∆ν ) -52(16) cm-1. Unfortunately,
support for the MW measurements was not available from the
experimental vibrational spectra since (i) there are a number of
Although all of the 3,4-dihalofuran-2,5-diones are known,
only the structure of the dichloro derivative has been reported
(a gas-phase electron-diffraction study),10 together with the
structure of the parent maleic anhydride in the solid phase by
X-ray crystallography38 and as a vapor by microwave spectro-
scopy8 and electron diffraction.7 The results of these studies
are collected together in Table 12. Bearing in mind that the
data refer to definitions of experimental parameters that differ
slightly, viz., rs (MW) vs ra (GED) and rR° (GED) ≡ rz (MW),
and that the errors for the GED determination of maleic
anhydride are relatively large,7 the studies to date suggest
strongly that a change in substituent leads to very little change
in the structure. Thus, the three structures investigated experi-
mentally demonstrate the same average ring size to within
experimental error [see rring(mean)], and show very little ring
distortion relative to a regular pentagon (108°), as judged by
the range of the internal ring angles.
To support our experimental findings, further ab initio
computations have been undertaken to optimize the structures
of maleic anhydride and its 3,4-dichloro and 3,4-dibromo
derivatives. At the MP2/6-31G(d) level, the agreement between
the parameters for which experimental data are available is good,
and allows the relative magnitudes of the theoretical values to
be compared with confidence.
The average ring size for the Cl and Br derivatives is predicted
to be slightly larger than for X ) H or F, attributable mainly to
the longer C2-C3 single-bond distances in the heavier con-
genors, but the variation falls over only 0.3 pm. The predicted
distortion of the ring shows a systematic increase, the trend in
internal ring-angle difference being H < F ) Cl < Br, but, as
found experimentally, the variation is very small [(0.6°(H) -
1.8°(Br)].
For the 3,4-disubstituted maleic anhydrides considered here
(X ) H, F, Cl, or Br), there is a significant variation in the size
of the substituent atom, Br ≈ Cl > F > H, and in its
electronegativity, F > Cl ≈ Br > H.11 These variations give
rise to structural changes which originate from four steric/
electronic effects. First, increasing the steric demands of the
substituent would lead primarily to a wider CdC-X angle and,
consequently, to a wider C-CdO angle. A second, similar
distortion would be expected on increasing the electronegativity
of the substituent atom as a result of greater electrostatic
repulsion of the pairs C-X/C-X and C-X/CdO. From the ab
initio values in Table 12, it is seen that neither trend is borne
out, in that for angle CdC-X the ordering is F > Cl > H >
Br and for C-CdO it is H > Br > Cl > F, the latter
demonstrating the reverse trend from that expected of the
features in the Raman spectrum of the liquid below 200 cm-1
,
so unambiguous assignment of two frequencies to the a2 and
b1 modes is not possible, and (ii) facilities were not available
to record far-infrared spectra which potentially would identify
the b1 mode, the a2 being inactive. However, the microwave
frequencies are consistent with those of maleic anhydride itself,
at 168(15) cm-1 (b1) and 266(20) cm-1 (a2), i.e., ∆ν ) -98-
(25) cm-1 28
both being ca. 0.6 of the analogous mode in the
,
parent anhydride (0.58 for the torsion and 0.61 for the bend),
suggesting a similar change in reduced mass for the two modes
on substituting H for F. Thus, it would appear that these modes
are incorrectly ordered in the ab initio computations and were
subsequently excluded from the force-field analysis. This
notwithstanding, inclusion of such low-frequency modes is
known to result in an overestimation of perpendicular amplitudes
of vibration (K).34
For vibrational frequencies in multiply bonded species, it is
not uncommon to find the greatest discrepancies between the
experimental and theoretical frequencies for low-magnitude
bending and torsional modes.35 It is more uncommon to find
the theoretical calculation opposing the relative magnitudes of
these experimental frequencies. However, force-field computa-
tions for difluoromaleic anhydride at a higher level, or employ-
ing a DFT approach, yielded almost identical predictions for
∆ν, viz., 47 cm-1 at MP2/6-311G(d) and 46 cm-1 at B3LYP/
6-31G(d), cf. 49 cm-1 at MP2/6-31G(d). Further, calculations
for the maleic anhydride and for dichloro- and dibromomaleic
anhydrides were also undertaken. For each, the relative ordering
of the lowest-frequency modes, even at the uncorrelated SCF/
6-31G(d) level, is in accord with the experimental observa-
tions.36,37 This suggests that the discrepancy between theory and
experiment for such modes in the present case must arise as a
result of the presence of fluorine in the molecule.

1766 J. Phys. Chem. A, Vol. 103, No. 12, 1999
Abdo et al.
SCHEME 2
the Edinburgh Electron-Diffraction Service (Grant GR/K44411)
and the Edinburgh ab initio facilities (Grant GR/K04194), and
to Rhoˆne-Poulenc Chemicals (Avonmouth) for financial support
(O.J.D.). We thank Professor A. C. Legon (University of Exeter)
for obtaining the FTMW spectra and Mr. S. Hawker (University
of Bristol) for assistance with analysis, Dr. T. M. Greene
(University of Oxford) and Dr. C. R. Pulham (University of
Edinburgh) for collecting the FT Raman spectra, and Dr. L.
Hedberg (Oregon State University) for providing a copy of the
ASYM40 program.
Supporting Information Available: Consisting of five
tables, listing (i) observed vibrational frequencies, (ii) internal
and symmetry coordinates, (iii) scale and quadratic force
constants, (iv) significant (g 50) elements of the correlation
matrix, and (v) Cartesian coordinates for the experimental (ED/
MW) and theoretical structures, and a plot of the molecular-
scattering intensity curves. This material is available free of
charge via the Internet at http://pubs.acs.org.
References and Notes
(1) Abdo, B. T.; Banks, R. E. Unpublished work.
(2) Abdo, B. T.; Banks, R. E. J. Fluorine Chem. 1992, 58, 360.
(3) Raasch, M. S.; Miegel, R. E.; Castle, J. E. J. Am. Chem. Soc. 1959,
81, 2678.
electronegativity. Another effect associated with an increase in
substituent electronegativity is well-known; namely, that bonds
adjacent to C-X are expected to become shorter [r(CdC) and
r(C-C)] and the internal (ipso) angle ( CdC-C) to widen.39
At the vicinal, carbonyl position r(CdO) and r(C-O) would
be expected to shorten to a lesser degree and the angles C-C-O
and C-CdO to narrow. The calculations predict H < F < Cl
< Br, F < H < Cl < Br for r(CdC) and r(C-C) and Cl < Br
) H < F for CdC-C. For r(CdO) and r(C-O) the ordering
is F ) Cl ) Br < H and Cl < Br ) H < F, and F < Br < Cl
< H and F < Cl < Br < H for C-C-O and C-CdO,
respectively. Thus, only the angles at the vicinal carbon follow
the trend anticipated from this third effect which is observed
widely in aromatic systems.40 However, for X ) F the average
ring size would be expected to be smallest, and this appears to
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Form A involves the localization of positive charge adjacent to
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lengths, a shorter r(C-C) bond, a wider C-CdO angle, and a
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This is not surprising since the trend for the stabilization of
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for X ) H. It is an analogue of form C which accounts for
fluorobenzene having the smallest dipole moment of the
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Physical Sciences Research Council (EPSRC) for support of

Molecular Structure of 3,4-Difluorofuran-2,5-dione
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