The Molecular Zoo
Entry for Formic Anhydride

(O=COC=O)

Jeremy Feasel (Class of 2004)

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Summary

Boogaard et al. attempted to determine the structure of Formic Anhydride in 1972 via electron diffraction³. Theoretical calculations of the characteristic radial distribution function (r.d.f.) for three different conformations were compared (approximately parallel H₁H₂, O₁O₂, or O₁H₂) with the observed spectra, ultimately yielding the asymmetric conformation shown above. The structural parameters for the electron diffraction structure that are found in the Tabular Results were obtained from a fit of the radial distribution function with the assumption of a constant C-H bond length of 1.1 Å. The bond angles suffered from large margins of error (in some cases, such as for the angle C₁O₃C₂, as large as 2°). These assumptions were necessary, however, as experimental conditions had produced large discrepancies in the tail of the r.d.f., which was smoothed out by fixing the O₁O₂ and C₁O₂ nonbonding distances to their resolved mean values. The final structural result contained two dihedrals, a C₁O₃C₂H₂ angle of 17° and a C₂O₃C₁O₁ angle of 26°, producing a pseudo-Gauche conformer if viewed from a Newman projection along the nonbonded C₁C₂ axis. This result suggests that torsional strain is alleviated between H₂ and O₁ by assuming a nonplanar conformation, and that such strain alleviation plays a larger role than the energy-minimizing effects of a stronger O₁-H₂ hydrogen bond.

In contrast, Vaccani et al. proposed a planar structure of formic anhydride in 1975 based on their microwave spectroscopic results¹. The preliminary calculations of the structural parameters produced estimates of bond lengths to 0.01Å, though the proposed parallel H₁O₁ conformation agreed with the results of Boogaard et al. Despite this obvious asymmetry, bond lengths were assumed to be equivalent for homogenous bonds. Utilizing measured moments of inertia and the inertial defect, the lowest-energy conformation of the molecule was found to favor planarity over the previously-reported dihedral angles and compare favorably with other planar molecules. To further support this theoretical structure, Vaccani et al. then went on to determine the microwave spectra of nine isotopically-substituted forms of formic anhydride, as well as the unsubstituted molecule at a greater level of precision. The resulting r_s structure quoted bond distances to 0.0001Å margins of error and angles to 0.01° margins of error. The new calculated inertial defect of -0.19086 amuŲ was attributed to the small frequency of the lowest normal vibration. The new data also indicate significant differences in bond lengths between the two CHO groups, as expected from the molecular asymmetry. No other conformers were found, and the inconsistency between the ED result of Boogaard and the MW result was attributed solely to the faulty assumption that each CH bond length was equal, thus resulting in the need for dihedral angles to accommodate the ED data. Again, the only conformer present was that illustrated above. The authors also determined potential surfaces and vibrations for the molecule.

The original ED- and MW-derived structural parameters can be compared using molecular modeling techniques to determine the minimum-energy conformer of Formic Anhydride starting from the published structural parameters. By beginning with each structure, the resulting energy-minimizations will not only be the local energy minimization, but hopefully the global minimum-energy configuration for the molecule. If the two values converge, it is plausible to say that, for that particular set of force field parameters, neither the MW or ED structures make up a minimum-energy configuration, but that the true minimum lies elsewhere (again, it should be emphasized that even the most complicated force fields are incomplete and each “true minimum” should be taken with a certain amount of skepticism). Based on the precision involved in the determination of the MW spectroscopic data, it can be assumed at this point that the published bond lengths, angles, and molecular symmetry display the global minimum for formic anhydride, and that the ED structure likely suffers from numerous faults, including the aforementioned bond distance and angle assumptions and large margins of error. From here, the validity of each molecular modeling tool can be analyzed with respect to the published data.

One important result from the modeling calculations supports the claim for planarity from the microwave study. When either the non-planar electron diffraction structure or the microwave structure was used as a starting structure, the structure resulting from energy minimization was planar. Both molecular mechanics and quantum mechanics yielded this result. It should also be noted that the asymmetric conformer obtained for formic anhydride was also observed in the case of the isoelectronic formimide (O=CNC=O).

The published data were converted to Cartesian coordinates and written as a SYBYL mol2 file in text format to the greatest level of precision available to each method. Coordinates were determined using simple geometrical relationships for the MW structure (due to its planar nature) and more complicated laws for the ED structure (asymmetry and dihedral angles proving to be a more difficult barrier). The resulting structures of these and all other calculated parameter sets can be found below in both mol2 and pdb format. All subsequent calculations from these preliminary mol2 files were performed using Spartan 2002 for Windows.

MMFF. Determination of equilibrium geometry using the Merck Molecular Force Field (MMFF94) produced equivalent parameters when either of the two structures (ED or MW) was used as a starting point. Bond distances agree favorably with either structure, though overshooting O₁C₁ and C₂O₂ (MW only) by approximately 0.04Å. True differences between the MMFF-derived global minima appear in the angle calculations. The MMFF overestimates O₁C₁O₃ and H₂C₂O₃ by approximately 7° and underestimates O₂C₂O₃ and H₁C₁O₃ by approximately 4°. In doing so, the distance between H₂ and O₁ is increased. It is likely that the force field fails to correlate to the MW spectra in determining bond angles by failing to fully account for the favorable hydrogen bonding interaction between these two molecules, instead favoring a reduction in any possible steric effects the pseudo-eclipsed conformation might have.

Tripos. Equilibrium geometries resulting from the application of the Tripos force field (denoted SYBYL in Spartan) were nearly identical, indicating a combined global minimum not equivalent to either published structure. Bond distances were, once again, approximately equivalent, though angles showed even larger differences than those found for the MMFF. While the C₁O₃C₂ angle remained approximately the same (to within 2°), the Tripos force field produced significantly larger angles for H₂C₂O₃ (+16°) and O₁C₁O₃ (+3°). Like the MMFF, it appears to incorrectly account for H-O energy-minimizing interactions. Furthermore, it sought to make the remaining O₂C₂O₃ (+8°) and H₁C₁O₃ (-6°) angles equivalent, despite the asymmetry in the molecule.

AM1. The semi-emperical quantum mechanical energy minimizations of the AM1 Hamiltonian again produced structures with nearly equivalent parameters when either original structure was used. Bond distances, as before, were approximately equivalent. Most bond angles matched well with those for the MW structure, save for O₂C₂O₃ (-14°) and H₂C₂O₃ (+9°). In this particular case the force field appears to have overcompensated in the opposite direction as the MMFF or Tripos fields, making angles on both sides of the molecule nearly equivalent for each atomically equivalent pair.

HF. The Hartree-Fock 3-21G* energy minimization, while the most advanced function in terms of pure quantum mechanical calculations, failed on every angle to match well with the MW structure by at least 3°. Approximate differences are enumerated in the notes below. Because this particular basis set utilizes only d-like orbitals when factoring in polarization of charge, p-like orbitals involved in calculating the polarization of charge for hydrogen atoms are ignored. As hydrogen bonding appears to play an important role in the energy minimization of Formic Anhydride, failing to factor this aspect in likely alters both affected bond angles (and therefore all others as well).

Wu et al. attempted in 1995 to produce a structure that accurately accounted for inconsistencies between the MW, ED, and IR⁵ spectra utilizing more advanced methods in molecular modeling and quantum mechanics⁴. Their resulting r_a⁰ structure is summarized in the tabular results below. By applying the 6-31G** force field to calculate B_z – B₀ correction factors, they were able to account for vibration-rotation interactions within the molecule, bringing the microwave structure to an r_a⁰ basis. The electron diffraction structure was similarly corrected by applying an r_a – r_a⁰ shrinkage correction given by

r_a – r_a⁰ = K⁰ – U²/r_a

Both corrected spectra were then weighted and brought into alignment with the IR spectra as well as recent photochemical decomposition data. Their results indicate a planar conformation and H₂O₁ asymmetrical configuration for the molecule, as would be expected given the numerous energy minimization results already described.

References

1. Vaccani, S., Bauder, A., and Günthard, Hs. H. “Microwave Spectrum, Dipole Moment and Conformation of Formic Anhydride.” Chem. Phys. Letters, 35, 457-460 (1975).
2. Vaccani, S., Roos, U., Bauder, A., and Günthard, Hs. H. “Microwave Spectra, Substitution Structure, and Vibrational Satellites of Formic Anhydride.” Chem. Physics, 19, 51-57 (1977).
3. Boogaard, A., Geise, H. J., and Miljhoff, F. C. “An Electron Diffraction Investigation of the Molecular Structure of Formic Anhydride.” J. Molecular Structure, 13, 53-58 (1972).
4. Wu, G., Shlykov, S., Alsenoy, C. Van, Geise, H. J., Sluyts, E., and Van der Veken, B. J. “Formic Anhydride in the Gas Phase, Studied by Electron Diffraction and Microwave Infrared Spectroscopy, Supplemented with ab-Initio Calculations of Geometries and Force Fields.” J. Phys. Chem, 99, 8595-8598 (1995).
5. Kuehne, H., Ha, T. K., Meyer, R., Guenthard, H. H. “Formic Acid Anhydride. Matrix Infrared Spectra of Five Isotopic Species, Vibrational Analysis, Emperical and Ab Initio Harmonic Force Field and Thermodynamic Functions.” J. Molec. Spectroscopy 77, 251-269 (1979)

SYBYL mol2 and Brookhaven pdb coordinate files of structures generated by various means
(You will be able to view these structures with Netscape or Explorer if you have installed Chime and click on the entry for the pdb file.)

• Original Microwave Structure derived from bond distances and angles given by Vaccani et al. (1977)
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Bond lengths and angles were derived from three-dimensional analysis of the rotational constants of nine isotopically substituted species (see table later in this entry), ignoring z-axis coordinates which proved to be below the limit of reliable r_s structure determination (< 0.2 Å) at the time. Reported values, taken to the last number reported, were then transformed into Cartesian coordinates for creation of the mol2 file.
• Original Electron Diffraction Structure derived from bond distances and angles given by Boogaard et al. (1972)
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Boogaard et al. interpreted the electron diffraction structure to include two dihedral angles, twisting O₁ and H₂ approximately 43° away from one another when viewed along the C₂C₁ (nonbonded) axis. The resulting structure takes on a pseudo-Gauche conformation. In most cases, uncertainties were significantly higher than those derived from the microwave spectrum (0.002 to 0.02Å, 0.5 to 2°). The distance/angle to Cartesian transformation involved significant and difficult geometric analysis due to asymmetry and a lack of planarity, and propagation of uncertainty was not included in these calculations. In order to determine bond lengths, the angle O₁C₁O₃ was fixed at 123.4° and angle O₂C₂O₃ determined relative to O₁C₁O₃ as 4.6° smaller. The value for C₂H₂ was not reported but assumed to be equivalent to C₁H₁ (1.10Å). Mean bond lengths for the O₁O₂ and C₁O₂ nonbonded distances were held fixed in order to produce smooth radial distribution functions (r.d.f.’s) and r.d.f difference spectra.
• MMFF94 (Spartan 02’) energy-minimized structure derived from the original microwave structure mol2 file above
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Reasonable agreement with the original MW structure observations. The molecule is planar; all bond distances differ by less than 0.03Å, while differences between angles are not greater than 4°, except in the cases of the O₁C₁O₃ and H₂C₂O₃ angles, which did not exceed 7°. Increasing both angles results in a larger distance between O₁ and H₂, which presumably interact through hydrogen bonding, an effect whose impacts on the total energy of the molecule may not be completely accounted for in this particular force field.
• MMFF94 (Spartan 02’) energy-minimized structure derived from the original electron diffraction mol2 file above
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Exactly equivalent to the MMFF minimization of the MW structure. Similar bond lengths with respect to the ED structure but elimination of the dihedral angles to produce a planar structure, thus also producing significant differences when compared to ED bond angles, especially concerning angles containing either hydrogen atom. Supports the hypothesis that the planar (MW) structure is the actual conformation of the molecule.
• Tripos (SYBYL) (Spartan 02’) energy-minimized structure derived from the original microwave structure mol2 file
• Sybyl pdb format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Equivalent to the MMFF-derived results to within 0.1 of either unit of measurement save for the C₁O₃C₂ angle, which is larger by 4°. Increasing this bong angle decreases interactions between O₁ and H₂ without changing angles centralized at either carbon atom.
• Tripos (SYBYL) (Spartan 02’) energy-minimized structure derived from the original electron diffraction mol2 file
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Nearly equivalent to the Tripos-minimized MW structure, save for inconsequential (< 0.05°) differences in dihedral angles (and correspondingly, small alterations in bond angles) likely resulting from incomplete convergence during minimization.
• AM1 Hamiltonian (Spartan 02’) semi-empirical quantum mechanics energy-minimized structure derived from the original microwave structure mol2 file
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Agreement to within 0.05Å with the MMFF-derived structure. Bond angles were somewhat different, favoring a larger C₁O₃C₂ angle and smaller O₂C₂O₃ angle, both of which favor the MW spectral results.
• AM1 Hamiltonian (Spartan 02’) semi-empirical quantum mechanics energy-minimized structure derived from the original electron diffraction mol2 file
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: As in the Tripos ED, nearly equivalent to the AM1-minimized MW structure, save for small (< 0.3°) differences in dihedral angles, though the small dihedrals did not significantly affect the other parameters.
• Hartree-Fock (Spartan 02’) ab initio quantum mechanics (3-21G* basis set) energy-minimized structure derived from the original microwave structure mol2
• Sybyl mol2 format (Windows mo2 extension)
• Brrokhaven pdb format
• Notes: On average, the results most strongly in agreement with both the MW and ED bond lengths, save for the C₂O₃ bond length, which strongly favors the MW structure result and is consequently 0.1Å larger than the ED structure result. Nearly all angles show significant (>4°) differences when compared with the MW structure. A larger O₁C₁O₃ favors the ED structural result, while a smaller H₁C₁O₃ favors the MW result. The value for O₂C₂O₃ is closer to the ED structural result (higher by 2°) than the MW result (lower by 6°), while the value for H₂C₂O₃ is greater than the MW result by only 4°, but smaller than the ED result by 10°. The angle C₁O₃C₂ is greater than both MW (by 3°) and ED (5°). All of these results seem to indicate that complex electronic effects aid in determining the exact structural parameters of Formic Anhydride that cannot be exactly replicated using the 3-21G* basis set.
• Hartree-Fock (Spartan 02’) ab initio quantum mechanics (3-21G* basis set) energy-minimized structure derived from the original electron diffraction mol2
• Sybyl mol2 format (Windows mo2 extension)
• Brookhaven pdb format
• Notes: Nearly equivalent to the Hartree-Fock minimization of the MW structure, save for two small (> 0.2°) dihedral angles, likely due to incomplete convergence.

Tabular Results of Structural Parameters

	Original	Original	MMFF	MMFF	SYBYL	SYBYL
Parameter	MW	ED	MW	ED	MW	ED
rC1O1 (Å)	1.1841	1.188	1.22	1.22	1.221	1.221
rC1H1 (Å)	1.1014	1.1	1.102	1.102	1.089	1.089
rC1O3 (Å)	1.3887	1.384	1.35	1.35	1.34	1.34
rC2O2 (Å)	1.1952	1.099	1.224	1.224	1.22	1.22
rC2H2 (Å)	1.0961	1.1	1.1	1.1	1.091	1.091
rC2O3 (Å)	1.3641	1.273	1.348	1.348	1.339	1.339
<O1C1O3 (°)	120.59	123.4	127.65	127.65	123.23	123.23
<H1C1O3 (°)	112.05	119.1	108.68	108.68	118.37	118.41
<O2C2O3 (°)	126.12	118.8	122.83	122.83	118.72	118.73
<H2C2O3 (°)	108.55	122	115	115	124.4	124.4
<C1O3C2 (°)	117.79	115.2	115.51	115.51	119.55	119.55
<C1O3C2H2 (°)	0	17	0	0	0	0.05
<C2O3C1O1 (°)	0	26	0	0	0	0.02
	AM1	AM1	HF	HF	Wu et al.
Parameter	MW	ED	MW	ED	ra^0 Geometry
rC1O1 (Å)	1.226	1.226	1.195	1.195	1.193
rC1H1 (Å)	1.105	1.105	1.072	1.072	1.086
rC1O3 (Å)	1.371	1.371	1.366	1.366	1.374
rC2O2 (Å)	1.222	1.222	1.187	1.187	1.18
rC2H2 (Å)	1.103	1.103	1.074	1.073	1.078
rC2O3 (Å)	1.392	1.392	1.386	1.386	1.394
<O1C1O3 (°)	119.12	119.13	124.15	124.12	124.2
<H1C1O3 (°)	110.59	110.6	109.3	109.31	112.7
<O2C2O3 (°)	112.11	112.11	120.94	120.94	120.8
<H2C2O3 (°)	117.83	117.82	112.7	112.71	116.3
<C1O3C2 (°)	120.33	120.33	121.66	121.67	118.6
<C1O3C2H2 (°)	0	0.2	0	-0.09	0
<C2O3C1O1 (°)	0	0.25	0	0.19	0

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Observed Rotational Constants in MHz for the Isotopomers of Formic Anhydride from Vaccani et al. (1977).

Notes: Uncertainties are given in parentheses following each value.

Each isotopomer is described by:

atom (following previously-defined numbering scheme) à isotope substituted

Isotopomer	A0 (MHz)	B0 (MHz)	C0 (MHz)
Unsubstituted	21879.9192(41)	3245.71696(72)	2829.45712(56)
H2 à D	20347.4274(65)	3241.61332(66)	2799.94590(63)
H1 à D	20247.4041(75)	3175.36413(92)	2747.92994(86)
H2, H1 à D	18910.9780(53)	3170.47837(65)	2719.05272(59)
C2 à C^13	21769.0975(62)	3227.86738(64)	2814.11174(57)
C1 à C^13	21701.3148(134)	3211.5775(14)	2800.5280(9)
C2, C1 à C^13	21591.0663(150)	3193.3913(10)	2784.9328(9)
O2 à O^18	21838.6649(110)	3075.6893(14)	2698.7721(13)
O1 à O^18	21159.1834(86)	3121.0205(12)	2722.6067(10)
O3 à O^18	20952.5609(68)	3245.9526(10)	2813.4711(8)