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 φ1 (O3dC2O1-C8) and φ2 (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 scheme used, are given in Figure 1. It should be noted that φ1 (acetyl side) is named first and φ2 (formyl side) is named second. So far a review,4 mostly on the chemical properties of FAA, has been published, but few structural studies of mixed anhydrides of formic and other open chain carboxylic acids have appeared. Earlier electron diffraction data of FAA have been interpreted5 to show the existence of one nonplanar conformer with torsion angles φ1 ) 46(3)° and φ2 ) 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 * 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
Figure 1. Atomic numbering scheme used for FAA, together with its possible planar conformations and their nomenclature.
diffraction geometry and taking as starting values the force constants of formic acid and maleic anhydride, these researchers also determined a force field for FAA. Again, lack of data allowed the determination of only a fraction of the off-diagonal interaction constants. 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 χi and χj means that the same change in the calculated data can be brought about by changes in either χi or χj. Thus, with correlation present, an imperfect model may produce a perfect match 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 © 1996 American Chemical Society
Formic Acetic Anhydride in the Gas Phase
Figure 2. Experimental leveled intensities, I(s), with final backgrounds, B(s), for FAA.
reliability of the constraints, they are best taken from highquality 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.
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. 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-
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 procedures,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 To the best of our knowledge no quantum chemical investigations of FAA have been published before. 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 φ1 and φ2, 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 φ1,φ2 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 (φ1 ) 0, φ2 ) 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
Figure 5. Calculated energies along selected lines in φ1,φ2 space, using the 4-21G basis (top) and the 6-31G** basis (bottom): (0) φ1 ) 0f180° and φ2 ) 0f180°; (+) φ1 ) 0° and φ2 ) 0f180°; (9) φ2 ) 180° and φ1 ) 0f180°; (2) φ2 ) 180° and φ1 ) 0f180°; (O) φ(H(5)-C(4)-C(2)-O(3)) ) 0f180°.
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 conformer (symm.) (sp,ap) (Cs) (sp,sp) (C1) (ac,sp) (C1) (ap,ap) (Cs)
4-21G ∆E φ1,φ2a 0.00 1.69 2.29 11.05
0, 180 16, 16 140, 3 180, 180
6-31G ∆E φ1,φ2 0.00 2.65 4.03 10.64
0, 180 22, 23 148, 4 180, 180
6-31**G ∆E φ1,φ2 0.00 3.78 4.30 9.65
0, 180 28, 24 130, 4 180, 180
a φ1, φ2 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
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). Conformation 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 φ1,φ2 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. 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) 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) ∆E(kcal/mol) dipole (D)
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 4.60 121.19 121.77 109.76 128.46 109.49 109.16 109.16 110.53 110.53 107.92 121.04 112.84 126.12 0.00 180.00 180.00 0.00 339.723 0.00 3.02
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 4.59 123.05 121.53 110.01 127.45 109.65 109.63 109.63 110.19 110.19 107.52 120.61 114.01 125.38 0.00 180.00 180.00 0.00 340.353 0.00 3.02
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 4.54 120.14 123.07 110.49 126.44 109.40 109.35 109.35 110.49 110.49 107.73 120.51 113.66 125.83 0.00 180.00 180.00 0.00 301.543 0.00 2.83
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 4.31 126.59 123.13 108.51 128.33 109.34 109.32 109.28 110.43 110.35 108.09 126.19 107.82 125.97 -16.63 -16.42 165.18 165.65 339.720 1.69 4.49
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 4.28 127.58 122.32 110.17 127.47 109.53 109.81 109.69 110.12 109.96 107.70 125.69 108.83 125.42 22.33 23.19 159.91 159.52 340.349 2.65 4.56
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 4.14 122.73 123.08 110.05 126.82 109.34 109.68 109.28 110.44 110.24 107.84 126.16 108.61 125.16 -27.97 -23.60 154.55 159.38 340.537 3.78 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. Displacements 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
Fij )
Φj(qi - ∆i) - Φj(qi + ∆i) 2∆i
(2)
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, abinitio 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 frequencies, 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 movements, 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) 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 ) χ(3,1,4,2) S19 ) θ(5,4,6)-θ(5,4,7) S20 ) θ(2,4,6)-θ(2,4,7) S21 ) χ(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′ 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 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
a r(i,j) bond distance between atoms i and j; θ(i,j,k), valence angle between atoms i, j, and k; χ(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.
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. 3500-2000 cm-1. Three methyl and one formate CH 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 corresponding 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 abinitio 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 indications that no true H-bond exists between H(10) and O(3). However, we will find below indications in the force field of the existence of an attractive interaction between H(10) and O(3).
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 scale factors 4-21G 6-31G**
group
symmetry coordinates Sia
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 -1
root-mean-square deviation (cm ) maximum deviation (cm-1)
4-21G
6-31G**
8.8 20
15.4 30
a See Table 3 for the definition of the symmetry coordinates. b Fixed. 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. c
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 molecular 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 inphase 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
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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
1 470 2 46 475 3 118 -23 1270 4 25 -7 32 404 5 1 0 0 7 502 6 1 -1 2 3 6 498 7 -21 109 13 3 0 1 1346 8 -8 10 3 0 0 0 19 483 9 28 2 -48 17 -1 8 1 4 104 10 48 -6 14 -21 -1 5 9 -6 -25 121 11 -4 0 -4 -31 8 0 -1 0 -1 2 56 12 1 0 0 -4 1 -13 0 0 1 1 1 50 13 8 0 -5 1 0 15 2 0 17 10 0 2 72 14 -7 32 7 1 0 0 18 -10 5 -3 0 0 1 115 15 4 -34 -6 0 0 0 29 -1 0 -1 0 0 -1 3 59 16 46 54 9 1 1 0 9 -9 2 11 0 0 2 2 -1 100 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 487 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 62 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 -1 50 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 13 -1 67 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 40 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 1 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
4 0 0
23
24
0.5 0
2
TABLE 6: Comparison between 4-21G Calculated and Experimental IR Data and Assignments (See Table 3 for Definition of Si) νi
exptl (cm-1)
calc (cm-1)
exptl int
calc int (106 cm/mol)
potential distribution (%)
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 -a 2970 2948 1808 1792 1442 1431 1378 1378 1200 1133 1049 998 980 930 630 580 550 -
3043 3001 2970 2942 1809 1790 1446 1439 1377 1365 1216 1115 1069 1000 982 914 621 586 537 376 198 123 119 103
vw vw vvw s vs vw vw m m vs m vs w m m w vvw w -
0.36 0.08 1.15 C-O > C-C > C-H. Stretch-stretch constants between bonds without a common nucleus are alternating negative and positive, depending whether there is an odd or an even number of bonds between
parameter
constraint 1
constraint 2
O(1)-C(2) O(1)-C(8) C(2)dO(3) C(8)-O(9) C(2)-C(4) 〈C(4)-H〉 C(8)-H(10) 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)
r1 r1 + ∆r1 r2 r2 + ∆r2 r3 r4 r4 + ∆r3 θ1 θ2 θ3 θ4 θ2 + ∆θ1 θ5 ι1 ι2
r1 r1 + ∆r1 r2 r2 + ∆r2 r3 r4 r4 + ∆r3 θ1 θ2 θ3 θ4 θ2 + ∆θ1 θ3 + ∆θ2 ι1 ι2
set (i) 4-21G ∆re
set (ii) ∆6-31G** ∆re
set (iii) ∆4-21G ∆rR°
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
∆r1 (Å) ∆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 model 1 set (i)
set (ii)
model 2 set (iii)
set (i)
set (ii)
set (iii)
r1 r2 r3 r4 θ1 θ2 θ3 θ4 θ5
Geometrical Parameters; rR°-Type 1.376(2) 1.377(2) 1.377(2) 1.376(2) 1.377(2) 1.191(2) 1.192(2) 1.192(2) 1.191(2) 1.192(2) 1.497(6) 1.501(6) 1.497(6) 1.498(6) 1.503(6) 1.056(13) 1.051(14) 1.054(12) 1.051(13) 1.047(14) 119.9(3) 119.4(3) 119.8(3) 119.4(3) 118.8(3) 122.3(3) 123.0(3) 122.4(3) 122.4(3) 123.0(3) 110.9(3) 110.2(3) 110.2(3) 110.7(3) 110.4(3) 109.1(3) 109.0(3) 109.1(3) 108.5(3) 106.7(3) 117.9(3) 118.0(3) 117.9(3)
k(u)
0.99(6)
1.377(2) 1.192(2) 1.498(6) 1.048(12) 119.4(3) 122.4(3) 110.7(3) 108.5(3)
Scale Factor on Amplidudes 0.99(6) 1.00(6) 1.03(6) 1.04(6)
1.04(6)
k1(20cm) 0.68(5) k2(35cm) 0.74(3) k3(60cm) 0.56(1)
Indices of Resolution 0.68(5) 0.69(5) 0.72(5) 0.76(3) 0.75(3) 0.76(3) 0.56(1) 0.56(1) 0.57(1)
0.73(5) 0.78(3) 0.57(1)
0.72(5) 0.76(3) 0.56(1)
R(ED)
1.60
1.61
1.58
a
1.58
Disagreement Factora 1.56 1.59
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 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 experimental 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 sufficient 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 vibrational 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 leastsquares analyses. Only one overall thermal parameter scale factor, k(u), was refined. The k(u) corrects for the difference
(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. 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 constraints: (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 subsequent conversion of rg to rR° values. The conversion of rg to rR° uses rR° ) rg - K°, with K° values taken from Table 8. Table 10 summarizes the least-squares results concerning disagreement factors, geometrical parameters, and other refinables, and Table 11 gives the correlation coefficients among parameters. In an attempt to discriminate among the six model/set combinations, 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 combinations are equal. Performing the tests at the 5% level of significance, none of the combinations can be rejected. Nevertheless, 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 accuracy 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 summarizes the best fitting geometry (model 1/set iii) of gaseous FAA.
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
θ1
θ2
θ3
θ4
θ5
k(u)
k1
k2
k3
100 -4 -15 31 -2 -11 -2 0 0 4 3 -11 -18
100 9 -3 -1 -8 -1 0 0 -28 -11 -6 6
100 -20 0 5 -2 0 0 -22 23 34 16
100 0 0 0 0 0 4 -46 -51 -24
100 0 0 0 0 0 1 0 0
100 0 0 0 1 -2 -3 0
100 0 0 0 -1 0 0
100 0 0 0 0 0
100 0 0 0 0
100 22 15 26
100 4 18
100 21
100
Formic Acetic Anhydride in the Gas Phase
J. Phys. Chem., Vol. 100, No. 28, 1996 11629
TABLE 12: Best Fitting Geometriesa (Å and deg) of FAA and FA FAA (this work) rg rR° C(2)dO(3) C(8)dO(9) C(2)-O(1) C(8)-O(1) C(2)-C(4) C(8)-H(10) 〈C(4)-H〉 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) O(9)dC(8)-O(1)-C(2) H(5)-C(4)-C(2)-O(1)
1.192 1.181 1.377 1.375 1.497 1.055 1.054 119.8 122.4 127.4 110.2 121.7 120.4 117.9 109.1 0.0 180.0 180.0
1.195 1.187 1.380 1.380 1.500 1.082 1.069
FA (ref 1) rR° rg
FAAb (ref 5) 1.195 1.195 1.397 1.397 1.495 1.10 1.10 113.2 122.4 125.4 112.1 118.0 122.0 120.0 109 45.6 159.2 180.0
1.193 1.180 1.374 1.394
1.196 1.189 1.378 1.397
1.078 1.105 118.6 124.2 120.8 122.9 116.3 0.0 180.0
a Individual CO/CC lengths have an estimated accuracy of 0.008 Å; individual CH lengths, of 0.15 Å. Individual valence angles involving heavy atoms have an estimated accuracy of 0.5; those involving H atoms have an accuracy of 1°. b rg bond lengths, rR angles.
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 error to those of FA. The absence of a H‚‚‚O interaction gives acetic anhydride (AA) very different properties: AA executes large amplitude skeletal vibrations which can be represented by a mixture of (sp,ac) and nonplanar (sp,sp) forms. Moreover, the molecule is thermally stable. The diversity in conformational behavior also causes the infrared intensity ratio I(ν6)/ 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. Obviously, also some dissimilarities exist between FAA and FA. The major difference is that a smaller electronic interaction occurs between the acetyl and formyl moieties of FAA than between the two formyl moieties of FA. The most conspicuous 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 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 Programming. Scientific responsibility, however, is assumed by the authors. Supporting Information Available: Primary electron diffraction data (2 pages). Ordering information is given on any current masthead page.
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