Furan

Lewis E. Johnson

Summary:

In their 1939 electron diffraction study of the structures of small aromatic systems, V. Schomaker and Linus Pauling found that the average ring bond distance in furan is 1.39 A. Through comparison with data for cyclopentadiene and butadiene, and assuming that the carbon-carbon single and double bond lengths were equivalent with cyclopentadiene, they were able to derive a complete heavy-atom structure for furan. Dihedral angles are not given, as it is assumed that the molecule is constrained to a planar conformation. The structure is also incomplete in that angles involving hydrogens are not provided.

Later, a 1962 study by Børge Bak et al. used microwave spectra of [2-¹³C], [3-¹³C], and [¹⁸O]-furan to determine the R_s structure of furan. Insufficient data were available to convert the structure to a R_e structure; the correction factor is unknown, however Bak et al. assumed that the R_e structure was very similar to the Rs structure. They also established from the microwave intensities a plane of symmetry through the oxygen and bisecting the bond between C3 and C4; C3 is equivalent to C4, and C2 is equivalent to C5.

The angles in the Bak et al structure compare well to the Pauling structure, with less than two degrees of difference, however deviation in the lengths is significant, likely due to Pauling’s use of non-aromatic cyclopentadiene as a starting structure for his calculations.

Computational Methods:

Computational structures were calculated at five levels of theory—classical mechanics using empirical force fields, ab initio quantum mechanics using semi-empirical approximations, ab initio quantum mechanics using Restricted Hartree-Fock methods, and post Hartree-Fock calculations using both Density Functional Theory and second-order Møller-Plesset perturbation theory.

The Class I Tripos SYBYL force field was used as a representative of lower-order classical mechanics, and the more advanced Class II MMFF94 force field was used for higher-order classical mechanics calculations. The MMFF94 structure was also used as the starting point for semi-empirical calculations.

Both the AM1 and the PM3 Hamiltonians, more modern parameterizations of Pople’s MNDO approximation, were used for semi-empirical calculations. Semi-empirical structures were then used as initial structures for Hartree-Fock SCF calculations using both the non-polarizable 3-21G basis set, and the polarizable 6-31G* basis set.

Hartree-Fock structures were then further minimized using two different correlated post-Hartree Fock methods: Density Functional Theory with a B3LYP functional, and second-order Møller-Plesset perturbation theory. Both calculations were run using a 6-31G* basis set.

In addition to energy minimization and geometry optimization, vibrational modes (ω_e) were also calculated at all levels of theory to verify that the structure was physically plausible. All structures were then exported as SYBYL Mol2 and Brookhaven PDB files.

Data:

Tables of experimental and calculated bond lengths and angles appear below. All data use internal coordinates based on the atom numbering in Figure 1:

Figure 1: Atom Definitions

Table 1: Bond lengths and angles for experimental and lower-order methods

(The links provide structure files in the pdb format for each method.)

Type	Experimental		Empirical Force Field		Semi-Empirical QM
Method	Microwave	electron- Diffraction	MMFF94	Tripos	AM1	PM3
Bond Length (A)
C2=C3	1.361	1.35	1.376	1.334	1.38	1.373
C3-C4	1.431	1.46	1.416	1.461	1.448	1.441
C2-O	1.362	1.41	1.358	1.337	1.395	1.378
C2-H	1.075	1.09	1.081	1.09	1.085	1.085
C3-H	1.077	1.09	1.081	1.09	1.086	1.086
Bond Angle (°)	106.55	107	106.8	101.09	106.57	106.9
O-C2=C3	110.68	109	110.4	116.36	110.1	110.2
C2=C3-C4	106.05	107	106.1	103.1	106.62	106.3
O-C2-H	115.92		115.6	121.42	114.45	115.5
C3=C2-H	133.4		134	122.22	135.45	134.3
C2=C3-H	126		126.1	128.76	127.75	127.8
C4-C3-H	127.95		127.7	128.14	125.63	125.8

Table 2: Bond lengths and angles for higher-order QM calculations

Type	Hartree-Fock QM		Post Hartree-Fock QM
Method	HF 3-21G	HF 6-31G*	B3YLP 6-31G*	MP2 6-31G*
Bond Length (A)
C2=C3	1.34	1.339	1.361	1.366
C3-C4	1.45	1.441	1.436	1.428
C2-O	1.38	1.344	1.364	1.367
C2-H	1.062	1.068	1.079	1.08
C3-H	1.065	1.07	1.081	1.081
Bond Angle (°)
O-C2=C3	107	107.1	106.8	106.6
C2=C3-C4	109.8	110.8	110.5	110.5
O-C2-H	106.7	105.6	106.1	106.2
C3=C2-H	116.5	116.1	115.6	115.5
C2=C3-H	133.7	133.1	133.8	134
C4-C3-H	126.7	126.8	126.6	126.3
O-C2=C3	126.6	127.6	127.4	127.5

Analysis:

All data were compared to the microwave R_s structure, which was assumed to be authoritative. The electron diffraction structure was not adequate for this role since it is incomplete and incorporates approximations based on cyclopentadiene. Squared error values were calculated for every bond length and angle for each method, then used to determine mean squared error for both lengths and angles. Methods are ranked by mean square values in Table 3, below.

Table 3: Error analysis

Rank	Length Errors		Angle Errors		Total Squared Error
	Method	MSE	Method	MSE	Method	MSE
1	B3LYP 6-31G*	1.22E-05	MMFF94	9.69E-02	MMFF94	9.70E-02
2	MP2 6-31G*	2.00E-05	MP2 6-31G*	1.26E-01	MP2 6-31G*	1.26E-01
3	MMFF94	1.04E-04	B3LYP 6-31G*	1.46E-01	B3LYP 6-31G*	1.46E-01
4	PM3	1.36E-04	HF 6-31G*	2.01E-01	HF 6-31G*	2.01E-01
5	HF 6-31G*	2.01E-04	HF 3-21G	5.93E-01	HF 3-21G	5.93E-01
6	HF 3-21G	2.88E-04	e- Diffraction	1.31E+00	e- Diffraction	1.31E+00
7	AM1	3.84E-04	PM3	1.32E+00	PM3	1.32E+00
8	Tripos	5.30E-04	AM1	2.21E+00	AM1	2.21E+00
9	e- Diffraction	7.32E-04	Tripos	3.34E+01	Tripos	3.34E+01

The MMFF94 force field and the advanced post Hartree-Fock methods produced results that were the most consistent with the microwave structure, with the MMFF minimization being the overall best in terms of total error. However, all three of the best computational structures are close to each other in quality. The Hartree-Fock methods provided the next-best structures, with a larger basis set improving the quality of the geometry, followed by the PM3 Hamiltonian, then the AM1 Hamiltonian. The Tripos SYBYL force field produced consistently poor results.

Level of theory was most important for bond lengths, with Density-Functional calculations resulting in almost an order of magnitude less error than lower order techniques, and MP2 calculations also producing very strong results. The PM3 Hamiltonian, however, produced a better overall estimate the bond lengths than even Hartree-Fock calculations with a 6-31G* basis set. The most striking difference between ab initio methods, however, was with the C-O bond length; methods using a basis set that did not incorporate a polarizability term consistently overestimated the bond length by up to .03 angstroms, while methods using a polarizable basis set produced excellent lengths for the bond.

A similar trend in quality of computational structures increasing in quality with level of theory was observed for the angle calculations, except that MMFF was able to produce geometries more congruent with experiment than any of the ab initio methods, likely due to its high-quality parameterization and efficacy at calculating electrostatic interactions between atoms. All other calculations had error levels consistent with their level of theory.

The electron diffraction structure preformed poorly compared to the higher-order computational methods; this is likely due to Pauling using a different molecule (cyclopentadiene) for determining initial geometry.

Structures:

[All structures are available as SPARTAN, Mol2, and PDB files—you can put the links in however you would like. The files are in the same folder as the report.]

References:

Børge Bak, D. Christensen, W. B. Dixon, L. Hansen-Nygaard, J. R. Andersen, and M. Schottländer. “The Complete Structure of Furan.” Journal of Molecular Spectroscopy 9, 124-129 (1962)

A. R. Leach. Molecular Modeling, 2ed. UK, Pearson Education. 2001.

V. Schomaker and L. Pauling. “The Electron Diffraction Investigation of the Structure of Benzene, Pyridine, Pyrazine, Butatidene-1,3, Cyclopentadiene, Furan, Pyrrole, and Thiophene. Journal of the American Chemical Society 61 1769-1780 (1939).

Appendix I: Rotational Constants of Furan

Table 4: Rotational constants for several furan isotopomers

Moment	Furan	[2-D]	[3-D]	[2,5-D2]	[2-^13C]	[3-^13C]	[^18O]
A	9446.96	9280.15	9383.47	9033.33	9295.41	9403.73	9447.66
B	9246.61	8638.48	8490.28	8160.52	9178.23	9043.68	8841.72
C	4670.88	4472.12	4455.53	4285.87	4616.25	4608.15	4565.37