Formic acetic anhydride in the gas phase, studied by electron diffraction and infrared spectroscopy, supplemented with ab-initio calculations of geometries and force fields

Article abstract of DOI:10.1021/jp9607982

The structure of formic acetic anhydride was studied by the joint analysis of gas-phase electron diffraction and infrared data, supported with extensive ab-initio calculations on the 4-21G and 6-31G** levels. All data agree with the gas phase at room temperature existing in the planar (sp,ap) conformer. Best electron diffraction geometry was obtained using geometrical constraints derived from 4-21G calculations after correction to r_α level. Also, the scaled 4-21G force field performed better than its 6-31G** counterpart. The new model of formic acetic anhydride is self-consistent, reproduces the IR frequencies with a root-mean-square deviation of 8.8 cm^-1, and results in an improved frequency assignment as well as in a good qualitative agreement between observed and calculated IR band intensities. Formic acetic anhydride is conformationally and spectroscopically very different from acetic anhydride, but strongly resembles formic anhydride, although differences remain. The similarities with formic anhydride are ascribed to an attractive nonbonded H (formyl)...O= interaction, while the dissimilarities are ascribed to a larger electronic interaction between two formyl moieties rather than between a formyl and an acetyl moiety.

Full text of DOI:10.1021/jp9607982

11620
J. Phys. Chem. 1996, 100, 11620-11629
Formic Acetic Anhydride in the Gas Phase, Studied by Electron Diffraction and Infrared
Spectroscopy, Supplemented with ab-Initio Calculations of Geometries and Force Fields
G. Wu, S. Shlykov,† C. Van Alsenoy, and H. J. Geise*
Department of Chemistry, UniVersity of Antwerpen (UIA), UniVersiteitsplein 1, B-2610 Wilrijk, Belgium
E. Sluyts and B. J. Van der Veken
Department of Inorganic Chemistry, UniVersity of Antwerpen (RUCA), Groenenborgerlaan 171,
B-2020 Antwerpen, Belgium
ReceiVed: March 15, 1996; In Final Form: April 24, 1996X
The structure of formic acetic anhydride was studied by the joint analysis of gas-phase electron diffraction
and infrared data, supported with extensive ab-initio calculations on the 4-21G and 6-31G** levels. All data
agree with the gas phase at room temperature existing in the planar (sp,ap) conformer. Best electron diffraction
geometry was obtained using geometrical constraints derived from 4-21G calculations after correction to rR°
level. Also, the scaled 4-21G force field performed better than its 6-31G** counterpart. The new model of
formic acetic anhydride is self-consistent, reproduces the IR frequencies with a root-mean-square deviation
of 8.8 cm-1, and results in an improved frequency assignment as well as in a good qualitative agreement
between observed and calculated IR band intensities. Formic acetic anhydride is conformationally and
spectroscopically very different from acetic anhydride, but strongly resembles formic anhydride, although
differences remain. The similarities with formic anhydride are ascribed to an attractive nonbonded H
(formyl)‚‚‚O) interaction, while the dissimilarities are ascribed to a larger electronic interaction between
two formyl moieties rather than between a formyl and an acetyl moiety.
Introduction
In this publication we report on the conformational analysis
of formic acetic anhydride (henceforth abbreviated as FAA;
Figure 1) in the gas phase. The molecule is of interest because
it is chemically intermediate between formic anhydride and
acetic anhydride (abbreviated as FA and AA, respectively), two
molecules widely differing in conformational behavior. FA was
proved1 to be a rather rigid molecule consisting in the gas phase
of only the planar (sp,ap) conformation, whereas AA was
shown2 to be neither planar nor rigid, exhibiting in the gas phase
large amplitude motions in which the two relevant OdC-O-C
torsion angles span almost the complete conformational space.
In conformity with the Cahn-Ingold-Prelog priority rules
and IUPAC recommendations3 the torsion angles æ1 (O3dC2-
O1-C8) and æ2 (O9dC8-O1-C2) are taken to characterize
the various possible conformations of FAA. The planar forms,
together with their IUPAC names and the atomic numbering
Figure 1. Atomic numbering scheme used for FAA, together with its
scheme used, are given in Figure 1. It should be noted that æ1
possible planar conformations and their nomenclature.
(acetyl side) is named first and æ2 (formyl side) is named
second.
diffraction geometry and taking as starting values the force
constants of formic acid and maleic anhydride, these researchers
So far a review,4 mostly on the chemical properties of FAA,
has been published, but few structural studies of mixed
also determined a force field for FAA. Again, lack of data
anhydrides of formic and other open chain carboxylic acids have
allowed the determination of only a fraction of the off-diagonal
appeared. Earlier electron diffraction data of FAA have been
interaction constants.
interpreted5 to show the existence of one nonplanar conformer
The major problem in the older work is the lack of resolution,
leading in the least-squares refinements to large correlation
between refinables. Correlation between refinables øi and øj
means that the same change in the calculated data can be brought
about by changes in either øi or øj. Thus, with correlation
present, an imperfect model may produce a perfect match
with torsion angles æ1 ) 46(3)° and æ2 ) 159(3)°, i.e. an
(sc,ap) conformation. Lack of resolution, however, rendered
the accuracy of the determination rather low. Furthermore,
Vledder et al.6 assigned the solution infrared and Raman spectra
of d0 through d4 deuteriated FAA species. Using the electron
between observed and calculated data. A joint analysis of data
from different techniques and the reduction of refinables through
the use of constraints may alleviate the problems. Since the
reliability of the total analysis is intimately linked to the
* Author to whom correspondence should be addressed.
† On leave from Institute of Chemical Technology, Department of
Physics, Ul, Engelsa 7, Ivanovo 153460, Russia.
X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00798-8 CCC: $12.00 © 1996 American Chemical Society

Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11621
mL of dry tetrahydrofuran. A less than stoichiometric amount
of sodium formate is employed in order to avoid the formation
of formic anhydride as much as possible. The reaction mixture
was stirred for 24 h at 0 °C and then filtered. Most of the
solvent and unreacted acetyl chloride were removed under
reduced pressure (ca. 20 mmHg) at 0 °C. The compound was
obtained by distilling the residue at 35 °C at a pressure of 20
mmHg. During the reaction no gas evolution was observed (CO
formation from decomposition).
The purity was checked from NMR spectra (CDCl3 solution,
tetramethylsilane as internal standard, room temperature). In
the 13C-NMR spectrum three peaks were seen with chemical
shifts of 167.7 ppm (formyl C), 155.9 ppm (acetyl C), and 21.0
ppm (methyl C). In the 1H spectrum signals were observed at
δ ) 9.10 ppm (formyl H), δ ) 2.30 ppm (methyl H). An
additional signal at δ ) 8.8 ppm was noted with an intensity
less than 2%, attributable to FA.12 From this we concluded
that no further purification was necessary, and freshly prepared
samples were used in the following experiments.
Figure 2. Experimental leveled intensities, I(s), with final backgrounds,
B(s), for FAA.
Electron diffraction intensities were recorded photographically
on the Antwerpen diffraction unit manufactured by Technische
Dienst, TPD-TNO, Delft, The Netherlands. Although FAA is
rather unvolatile at room temperature, but to avoid interference
by decomposition products, we performed the measurements
at 300 K and kept the exposure time below 2 min. The resulting
photographic recordings showed relatively low optical densities
(0.2-0.6 D), for some of which the correlation of plate density
with real incident intensity is not strictly linear. An accelerating
voltage of 60 kV, stabilized within 0.01% during the exposures,
was used. The electron wavelength was calibrated against the
known CC bond length of benzene,14 resulting in λ ) 0.048 712-
(2) Å. Three, four, and four plates (Kodak Electron Image)
were selected from recordings at the nozzle-to-plate distances
of 599.25(2), 350.83(2), and 200.19(2) mm, respectively.
Optical densities were measured on a modified, microprocessor-
reliability of the constraints, they are best taken from high-
quality ab-initio calculations. The major advantage of the
combined approach is that it produces a model in agreement
with all available gas-phase structural data. We aim to produce
for FAA such a self-consistent model (see ref 7 for procedures
and refs 1, 2, and 8-11 for examples).
Experimental Section
Following a procedure described by Schijf and Stevens,12
FAA was synthesized according to eq 1:
HCOONa + CH3COCl f HCOOCOCH3 + NaCl (1)
Freshly distilled acetylchloride, 39.3 g (0.5 mol), was added to
27.2 g (0.4 mol) of finely powdered sodium formate in 100
Figure 3. Experimental (O) and theoretical (s) sM(s) curve for FAA.

11622 J. Phys. Chem., Vol. 100, No. 28, 1996
Wu et al.
Figure 4. Infrared spectrum of gaseous FAA.
controlled, rotating ELSCAN E-2500 microdensitometer.15
Optical density values were converted to intensities using the
one-hit model of Foster.16 Coherent scattering factors were
taken from Ross et al.,17 and incoherent scattering factors from
Tavard et al.18 The data were processed by standard proce-
dures,19 yielding leveled intensities in the following ranges:
60 cm: 3.75 e s e 12.75 Å-1
35 cm: 7.00 e s e 21.75 Å-1
20 cm: 13.00 e s e 33.00 Å-1; all with ∆s ) 0.25 Å-1
Leveled intensities with final backgrounds and the combined
sM(s) curve are given in Figures 2 and 3, respectively.
Gas-phase infrared spectra between 4000 and 500 cm-1 were
recorded at room temperature at a pressure of 5 hPa on a Bruker
113V FTIR spectrometer using a 29 cm gas cell with KBr
windows (see Figure 4). The comparison with the frequencies
observed by Vledder et al.6 for the d0 species in a CCl4 solution
shows a root-mean-square deviation of 6.7 cm-1 and a maximum
deviation of 11 cm-1
.
Theoretical Models
Figure 5. Calculated energies along selected lines in æ1,æ2 space, using
To the best of our knowledge no quantum chemical inves-
tigations of FAA have been published before.
the 4-21G basis (top) and the 6-31G** basis (bottom): (0) æ1
)
0f180° and æ2 ) 0f180°; (+) æ1 ) 0° and æ2 ) 0f180°; (9) æ2 )
180° and æ1 ) 0f180°; (2) æ2 ) 180° and æ1 ) 0f180°; (O)
æ(H(5)-C(4)-C(2)-O(3)) ) 0f180°.
In this work we applied Pulay’s gradient method,20-22 the
program BRABO-MIA,23,24 and the 4-21G,25 6-31G, and
6-31G** basis sets.26,27 Fully relaxed geometry optimizations
were performed searching the conformational space of the
torsion angles æ1 and æ2, until convergence was reached, i.e.
until the largest residual force on any atom was less than 10-3
mdyn.28 Figure 5 presents calculated energies along those lines
in the æ1,æ2 plane which connect minimum energy forms as
they occur in AA or in FA.1,2 It shows that in FAA four rotation
forms, given in Table 1, are energy-minimum structures. Of
these, just as in FA, the planar (sp,ap) form (æ1 ) 0, æ2 )
180°, Figure 1) is the most stable conformation. Rotamers with
an energy 2 kcal/mol or more above that of the most stable
form are of little interest because of their low abundance in the
gas phase at room temperature. Even though the calculated
energy differences are basis set dependent (Table 1), only the
nonplanar (sp,sp) form and the (sp,ap) form remain as possible
candidates. Table 2 gives their optimized geometries together
with some other characteristics. Nevertheless, one notes that
the energy difference between the nonplanar (sp,sp) form and
the (sp,ap) form rises steeply with increasing size of the basis
set. We consider this a first indication for the sole occurrence
of (sp,ap).
As noted in similar molecules,2,11 the 6-31G** basis set yields
CO and CC bond lengths up to 0.030 Å shorter and CH lengths
up to 0.016 Å longer than the 4-21G basis. Differences in
valence angles are less than 2°, except C(2)-O(1)-C(8) in the
(sp,ap) form being 3.9° larger in the 4-21G results.
The most striking features in the geometries of the possible
conformers are as follows: (i) in the (sp,ap) form C(2)-O(1)
and C(8)-O(1) are of (almost) equal length, and C(2)dO(3) is

Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11623
TABLE 1: Calculated Relative Energies ∆E (kal/mol) and
Torsion Angles OdC-O-C (deg) for All Converged
Energy-Minimum Conformers
parts and thus the quasi-equality of C(2)O(3) ≈ C(8)O(9) and
the sequence C(2)O(1) >C(8)O(1) remain (argument 1). Con-
formation dependency also manifests itself in the valence angles
C(2)-O(1)-C(8) and O(1)-C(8)dO(9), which are 5.4° and
5.2°, respectively, larger in the (sp,sp) form than in the (sp,ap)
form. This allows the O(9)‚‚‚O(3) distance in (sp,sp) to grow
to 2.9 Å, i.e. just above the sum of the van der Waals radii (2.8
Å). To keep the formyl moiety planar, the angle H(10)-C(8)-
O(1) decreases 5.0° in going from (sp,ap) to (sp,sp). It is noted
that in (sp,ap) the distance H(10)‚‚‚O(3) is 2.3 Å. Although
too large for a true hydrogen bond,30 it is about 0.3 Å smaller
than the sum of the van der Waals radii and a first sign of an
attractive H‚‚‚O interaction as a stabilizing factor for the
(sp,ap) form of FAA.
To check upon the vibrational mobility of FAA, we calculated
the energy barriers to rotation along selected lines in æ1,æ2
space. The results, presented in Figure 5, show a remarkable
resemblance with those calculated for FA1 in the steepness and
the height of the barriers and apply equally to the 4-21G as to
the 6-31G** calculations.
4-21G
6-31G
æ1,æ2
0, 180 0.00
22, 23 3.78
6-31**G
conformer
(symm.)
∆E
æ1,æ2a
∆E
∆E
æ1,æ2
(sp,ap) (Cs)
(sp,sp) (C1)
(ac,sp) (C1)
0.00
1.69
0, 180
16, 16
0.00
2.65
0, 180
28, 24
2.29 140, 3
4.03 148, 4
4.30 130, 4
(ap,ap) (Cs) 11.05 180, 180 10.64 180, 180 9.65 180, 180
a æ1, æ2 denote torsion angles (O(3)dC(2)-O(1)-C(8) and
O(9)dC(8)-O(1)-C(2), respectively.
about 0.009 Å longer than C(8)dO(9); (ii) in the nonplanar
(sp,sp) form C(2)-O(1) is about 0.020 Å longer than C(8)-
O(1), and C(2)dO(3) and C(8)dO(9) are of about equal length.
To rationalize these results, we use two arguments. One, in
the absence of disturbing effects C(2)O(3) ≈ C(8)O(9), but
C(2)O(1) > C(8)O(1). We take this from the observed
geometries of methyl acetate29 and methyl formate.10 In the
acetate the CdO length is only slightly larger, but the C-O
length is significantly (0.019 Å) longer than in the formate. The
second argument is that the order of importance b > c and d >
e applies to the resonance hybrids (see Figure 6) in the (sp,ap)
form, but that b ≈ c and d ≈ e in the nonplanar (sp,sp) form.
We take this from our previous analysis of FA1 and from the
comparison of the Mulliken atomic charges presented in Figure
7. Then, in the (sp,ap) form of FAA, the mesomeric effect
causes C(2)dO(3) to increase more than C(8)dO(9). The
accompanying larger decrease of C(2)-O(1) compared to
C(8)-O(1), however, is canceled by the higher starting value
of the C(2)-O(1) length. In the nonplanar (sp,sp) form, the
mesomeric influences are quasi-equally divided over both acyl
Finally, we enumerated the barrier of rotation of the methyl
group. Minimum energy forms were found when a C-H bond
eclipses a CdO bond, with a barrier to rotation of 1.1 kcal/mol.
Vibrational Spectroscopy
Up to now only the solution IR and Raman spectra of FAA
were empirically assigned.6 In this work we report and assign
the gas-phase IR spectra in order to have a consistent reference
for our force field calculations.
For the (sp,ap) rotamer, two harmonic force fieldssone using
the 4-21G and the other using the 6-31G** basis setswere
TABLE 2: Ab-Initio Optimized Geometries (re-Type) of the Conformations (Bond Distances in Angstroms, Angles in Degrees)
(sp,ap) (Cs symm.)
(sp,sp) (C1 symm.)
parameters
4-21G
6-31G
6-31**G
4-21G
6-31G
6-31**G
r O(1)-C(2)
1.387
1.387
1.199
1.498
1.077
1.081
1.081
1.190
1.074
3.50
2.74
3.93
3.68
4.60
1.380
1.380
1.206
1.484
1.084
1.089
1.089
1.193
1.081
3.50
2.77
3.96
3.68
4.59
1.357
1.358
1.181
1.495
1.083
1.088
1.088
1.172
1.085
3.42
2.69
3.86
3.63
4.54
1.400
1.379
1.192
1.502
1.077
1.081
1.081
1.191
1.076
2.94
2.89
2.90
3.02
4.31
1.394
1.375
1.198
1.488
1.084
1.088
1.089
1.194
1.081
2.95
2.90
2.98
3.68
4.28
1.372
1.352
1.174
1.497
1.084
1.088
1.088
1.171
1.092
2.83
2.80
2.86
3.61
4.14
r O(1)-C(8)
r C(2)dO(3)
r C(2)-C(4)
r C(4)-H(5)
r C(4)-H(6)
r C(4)-H(7)
r C(8)dO(9)
r C(8)-H(10)
r C(2)‚‚‚O(9)
r O(3)‚‚‚C(8)
r O(3)‚‚‚O(9)
r C(4)‚‚‚C(8)
r C(4)‚‚‚O(9)
C(2)-O(1)-C(8)
O(1)-C(2)-O(3)
O(1)-C(2)-C(4)
O(3)-C(2)-C(4)
C(2)-C(4)-H(5)
C(2)-C(4)-H(6)
C(2)-C(4)-H(7)
H(5)-C(4)-H(6)
H(5)-C(4)-H(7)
H(6)-C(4)-H(7)
O(9)-C(8)-O(1)
H(10)-C(8)-O(1)
H(10)-C(8)-O(9)
O(3)-C(2)-O(1)-C(8)
O(9)-C(8)-O(1)-C(2)
C(4)-C(2)-O(1)-C(8)
H(10)-C(8)-O(1)-C(2)
-E(hartrees)
121.19
121.77
109.76
128.46
109.49
109.16
109.16
110.53
110.53
107.92
121.04
112.84
126.12
0.00
123.05
121.53
110.01
127.45
109.65
109.63
109.63
110.19
110.19
107.52
120.61
114.01
125.38
0.00
120.14
123.07
110.49
126.44
109.40
109.35
109.35
110.49
110.49
107.73
120.51
113.66
125.83
0.00
126.59
123.13
108.51
128.33
109.34
109.32
109.28
110.43
110.35
108.09
126.19
107.82
125.97
-16.63
-16.42
165.18
165.65
339.720
1.69
127.58
122.32
110.17
127.47
109.53
109.81
109.69
110.12
109.96
107.70
125.69
108.83
125.42
22.33
23.19
159.91
159.52
340.349
2.65
122.73
123.08
110.05
126.82
109.34
109.68
109.28
110.44
110.24
107.84
126.16
108.61
125.16
-27.97
-23.60
154.55
159.38
340.537
3.78
180.00
180.00
0.00
339.723
0.00
180.00
180.00
0.00
340.353
0.00
180.00
180.00
0.00
301.543
0.00
∆E(kcal/mol)
dipole (D)
3.02
3.02
2.83
4.49
4.56
4.06

11624 J. Phys. Chem., Vol. 100, No. 28, 1996
Wu et al.
Figure 6. Resonance hybrids of FAA. Only the (sp,ap) form is shown.
enumerated by applying a two-sided curvilinear distortion25 to
each internal coordinate from its equilibrium geometry. Dis-
placements of (0.01 Å for bond lengths, (0.05 rad for valence
angles, and 0.5 rad for torsion angles were employed. For each
of these distorted geometries the dipole moments and forces
on the internal coordinates were determined. Force constants,
Fij, follow from
Φj(qi - ∆i) - Φj(qi + ∆i)
Fij )
(2)
2∆i
in which Φj denotes the force acting along the internal
coordinate qj and ∆i is the displacement along qi. The force
field in combination with the geometry the Wilson-GF method31,32
allows one to obtain the vibrational frequencies. Since the
(sp,ap) rotamer has Cs symmetry, its 24 normal vibrations can
be divided into 16 of A′ symmetry species and 8 of A′′, the
former species containing all in-plane, the latter all out-of-plane
vibrations. It is well-known, however, that partly due to neglect
of electron correlation, partly due to basis set truncation, ab-
initio SCF methods systematically overestimate the force
constants. They may be scaled down using the linear scaling
formula
Fij(scaled) ) Fij(unscaled)(RiRj)1/2
(3)
where Ri denotes a scale factor belonging to internal coordinate
qi.33,34 After defining the local symmetry coordinates Si in terms
of internal coordinates qi (see Table 3), the Ri values can be
determined fitting the calculated vibrational frequencies to
assigned experimental gas-phase IR frequencies. In this case,
as in most cases, the systematic errors in the force field
calculations cannot be corrected by one scale factor. With one
R ) 0.83, a root-mean-square deviation of 29 cm-1, and a
maximum deviation of 54 cm-1 for the 4-21G force field and
for the 6-31G** force field were found values of R ) 0.82,
rms ) 29 cm-1, and ∆(max) ) 73 cm-1. In a more realistic
view the deficiencies of a particular basis set for, for example,
stretching constants may be different from those of bending
constants, while modes involving CO may differ from those
involving CH. With FA1 four factors sufficed, whereas with
FAA six scale factors were taken (see Table 4) to arrive at a
similar agreement between calculated and experimental frequen-
cies, i.e. a root-mean-square deviation of 8.8 cm -1 and largest
discrepancy of 20 cm -1. The differences with the formic
anhydride scaling are the following. The torsions and the
C(2)O(1)C(8) bending are placed into one group to which the
fixed value R ) 0.80 is attributed, because no corresponding
experimental frequencies are available. For bending move-
ments, two groups rather than one were required. We attribute
Figure 7. Mulliken charges on atoms (a) in the (sp,ap) rotamer of
FAA, (b) in the (sp,ap) rotamer of FA, and (c) in the (sp,sp) rotamer
of FA.
these differences to the asymmetric nature of the FAA molecule.
Furthermore, to our surprise, the 6-31G** force field did not
perform as well as the 4-21G counterpart. In particular, we
were unable to properly fit the two CO absorptions at 1200
and 1050 cm-1 with the scaled 6-31G** force constants.
Hence, the following spectral analysis is focused on the scaled
4-21G force field presented in Table 5. The comparison
between calculated and experimental frequencies based on the
L-1 matrix31,32 is given in Table 6. Furthermore, we calculated
δqi/δQi with Qi representing a vibrational normal coordinate.
These derivatives were then used to enumerate δµi/δQi and
absolute band intensities. The latter are an invaluable aid in
the frequency assignment discussed below. Before doing so,
we tested that the agreement between calculations and experi-

Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11625
TABLE 3: Definitions of Symmetry Coordinates Si in Terms of Internal Coordinates Following Recommendations of Ref 25
symmetry coordinatesa
symmetry species
assignment
S1 ) r(1,2)
S2 ) r(1,8)
S3 ) r(2,3)
S4 ) r(2,4)
S5 ) r(4,5) + r(4,6) + r(4,7)
S6 ) 2r(4,5)-r(4,6)-r(4,7)
S7 ) r(8,9)
S8 ) r(8,10)
S9 ) 2θ(1,2,4)-θ(3,2,4)-θ(1,2,3)
S10 ) θ(1,2,3)-θ(3,2,4)
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′
A′′
A′′
A′′
A′′
A′′
A′′
A′′
A′′
ν C(2)-O(1)
ν C(8)-O(1)
ν C(2)dO(3)
ν C(2)-C(4)
ν sym CH3
ν asym CH3
ν C(8)-O(9)
ν C(8)-H(10)
δ O(1)-C(2)-C(4) bending
Fr O(3)dC(2)-O(1) bending
δ sym CH3 bending
δ asym CH3 bending
Fr sym CH3 bending
δ O(9)dC(8)-O(1) bending
Fr O(9)dC(8)-H(10) bending
δ C(2)-O(1)-C(8) bending
ν asym CH3
S11 ) θ(5,4,6)+θ(5,4,7)+θ(6,4,7)-θ(2,4,5)-θ(2,4,6)-θ(2,4,7)
S12 ) 2θ(6,4,7)-θ(5,4,6)-θ(5,4,7)
S13 ) 2θ(2,4,5)-θ(2,4,6)-θ(2,4,7)
S14 ) 2θ(1,8,9)-θ(1,8,10)-θ(10,8,9)
S15 ) θ(9,8,10)-θ(1,8,10)
S16 ) θ(2,1,8)
S17 ) r(4,6)-r(4,7)
S18 ) ø(3,1,4,2)
π C(2)dO(3) out-of-plane bending
δ asym CH3 bending
Fr asym CH3 bending
π C(8)-H(10) out-of-plane bending
τ O(1)-C(2) torsion
τ C(2)-C(4) torsion
τ O(1)-C(8) torsion
S19 ) θ(5,4,6)-θ(5,4,7)
S20 ) θ(2,4,6)-θ(2,4,7)
S21 ) ø(10,1,9,8)
S22 ) ι(8,1,2,3)+ι(8,1,2,4)
S23 ) ι(1,2,4,5)+ι(3,2,4,5)+ι(1,2,4,6)+ι(3,2,4,6)+ι(1,2,4,7)+ι(3,2,4,7)
S24 ) ι(2,1,8,9)+ι(2,1,8,10)
a r(i,j) bond distance between atoms i and j; θ(i,j,k), valence angle between atoms i, j, and k; ø(i,j,k,l), out-of-plane deformation of atom i out of
j,k,l plane; ι(i,j,k,l), torsion angle between atoms i,j,k,l along bond j,k. See Figure 1 for atomic numbering scheme.
TABLE 4: Definition of Groups of Symmetry Coordinates
Si Used in the Scaling of the Force Fields, Together with the
Results of the Scaling Procedure
ment is not a fortuitous result of the least-squares scaling
procedure by enumerating the 4-21G force field of the nonplanar
(sp,sp) rotamer. The comparison of CdO stretching frequencies
obtained from the unscaled force fields showed splits (∆ ) ν5
- ν6) of 100 cm-1 (nonplanar (sp,sp)) and 30 cm-1 (sp,ap).
Since only the latter value can be brought to match experiment
(∆ )16 cm-1) with a physically realistic scale factor, the
calculated ∆ values justify the sole occurrence of the (sp,ap)
form. In passing we note that going from the gas phase to a
0.18 M solution in CCl4,6 the CdO frequencies shift only
slightly (ca. 16 cm-1) to lower values, and their ∆ value
remained almost the same (16 cm-1, gas Vs 19 cm-1, solution)
as well as the intensity ratio I(ν6)/I(ν5) (1.3(2), gas Vs 1.2(2),
solution). This proves once more the absence of any shifting
conformer equilibrium.
scale factors
symmetry
group
coordinates Sia
4-21G
6-31G**
1
2
3
4
5
6
S1, S2, S8
S3, S7
S4, S5, S6, S17
S9, S10, S13, S14, S18, S20
S11, S12, S15, S19, S21
S16, S22, S23, S24
0.797
0.870
0.833
0.763
0.881
0.800b
0.832
0.833
0.759
0.748
0.821
0.800b
performancec
4-21G
6-31G**
root-mean-square deviation (cm-1
maximum deviation (cm-1
)
8.8
20
15.4
30
)
3500-2000 cm-1
. Three methyl and one formate CH
a See Table 3 for the definition of the symmetry coordinates. b Fixed.
c Measured as the root-mean-square and maximum deviation between
the experimental frequency set (Table 6) and the frequencies calculated
after the scaling of the ab-initio force fields.
stretching vibrations may occur in the 3500-2000 region, but
only three weak bands were observed. Low intensities of CH
stretchings were predicted by the calculations (Table 6) and have
also been noted in other anhydrides. Of these three bands, the
comparatively strong C(formyl)-H vibration is of interest. The
C(8)-H(10) bond is directed along the b-axis of the inertia
frame (Figure 7), and thus one expects a B-type band profile
for the corresponding vibration mode. In the frequency window,
only at 2970 cm-1 could a B-type profile be seen from the
enlarged IR spectra. This together with the strongly localized
character (Table 6) of the C(8)-H(10) stretching causes one to
expect the corresponding frequency to be below the asymmetric
C(methyl)-H stretching frequencies.35 However, this order
could only be reproduced by the calculations if the correspond-
ing symmetry coordinate S8 was separated in the scaling
procedure from the C(methyl)-H symmetry coordinates S5, S6,
and S17. This phenomenon was also noted in the analysis of
ethyl formate11 and indicates that systematic errors in SCF ab-
initio calculations involving C(formyl)-H differ from those
involving C(methyl)-H. The frequency and the degree of
localization of the C(formyl)-H stretching are further indica-
tions that no true H-bond exists between H(10) and O(3). How-
ever, we will find below indications in the force field of the
existence of an attractive interaction between H(10) and O(3).
2000-1600 cm-1
.
This region contains two carbonyl
stretchings (ν5 at 1808 cm-1 and ν6 at 1792 cm-1; ∆(ν5-ν6) )
16 cm-1). Carbonyl stretching in anhydrides has attracted much
attention, because their frequencies, band contours, and relative
intensities are regarded to be intimately correlated with molec-
ular conformation and electron structure.36-39
The potential distribution (Table 6) shows that, as in other
anhydrides, the high-frequency ν5 must be assigned to the in-
phase stretching of the two CdO, and the low-frequency ν6 to
the out-of-phase CdO stretchings. In FAA the intriguing aspect
is the extremely small split (∆ ) 16 cm-1), compared to ∆ )
55 cm-1 or more in FA1 and AA2 as well as in most other
saturated open chain anhydrides.39 A low ∆ value signals a
low coupling, i.e. significantly reduced electronic and kinematic/
mechanical interactions.40 Compared to FA, the heavy methyl
group in FAA will decrease the mechanical interaction, but in
all likelihood only to a small extent. In fact, ∆ did not change
when in FAA the CH3 group was replaced by CD3.6 Next,
comparison of FAA force constants with those of FA1 reveals
that C(2)-O(1) and C(8)-O(1) have more single-bond character

11626 J. Phys. Chem., Vol. 100, No. 28, 1996
Wu et al.
TABLE 5: Scaled 4-21 Force Constants (×100, in mdyn Å-1 or mdyn Å-1 rad-1) Based on Symmetry Coordinates Defined in
Table 3
Si
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1
2
3
4
5
6
7
8
9
470
46 475
118 -23 1270
32 404
25 -7
1
1
0
-1
0
2
13
3
-48
14 -21 -1
-4 -31
0
-5
7
-6
9
0
0
0
0
0
0
7
3
3
0
502
6
0
498
1
0
-21 109
-8
28
1346
19 483
10
2
0
17 -1
8
5
0
1
9
-1
0
4
104
10
48 -6
-6 -25 121
11 -4
12
13
0
0
0
8
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
-1
1
17 10
2
1
56
1
0
0
0
0
0
0
0
0
0
0
0
0
1
8
-4
1
1
0
1
0
0
0
0
0
0
0
-13
15
0
50
2
0
0
0
0
0
0
0
0
0
0
0
2
72
1
-1
2
0
0
0
0
0
0
0
0
14 -7
32
-34
54
0
18 -10
29 -1
5
0
2
0
0
0
0
0
0
0
0
-3
-1
11
0
0
0
0
0
0
0
115
3
2
0
0
0
0
0
0
15
16
17
18
19
20
21
22
23
24
4
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
59
-1 100
9
0
0
0
0
0
0
0
0
-9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
487
3
0
0
0
0
0
0
0
62
14 -1 50
17 13 -1 67
0
0
2
1
0
0
1
0
0
0
0
0
40
1
0
4
0
0
0
0
0
0
0
0
-2 -2
0
0.5
0
0
0
0
1
1
2
TABLE 6: Comparison between 4-21G Calculated and Experimental IR Data and Assignments (See Table 3 for
Definition of Si)
exptl
calc
calc int
νi
(cm-1
)
(cm-1
)
exptl int
(106 cm/mol)
potential distribution (%)
S6(97)
S17(100)
S8(98)
S5(97)
S7(65), S3(22)
S3(60), S7(22)
S19(87)
S12(84)
S11(84)
assignment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
3038
-
3043
3001
2970
2942
1809
1790
1446
1439
1377
1365
1216
1115
1069
1000
982
914
621
586
537
376
198
123
119
vw
-
vw
vvw
s
vs
vw
vw
m
m
vs
m
vs
w
m
0.36
0.08
1.15
<0.01
17.25
34.98
0.76
2.08
4.36
0.25
42.32
2.22
47.70
0.29
10.96
3.05
2.13
1.61
1.42
0.37
1.05
2.33
0.06
2.63
A′ νas. CH3
A′′ νas. CH3
A′ νC8-H10
A′ νs. CH3
a
2970
2948
1808
1792
1442
1431
1378
1378
1200
1133
1049
998
980
930
630
580
550
-
A′ νC8dO9, νC2dO3
A′ νC2dO3, νC8dO9
A′′ δas. CH3
A′ δas. CH3
A′ δs. CH3
S15(86)
A′ FC8-H10
S1(27), S13(22), S10(22), S4(14)
S20(70), S19(15), S18(14)
S2(37), S13(19), S1(17)
S21(97)
S2(43), S14(18), S13(17), S4(12)
S1(31), S14(24), S4(20)
S10(46), S4(37)
S18(73), S20(23)
S14(43), S9(25), S1(22)
S9(47), S10(28), S13(11)
S16(64), S9(24)
S22(92)
A′ νC2-O1, FC2dO3, FCH3
A′′ FCH3, δas. CH3, γCdO
A′ νC8-O1, FCH3
A′′ γC-H
A′ νC8-O1, δC8dO9, FCH3, νC2-C4
A′ νC2-O1, δC8dO9, νC2-C4
A′ FC2dO3, νC2-C4
m
w
vvw
w
A′′ γCdO, FCH3
A′ δC8dO9, δO1-C2-C4, νC2-O1
A′ δO1-C2-C4, FC2dO3, FCH3
A′ δC2-O1-C8, δO1-C2-C4
A′′ ιC8-O1-C2dO3
-
-
-
-
-
-
-
S23(78)
S24(93)
A′′ ιO-C-C-H
A′′ ιC2-O1-C8dO9
-
103
-
a (-) not observed; v, stretching; δ, deformation; F, rocking; γ, out-of-plane bending; ι, torsion; w, weak; m, moderate; s, strong; v, very strong.
and O(1) more sp3 character in FAA than in FA. Hence, we
conclude that asymmetric substitution of the OdC-O-CdO
chain reduces the electronic interaction between the acyl
moieties and is the major cause of the small ∆ in FAA and
other mixed formic acid anhydrides, HCOOCOR with R ) CH3,
C2H5, n-C3H7, iso-C3H7, and t-C4H9.12
other C- and O-containing vibrations, including the strong ones
ν11 and ν13, show low localization percentages and may be
classified as skeletal vibrations. This delocalization seems to
increase with the size of the molecular backbone. The highest
localization percentage in any of the C, O vibrations ranges
from 58% in FA, to over 43% in FAA, and to 38% in AA.
Below 500 cm-1 no experimental frequencies were recorded,
and the scale factor for, inter alia, the C-O torsion force
constants had to be estimated. Nevertheless, the values of
F(22,22) and F(24,24) are very close to the corresponding con-
stants in FA, as are the other more reliably scaled force con-
stants. We conclude that FAA and FA are about equally rigid.
To end the vibrational spectroscopy section, we discuss some
details of the scaled force field revealing facts of general validity
1600-500 cm-1. In this region 13 bands were observed, of
which the calculated frequencies and intensities well agree with
experiment. Our calculations show that the strongest absorp-
tions (ν11 at 1200 cm-1 and ν13 at 1049 cm-1) both have C-O
stretchings as the highest contributors. In this we disagree with
Vledder et al.,6 who ascribed ν13 to the methyl rocking mode.
Only the various CH-containing modes ν7-ν10, ν12, and ν14 are
sufficiently localized to allow a meaningful assignment. All

Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11627
TABLE 7: Comparison of FAA and FA Scaled Force Constantsa in Relation to Their Structures
CdO bond length force constant CdO bond length force constant OdC-O angle
force constant
C-O-C angle
force constant
stretch
(Å)
(mdyn Å-1
)
stretch
(Å)
(mdyn Å-1
)
bending (deg) (mdyn Å-1 rad-1
)
bending (deg) (mdyn Å-1 rad-1
)
FAA, sp
FA, sp
FAA, ap
FA, ap
1.199
1.197
1.190
1.188
12.70
13.09
13.46
13.60
FA, ap
1.393
1.387
1.386
1.372
4.49
4.75
4.70
4.97
FA, sp
FAA, sp 121.8
FAA, ap 121.0
124.2
1.22
1.21
1.15
1.10
FA
FAA
121.4
121.2
1.16
1.00
FAA, ap
FAA, sp
FA, sp
FA, ap
120.8
a FAA force constants taken from Table 5; FA force constants taken from Table 4 of ref 1.
TABLE 8: Calculated (4-21G) Vibrational Amplitudes u,
Perpendicular Amplitudes K°, and Shrinkage Corrections,
K° - u2/r (Å × 1000)
K° -
K° -
atom pair
u
K° u2/r
atom pair
u
K° u2/r
O(1)-C(2)
O(1)-C(8)
C(2)-O(3)
C(8)-O(9)
C(2)-C(4)
C(4)-H(5)
C(4)-H(6)
C(4)-H(7)
C(8)-H(10)
O(1)‚‚‚O(3)
O(1)‚‚‚C(4)
O(1)‚‚‚H(5)
O(1)‚‚‚H(6)
O(1)‚‚‚H(7)
O(1)‚‚C(8)
O(1)‚‚‚O(9)
O(1)‚‚‚H(10)
C(2)‚‚‚H(5)
C(2)‚‚‚H(6)
C(2)‚‚‚H(7)
C(2)‚‚‚C(8)
C(2)‚‚‚O(9)
49
50
38
37
51
77 32
78 35
78 35
78 27
53
66
99 13
223 15
223 15
50
54
99 22
106 18
107 19
107 19
3
5
3
6
3
2
4
2
7
2
27
23
23
21
1
O(3)‚‚‚C(4)
O(3)‚‚‚H(5)
O(3)‚‚‚H(6)
O(3)‚‚‚H(7)
O(3)‚‚‚C(8)
O(3)‚‚‚O(9)
60
2
0
7
2
143 14
166 11
166 11
94
93
2
2
1
-1
-2
6
0
-1
4
42
42
6
4
8
43
-2
-9
4
-2
-9
4
O(3)‚‚‚H(10) 172 18
C(4)‚‚‚C(8)
C(4)‚‚‚O(9)
C(4)‚‚‚H(10) 134
70
81
1
0
9
3
4
2
H(5)‚‚‚H(6)
H(5)‚‚‚H(7)
H(5)‚‚‚C(8)
H(5)‚‚‚O(9)
125 51
125 51
111
106
10
-4
-4
4
8
6
5
5
H(5)‚‚‚H(10) 181 15
3
H(6)‚‚‚H(7)
H(6)‚‚‚C(8)
H(6)‚‚‚O(9)
126 52
205
263
17
13
14
14
1
0
8
8
6
H(6)‚‚‚H(10) 211 14
H(7)‚‚‚C(8)
H(7)‚‚‚O(9)
205
263
8
6
64
61
2
1
H(7)‚‚‚H(10) 211 14
C(2)‚‚‚H(10) 140 16
O(9)‚‚‚H(10)
92 25
21
TABLE 9: Model Construction with Definition of Refinable
Parameters, and Values of Constraints ∆
parameter
constraint 1
constraint 2
O(1)-C(2)
r1
r1
O(1)-C(8)
r1 + ∆r1
r2
r1 + ∆r1
r2
C(2)dO(3)
C(8)-O(9)
r2 + ∆r2
r2 + ∆r2
C(2)-C(4)
r3
r3
C(4)-H
C(8)-H(10)
r4
r4
Figure 8. Radial distribution functions of FAA, calculated for (a) the
nonplanar (sp,sp) rotamer and (b) the (sp,ap) rotamer to be compared
with (c) the experimental radial distribution curve of FAA at 300 K.
In the data evaluation a damping factor of exp(-0.001s2) was used.
(d) Difference curve c - b. Parameters of the model are listed in Table
12.
r4 + ∆r3
r4 + ∆r3
C(2)-O(1)-C(8)
O(1)-C(2)dO(3)
O(1)-C(2)-C(4)
C(2)-C(4)-H
O(1)-C(8)dC(9)
O(1)-C(8)-H(10)
O(3)dC(2)-O(1)-C(8)
O(9)dC(8)-O(1)-C(2)
θ1
θ1
θ2
θ2
θ3
θ3
θ4
θ4
θ2 + ∆θ1
θ2 + ∆θ1
θ5
ι1
ι2
θ3 + ∆θ2
as well as corroborating the conclusion that FAA strongly
resembles FA, but with a more single-bonded, ether-like
C-O-C link between the acetyl and formyl moieties. First,
bond lengths and stretching force constants should and indeed
show an inverse relationship. They do so even when one
includes the FA force constants, as demonstrated in Table 7.
The CdO and C-O sequences as well as those of OdC-O
and C-O-C, also given in Table 7, strengthen the above
conclusion. In fact they clearly demonstrate that as far as C-O,
OdC-O, and C-O-C are concerned, the difference of FAA
vs FA is more important than the difference in conformation
(sp vs ap), whereas as far as CdO, the opposite holds. Second,
as we noted before,1,2,11 it may be seen (Table 5) that stretch-
stretch constants between bonds sharing a common nucleus are
positive and diminish in the order CdO > C-O > C-C >
C-H. Stretch-stretch constants between bonds without a
common nucleus are alternating negative and positive, depend-
ing whether there is an odd or an even number of bonds between
ι1
ι2
set (i)
4-21G ∆re
set (ii)
∆6-31G** ∆re
set (iii)
∆4-21G ∆rR°
∆r1 (Å)
0.000
-0.009
-0.006
-0.73
3.08
0.001
-0.009
-0.001
-2.46
3.17
-0.002
-0.011
0.001
-0.73
3.08
∆r2 (Å)
∆r3 (Å)
∆θ1 (deg)
∆θ2 (deg)
them. Their absolute values show the same ordering with bond
type as above. Third, despite the long H(10)‚‚‚O(3) distance
(2.3 Å), a significant interaction exists between the C(8)-H(10)
stretch and the O(1)-C(2)dO(3) angle bending (F(8,10) )
-0.06, being 5% of F(10,10)). Furthermore, it behaves
similarly to the C(2)dO(3) stretch/O(1)-C(8)-H(10) rocking
interaction (F(3,15) ) -0.06), but differently from the C(4)-
C(2)/O(1)-C(8)dO(9) interaction (F(4,14) ) 0.01). These

11628 J. Phys. Chem., Vol. 100, No. 28, 1996
Wu et al.
TABLE 10: Results of Least-Squares Refinements of
Constrained Models Defined in Table 9
(if any) between the actual temperature of the diffracting
molecules and the temperature taken in the calculation (300 K).
Conversely, when u parameters are fixed to the calculated
values, k(u) together with the indices of resolution measures
the quality of the ED data set. The closer to unity these indicator
parameters are, the better the data set.
model 1
set (ii)
model 2
set (ii)
set (i)
set (iii)
set (i)
set (iii)
Geometrical Parameters; rR°-Type
r1
r2
r3
r4
θ1
θ2
θ3
θ4
θ5
1.376(2) 1.377(2) 1.377(2) 1.376(2) 1.377(2) 1.377(2)
1.191(2) 1.192(2) 1.192(2) 1.191(2) 1.192(2) 1.192(2)
1.497(6) 1.501(6) 1.497(6) 1.498(6) 1.503(6) 1.498(6)
1.056(13) 1.051(14) 1.054(12) 1.051(13) 1.047(14) 1.048(12)
119.9(3) 119.4(3) 119.8(3) 119.4(3) 118.8(3) 119.4(3)
122.3(3) 123.0(3) 122.4(3) 122.4(3) 123.0(3) 122.4(3)
110.9(3) 110.2(3) 110.2(3) 110.7(3) 110.4(3) 110.7(3)
109.1(3) 109.0(3) 109.1(3) 108.5(3) 106.7(3) 108.5(3)
117.9(3) 118.0(3) 117.9(3)
Furthermore, geometrically constrained models of FAA were
constructed as defined in Table 9. We tested two models. In
model 1, the angle O(1)-C(8)-H(10) is taken as a refinable
parameter, whereas in model 2 the angle is constrained to follow
the O(1)-C(2)-C(4) angle parameter.
Each model was further tested using three sets of con-
straints: (i) those directly taken from re (4-21G) values (Table
2); (ii) those directly taken from re (6-31G**) values; want of
appropriate correction procedures prevents obtaining the 6-31G**
constraints at the rR° level; (iii) those after correction of re
(4-21G) values to rg using regression type corrections41 and sub-
sequent conversion of rg to rR° values. The conversion of rg to
rR° uses rR° ) rg - K°, with K° values taken from Table 8.
Scale Factor on Amplidudes
k(u)
0.99(6) 0.99(6) 1.00(6) 1.03(6) 1.04(6) 1.04(6)
Indices of Resolution
k1(20cm) 0.68(5) 0.68(5) 0.69(5) 0.72(5) 0.73(5) 0.72(5)
k2(35cm) 0.74(3) 0.76(3) 0.75(3) 0.76(3) 0.78(3) 0.76(3)
k3(60cm) 0.56(1) 0.56(1) 0.56(1) 0.57(1) 0.57(1) 0.56(1)
Disagreement Factora
R(ED)
1.58
1.60
1.56
1.59
1.61
1.58
Table 10 summarizes the least-squares results concerning
disagreement factors, geometrical parameters, and other refin-
ables, and Table 11 gives the correlation coefficients among
parameters.
a Defined as R ) [∑w(Iobs - Icalc)2/∑wIobs2] × 100%.
values strongly resemble those in FA. Moreover, replacing in
FAA the atom H(10) by D anomalously increases the split
In an attempt to discriminate among the six model/set com-
binations, we compared the ratio of the R values of two such
combinations with tabulated42 values of R (p,n-p,R), in which
p denotes the number of refinables (degrees of freedom, here
14), n the number of data points involved (here 104), and R the
chosen level of significance. If the R value ratio is larger than
R , then one rejects the hypothesis at the 100R% significance
level that the molecular models represented by the two com-
binations are equal. Performing the tests at the 5% level of
significance, none of the combinations can be rejected. Nev-
ertheless, we prefer the combination model 1/set iii with the
lowest R value and k(u) closest to unity. Moreover, it gives
results most consistent with previous results of FA and AA;1,2
for example, the best geometrical constraints come from 4-21G
calculated geometries after correction to rR° level. The indices
of resolution in FAA are somewhat lower than in FA and AA.
They reflect the lower optical densities (see the Experimental
Section) and suggest slightly less accurate intensities. In line
with this, the esd’s of the geometrical parameters are slightly
larger in FAA than FA. Furthermore, the largest correlation
coefficients indicate the C-C and C-H bond lengths to be the
least accurate parameters, as is also indicated by the esd’s. This
led us to conclude that individual CO/CC lengths have an accu-
racy of (0.008 Å and CH of (0.015 Å. Individual valence
angles involving heavy atoms are estimated to have an accuracy
of (0.5°, and those involving H atoms 1 (1°. Table 12 sum-
marizes the best fitting geometry (model 1/set iii) of gaseous
FAA.
between the CdO frequencies to 35 cm-1 6
These are all
.
manifestations of an H(10)‚‚‚O(3) interaction.
Electron Diffraction
We start by noting (Table 2) that prominent distances occur
in (sp,sp) near 3 Å, whereas they are absent in (sp,ap). The
comparison of the theoretical radial distribution functions of
these two rotamers with the experimental one resulting from
the electron diffraction experiments is presented in Figure 8.
Clearly, near 3 Å no distances whatsoever are seen in the ex-
perimental curve, and the agreement between experiment and
(sp,ap) model is excellent. We consider the combined evidence
of the ab-initio calculations, the force field scaling experiments,
the I(ν6)/I(ν5) ratios, and the radial distribution function suf-
ficient to prove that (sp,ap) is the only rotamer present in FAA.
Although this is a welcome simplification, the problem of
overlapping distances and the limited number of experimental
data points largely remains. Hence, the number of refinable
vibrational and geometrical parameters must be reduced. We
used the same semirigid approach for FAA as we did before
for FA,1 because both molecules were shown (see above) to
have the same rigidity. Vibrational amplitudes, u, and vibra-
tional amplitudes perpendicular to the internuclear distances,
K°, computed from the force field,31,32 are given in Table 8.
They were kept fixed during the following constrained least-
squares analyses. Only one overall thermal parameter scale
factor, k(u), was refined. The k(u) corrects for the difference
TABLE 11: Correlation Coefficients (×100) among Parameters (See Table 9 and Text for Definition of Parameters)
r1
r2
r3
r4
θ1
θ2
θ3
θ4
θ5
k(u)
k1
k2
k3
r1
r2
r3
r4
100
-4
-15
31
100
9
100
-20
0
5
-2
0
-3
-1
-8
-1
0
100
0
0
0
0
0
4
-46
-51
-24
θ1
θ2
θ3
θ4
θ5
k(u)
k1
-2
-11
-2
0
100
0
0
0
0
0
1
0
0
100
0
0
100
0
100
0
0
0
4
3
0
0
0
1
0
0
100
0
-28
-11
-6
6
-22
23
34
16
100
22
15
-2
-3
0
-1
0
0
0
0
0
0
100
4
18
k2
k3
-11
-18
0
100
21
0
26
100

Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11629
References and Notes
TABLE 12: Best Fitting Geometriesa (Å and deg) of FAA
and FA
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Van der Veken, B. J. J. Phys. Chem. 1995, 99, 8589.
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Van der Veken, B. J. J. Am. Chem. Soc., submitted.
(3) IUPAC(1974). Nomenclature of Organic Chemistry, Section E:
Stereochemistry, Recommendations; Pergamon Press: Oxford, 1974.
(4) Strazzolini, P.; Giumanini, A. G.; Cauci, S. Tetrahedron 1990, 46,
1081.
FAA (this work)
rR° rg
FA (ref 1)
FAAb
(ref 5)
rR°
rg
C(2)dO(3)
C(8)dO(9)
1.192 1.195
1.181 1.187
1.377 1.380
1.375 1.380
1.497 1.500
1.055 1.082
1.054 1.069
1.195
1.195
1.397
1.397
1.495
1.10
1.193 1.196
1.180 1.189
1.374 1.378
1.394 1.397
C(2)-O(1)
C(8)-O(1)
(5) Vledder, H. J.; Mijlhoff, F. C.; Van Well, F. P.; Dofferhoff, G. M.
T.; Leyte, J. C. J. Mol. Struct. 1971, 9, 25.
C(2)-C(4)
C(8)-H(10)
1.078 1.105
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10, 57.
(7) Geise, H. J.; Pyckhout, W. In Stereochemical Application of Gas
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ers: Deerfield Beach, FL, 1988; Vol. I, Chapter 10.
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Scha¨fer, L. J. Am. Chem. Soc. 1980, 102, 2189.
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N.; Scha¨fer, L. J. Am. Chem. Soc. 1982, 104, 1476.
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Coppens, P.; Traetteberg, M. J. Mol. Struct. 1986, 147, 85.
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Veken, B. J. J. Phys. Chem. 1995, 99, 10201.
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C(4)-H
1.10
C(2)-O(1)-C(5)
O(3)dC(2)-O(1)
O(3)dC(2)-C(4)
O(1)-C(2)-C(4)
O(9)dC(8)-O(1)
O(9)dC(8)-H(10)
O(1)-C(8)-H(10)
C(2)-C(4)-H
O(3)dC(2)-O(1)-C(8)
119.8
113.2
122.4
125.4
112.1
118.0
122.0
120.0
109
118.6
124.2
122.4
127.4
110.2
121.7
120.4
117.9
109.1
0.0
120.8
122.9
116.3
45.6
159.2
180.0
0.0
180.0
O(9)dC(8)-O(1)-C(2) 180.0
H(5)-C(4)-C(2)-O(1) 180.0
a Individual CO/CC lengths have an estimated accuracy of 0.008
Å; individual CH lengths, of 0.15 Å. Individual valence angles in-
volving heavy atoms have an estimated accuracy of 0.5; those involving
H atoms have an accuracy of 1°. b rg bond lengths, rR angles.
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Self-Consistent Molecular Model: Conclusions
It was shown that in the gas phase at room temperature the
mixed formic acetic anhydride, FAA, exists in the planar
(sp,ap) conformation, just as formic anhydride, FA. The
conformation is the result of an attractive H(formyl)‚‚‚O(3)
interaction present in both molecules, which also causes those
molecules to be rigid to almost the same degree. Furthermore,
the interaction was identified1 as one of the reasons that FA is
easily decomposed by heat into carbon monoxide and carboxylic
acid. Hence, FAA and other open chain mixed formic
anhydrides should and indeed do split off CO easily.12 Also,
Table 12 shows that, with the possible exception of C(8)-O(1),
the geometrical parameters of FA are equal within experimental
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large amplitude skeletal vibrations which can be represented
by a mixture of (sp,ac) and nonplanar (sp,sp) forms. Moreover,
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I(ν5) to be 1.3 for FAA and 1.9 for FA,43 compared to 0.85 for
AA.2 In addition, the ratio of AA changes going from the
gaseous to the liquid state; those of FAA and FA do not.
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FA. The major difference is that a smaller electronic interaction
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result is the small split of 16 cm-1 in FAA. It follows that
similar small splittings should occur in anhydrides RCOOCHO
(R ) alkyl), which is indeed observed.12
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Acknowledgment. C.V.A. acknowledges support as a Senior
Research Associate by the Belgian National Science Foundation,
N.F.W.O. This text also presents research results of the Belgian
Programme on Interuniversity Attraction Poles initiated by the
Belgian State (Prime Minister’s Office), Science Policy Pro-
gramming. Scientific responsibility, however, is assumed by
the authors.
Supporting Information Available: Primary electron dif-
fraction data (2 pages). Ordering information is given on any
current masthead page.
JP9607982