Gas phase structure and conformational properties oftrifluoroacetic anhydride, CF3C(O)OC(O)CF3

Angelika Hermann, Heinz Oberhammer*

Institut fur Physikalische und Theoretische Chemie, Universitat Tubingen, Auf der Morgenstelle 8, Tubingen 72076, Germany

Received 7 February 2003; accepted 11 March 2003

Available online 11 March 2004

Abstract

The geometric structure of trifluoroacetic anhydride, CF3C(O)OC(O)CF3, has been studied by gas electron diffraction (GED) and quantum

chemical calculations (MP2 and B3LYP with 6-31G* basis sets). The GED analysis results in a single conformer with synperiplanar

orientation of the two C¼O bonds. This analysis, however, cannot discriminate between a planar equilibrium structure (C2v symmetry) with

large amplitude torsional motions around the O–C bonds and a nonplanar equilibrium structure (C2 symmetry) with a low barrier at the planar

arrangement. An effective dihedral angle fðC�O�C¼O ¼ 18ð4Þ� is obtained. Both quantum chemical methods predict a nonplanar

equilibrium structure of C2 symmetry and fðC�O�C¼OÞ ¼ 16:5� and 13.98, respectively.

# 2004 Elsevier B.V. All rights reserved.

Keywords: Geometric structure; Conformational properties; Trifluoroacetic anhydride; Gas electron diffraction; Quantum chemical calculations

1. Introduction

Anhydrides of the type XC(O)–O–C(O)X can adopt

different conformations, depending on the orientations of

the two carbonyl groups. The orientation of each C¼O bond

relative to the opposite O–C bond can be synperiplanar (sp),

synclinal (sc), anticlinal (ac) or antiperiplanar (ap).1 The

three possible conformations for such compounds are shown

in Scheme 1, where s can be sp or sc and a can be ap or ac.

The parent compound, formic anhydride, HC(O)–O–

C(O)H, has been studied extensively by gas electron dif-

fraction (GED) [1,2], microwave spectroscopy [3], and

quantum chemical calculations [4]. All investigations

result in a planar [sp, ap] conformation which is stabilized

by an intramolecular O � � �H bond. For acetyl anhydride,

MeC(O)–O–C(O)Me, two GED studies report different

conformational properties. Whereas the earlier investigation

results in a single conformer with C2 symmetry and [sc, sc]

orientations of the two C¼O bonds [5], the more recent

study results in a 2:1 mixture of [sp, ac] and [sp, sp] forms

[6]. This latter result is confirmed by quantum chemical

calculations. Only a single [sp, sp] conformer with large

amplitude torsional vibrations around the O–C bonds was

observed in a recent GED study of bisfluoroformyl ether

(dicarbonic difluoride), FC(O)–O–C(O)F [7]. The GED

experiment cannot discriminate between a planar and a

slightly nonplanar equilibrium structure, but different quan-

tum chemical calculations (HF, MP2 and B3LYP) predict

nonplanar equilibrium structures with dihedral angles

f(C–O–C¼O) between 10 and 158 and very low barriers

(0.01–0.06 kcal mol�1) at the exactly planar conformation.

Trifluoroacetic anhydride, CF3C(O)–O–C(O)CF3 (1), has

been studied more than 30 years ago by GED using a rigid

model. Only a single conformer has been observed with a

slightly nonplanar skeleton of C2 symmetry and [sp, sp]

orientations of the two C¼O bonds [8]. Some bond angles in

the acetyl groups, determined in that study, possess rather

unusual values. In the present paper we report a re-inves-

tigation of the structure and conformational properties of

this anhydride, using GED in combination with quantum

chemical calculations.

2. Quantum chemical calculations

Possible conformations of 1 are characterized by the tor-

sional angles around the two O–C bonds, f1(C2–O–C1¼O)

and f2(C1–O–C2¼O2). Geometry optimizations were per-

formed with different starting values for f1 and f2, using

Journal of Fluorine Chemistry 125 (2004) 917–921

* Corresponding author. Tel.: þ49-7071-2976907;

fax: þ49-7071-295490.

E-mail address: heinz.oberhammer@uni-tuebingen.de (H. Oberhammer).1 sp corresponds to dihedral angles j(C–O–C¼O) of 0 � 30�, sc to

60 � 30�, ac to 120 � 30� and ap to 180 � 30�.

0022-1139/$ – see front matter # 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jfluchem.2003.03.001

the hybrid method B3LYP and the MP2 approximation with

6–31G* basis sets. Both methods produce similar results and

predict two stable conformers, [sp, sp] and [sp, ac]. Their

dihedral angles, relative energies and Gibbs free energies are

listed in Table 1. The [ac, ac] structure does not represent a

stable conformation.

Geometry optimizations with such a starting structure

converged towards the [sp, ac] conformer. The low energy

[sp, sp] form possesses a slightly nonplanar structure with C2

symmetry and f ¼ f1 ¼ f2 of 13.98 (B3LYP) and 16.58(MP2), respectively. The [sp, ac] conformer is predicted to

be higher in energy by 2.16 and 2.14 kcal mol�1, respec-

tively. The B3LYP method results in a relative Gibbs free

energy of 2.48 kcal mol�1, which corresponds to a contribu-

tion of less than 2% at room temperature. The negative value

of f2 in the [sp, ac] conformer implies, that both C¼O bonds

lie on the same side of the C1–O–C2 plane.

The potential function for the symmetric torsional motion

of the [sp, sp] conformer, which has been derived with the

MP2 approximation for fixed values of f ¼ f1 ¼ f2

between 0 and 408 is shown in Fig. 1. This approximation

and the B3LYP method predict a double–minimum potential

with barriers at f ¼ 0� of 0.11 kcal mol�1 (MP2) and

0.14 kcal mol�1 (B3LYP). The function derived with the

B3LYP method is very similar and is not shown in Fig. 1. All

quantum chemical calculations were performed with the

GAUSSIAN98 program package [9]. Vibrational amplitudes

were derived from the calculated (B3LYP) Cartesian force

constants with the program ASYM40 [10].

3. Experimental

A commercial sample of trifluoroacetic anhydride (ABCR

Fluorochemicals 99.9%) was used without further purifica-

tion. Electron diffraction intensities were recorded with a

Gasdiffraktograph KD–G2 [11] at 25 and 50 cm nozzle-to-

plate distances and with an accelerating voltage of about

60 kV. The sample was cooled to �30 8C and the inlet

system and nozzle were at room temperature. The photo-

graphic plates were analyzed with the usual methods [12]

and averaged molecular intensities in the s-ranges 2–18

and 8–35 A�1 (s ¼ ð4p=l)sin W/2, l ¼ electronwavelength,

W ¼ scatteringangle) are shown in Fig. 2.

4. Electron diffraction analysis

The experimental radial distribution function (RDF),

which was derived by Fourier transformation of the mole-

cular intensities with an artificial damping function

exp(�gs2), g ¼ 0:0019 A2, is shown in Fig. 3. The RDF

is reproduced best with a slightly nonplanar [sp, sp] con-

former. In the first step, a rigid structural model was refined

by least squares fitting of the molecular intensities. In this

refinement the molecule was constrained to C2 symmetry.

Vibrational amplitudes were collected in groups (see

Table 2) and amplitudes, which either caused high correla-

tions between geometric parameters or which were poorly

determined by the GED experiment, were set to calculated

values. With these assumptions nine geometric parameters

(p1–p9) and eight vibrational amplitudes (l1–l8) were

refined simultaneously. The following correlation coeffi-

cients had values larger than |0.6|: p2=p4 ¼ �0:91,

p2=p8 ¼ �0:88, and p4=l8 ¼ 0:92. The agreement factor

was R ¼ 5:19%. The results of this refinement are given in

Table 2 (vibrational amplitudes) and Table 3 (geometric

parameters), together with calculated values. A molecular

model is shown in Fig. 4. The experimental dihedral

angle f ¼ 18(4) obtained in this GED analysis represents

an ‘‘effective’’ value due to a large amplitude torsional

vibration.

It is evident from the calculated torsional potential

functions (Fig. 1) that a rigid model is not quite adequate

Scheme 1.

Fig. 1. Potential functions for symmetric torsion (f ¼ f1 ¼ f2) obtained

from MP2/6-31G* calculation and from GED with a double-minimum

potential (GED-DM) or single-minimum potential (GED-SM). The

GED-DM curve is shifted by 0.5 kcal mol�1, the GED-SM curve by

1.0 kcal mol�1.

Table 1

Calculated dihedral angles f1 and f2, relative energies DE and Gibbs free

energies DG0 for [sp, sp] and [sp, ac] conformers of 1

B3LYP/6-31G* MP2/6-31G*

[sp, sp] [sp, ac] [sp, sp] [sp, ac]

f1(C2–O–C1¼O) 13.9 10.9 16.5 8.6

f2(C1–O–C2¼O) 13.9 �129.5 16.5 �118.1

DE (kcal mol�1) 0.00 2.16 0.00 2.14

DG0 (kcal mol�1)a 0.00 2.48 – –

a Includes the factor �RT ln 2 for different multiplicities of the two

conformers.

918 A. Hermann, H. Oberhammer / Journal of Fluorine Chemistry 125 (2004) 917–921

for this molecule. The predicted (B3LYP) frequency for the

symmetric torsional vibration of the carbon–oxygen skeleton

is 19 cm�1. Therefore, the molecular intensities were fitted

with a dynamic model, which is composed of pseudo-con-

formers with C2 symmetry and different dihedral angles ffrom 0 to 608. Each conformer is weighted by a Boltzman

factor. As suggested by the quantum chemical calculations,

a double–minimum potential of the form V ¼ V0½1�ðf=feÞ

22 was used. V0 is the barrier at f ¼ 0� and fe is

the equilibrium value for the dihedral angle corresponding to

the minimum of the potential function. Vibrational ampli-

tudes for torsion dependent interatomic distances were set to

values, which were derived from the calculated force field

without the contributions of the torsional frequency. Only six

vibrational amplitudes were refined in these least squares

analyses. Because of a high correlation between V0 and fe, it

was not possible to refine both parameters simultaneously.

Thus, refinements of bond lengths, bond angles and fe with

fixed V0 values were performed. For V0 ¼ 0:11 kcal mol�1

(value predicted by MP2 method) the refined dihedral angle

was fe ¼ 17ð3Þ�. For larger V0 values the refined dihedral

angle decreases and vice versa. For V0 � 0:30 kcal mol�1 the

agreement factor remained nearly constant (5.27–5.29%). All

potential functions for the various (V0, fe) pairs, however,

possess a very similar gross shape. The double-minimum

potential with V0 ¼ 0:11 kcal mol�1 and fe ¼ 17ð3Þ� is

shown in Fig. 1 (curve GED-DM). If a single-minimum

quartic potential function, V ¼ kf4, is used for the torsional

motion, the lowest agreement factor R ¼ 5:29% was

obtained for k ¼ 9ð5Þ kcal rad�4. This potential function

(see Fig. 1, curve GED-SM) is again very similar to the

curves obtained with double-minimum potentials. The bond

Fig. 2. Averaged molecular intensities for long (top) and for short (bottom) nozzle-to-plate distances and residuals.

Fig. 3. Experimental radial distribution function and difference curve.

Important interatomic distances are indicated by vertical bars. Fig. 4. Molecular model with atom numbering.

A. Hermann, H. Oberhammer / Journal of Fluorine Chemistry 125 (2004) 917–921 919

lengths and bond angles obtained with the various dynamic

models agree with those of the rigid model (Table 3) within

their error limits.

5. Discussion

Trifluoroacetic anhydride exists in the gas phase as a

single conformer with [sp, sp] orientation of the two C¼O

bonds. This result agrees with that for bisfluoroformyl ether

(dicarbonic difluoride), FC(O)–O–C(O)F [7], but it is in

contrast to the conformational properties of the parent

compound, acetyl anhydride, which exists as a 2:1 mixture

of [sp, ac] and [sp, sp] forms [6]. The presence of a single

conformer in 1 is demonstrated also by matrix IR spectra

where two C¼O vibrations are observed at 1883 (vs) and

1816 (s) cm�1 [13]. The calculated (B3LYP) frequencies

with intensities in km/mol for the [sp, sp] conformer are

1949 (228) and 1878 (137) cm�1. The GED analysis for

1 cannot discriminate unambiguously between a planar

equilibrium structure with a large-amplitude torsional

motion and a nonplanar equilibrium structure with a low

barrier at the planar arrangement. With the assumption that

only small-amplitude vibrations occur in this compound

(rigid model), a nonplanar structure with C2 symmetry

and effective dihedral angles f1 and f2 of 18(4)8 is obtained.

If the torsional vibration is described with a dynamical

model, the experimental molecular intensities are fitted

almost equally well with a single-minimum potential (planar

equilibrium structure) and with a double-minimum potential

(nonplanar equilibrium structure) for the torsional motion.

Both potential functions have a very similar overall shape

(see Fig. 1). The two quantum chemical methods, MP2 and

B3LYP with 6-31G* basis sets, predict double-minimum

potentials with very low barriers for the planar structure of

0.11 and 0.14 kcal mol�1, respectively. The shape of this

potential function can be rationalized as a delicate balance

between steric repulsion of the two carbonyl oxygen atoms

(O1 � � �O2) which favors a nonplanar structure and conjuga-

tion between the np lone pair of the central oxygen atom and

Table 2

Interatomic distances, experimental and calculated vibrational amplitudes in A for trifluoroacetic anhydride

Atom pair Distance Amplitude GEDa Amplitude B3LYPb Atom pair Distance Amplitude GEDa Amplitude B3LYPb

C¼O 1.19 0.036c 0.036 C2 � � �F2 3.88 0.217c 0.217

C–F 1.33 0.045c 0.045 C2 � � �F3 4.06 0.173(38) l3 0.190

O–C 1.37 0.048c 0.048 O1 � � �C4 4.24 0.141(37) l4 0.150

C–C 1.53 0.051c 0.051 O1 � � �F5 4.49 0.374c 0.374

F1 � � � F2 2.16 0.057(3) l1 0.056 F2 � � � F6 4.51 0.459c 0.459

O � � �O1 2.29 0.055(3) l1 0.054 C3 � � �C4 4.60 0.091(24) l2 0.111

O � � �C3 2.33 0.066c 0.066 F3 � � � F6 4.67 0.487c 0.487

C1 � � � F1 2.36 0.069c 0.069 C3 � � �F6 4.68 0.225(74) l7 0.288

C1 � � �C2 2.37 0.064c 0.064 C2 � � �F1 4.69 0.094(37) l8 0.086

O1 � � �C3 2.41 0.060c 0.060 C3 � � �F5 4.76 0.255(74) l7 0.295

O1 � � �F1 2.70 0.091(24) l2 0.101 O1 � � �F6 4.93 0.141(37) l4 0.144

O � � � F2 2.72 0.173(38) l3 0.188 O1 � � �F5 5.11 0.175c 0.175

C1 � � �O2 2.84 0.141(37) l4 0.143 F2 � � � F5 5.19 0.474c 0.474

O1 � � �O2 2.86 0.093(25) l5 0.093 C3 � � �F4 5.81 0.090c 0.090

O1 � � �F2 3.30 0.159c 0.159 F1 � � � F5 5.94 0.282c 0.282

O � � � F1 3.50 0.092(17) 0.063 F1 � � � F6 5.98 0.274c 0.274

C1 � � �C4 3.61 0.079 0.070 F1 � � � F4 6.98 0.079c 0.079

a Error limits are 3s values. For atom numbering see Fig. 4.b 6-31G* basis sets.c Not refined.

Table 3

Experimental and calculated geometric parameters for trifluoroacetic anhydride

GEDa MP2/6-31G* B3LYP/6-31G* HF/6-31G*

C¼O 1.188(4) p1 1.201 1.190 1.165

O–C 1.373(12) p2 1.388 1.383 1.353

C–C 1.533(6) p3 1.5335 1.546 1.531

(C–F)mean 1.333(4) p4 1.342 1.338 1.311

C–O–C 122.7(12) p5 119.7 121.8 122.9

O–C¼O 128.1(11) p6 127.5 127.3 126.8

O–C–C 107.2(10) p7 107.2 107.7 108.6

F–C–F 108.1(4) p8 108.9 109.0 109.0

f(C–O–C¼O) 18(4) p9 16.5 13.9 18.8

a ra values in A and 8. Error limits are 3s values. For atom numbering see Fig. 4.

920 A. Hermann, H. Oberhammer / Journal of Fluorine Chemistry 125 (2004) 917–921

the two C¼O bonds which favors a planar skeleton. Rotation

of the two acetyl groups around the O–C bonds by 188(effective torsional angle) increases the O1 � � �O2 distance

from 2.76 A in the planar structure to 2.86 A. Simulta-

neously, the orbital interaction due to conjugation is reduced

from 70.8 to 65.7 kcal mol�1 upon this rotation, according to

a natural bond orbital (NBO) analysis.

For a comparison between experimental and calculated

bond lengths the differences between vibrationally averaged

ra values and calculated equilibrium re values have to be

taken into account. Ra distances are systematically longer

than re values by about 0.004–0.008 A. Considering these

differences, all calculated bond distances in Table 3 are

slightly too long. The agreement between experimental and

calculated bond angles is better than �28.The results of the present study agree with those of the

early GED study with respect to the conformation of 1.

Andreassen et al. [8] also reported the presence of a single

[sp, sp] conformer with a nearly planar skeleton. The bond

lengths of both investigations are similar. The bond angles in

the acetyl group, however, differ strongly, with O–C–C ¼122:6(4)8, instead of 107.2(10)8 obtained in the present

study. These differences in bond angles lead also to a smaller

dihedral angle f ¼ 10ð2Þ�, compared to 18(4)8 in this study.

Acknowledgements

We gratefully acknowledge financial support by the

Deutsche Forschungsgemeinschaft.

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