Chemistry

Academician B. A. Arbuzov, V. A. Naumov, N. V. Alekseev

ELECTRON-DIFFRACTION STUDY OF THE STRUCTURE OF THE $\alpha$-PINENE OXIDE MOLECULE

Earlier ($^{1}$), in studying $\alpha$-pinene oxide by the method of proton magnetic resonance, a conformational formula for $\alpha$-pinene oxide was proposed. It was shown that one of the gem-dimethyl groups interacts with the oxide ring, whereas the second does not interact with it. As for the conformation of the cyclohexene oxide ring in the $\alpha$-pinene oxide molecule, it was accepted, according to literature data, as a half-chair, analogous to cyclohexene oxide ($^{2}$).

Fig. 1

The aim of the present work is an electron-diffraction study of the structure of the $\alpha$-pinene oxide molecule. Electron-diffraction patterns of the vapor of the compound under investigation were obtained on an EG-100A electron-diffraction apparatus ($^{3}$). In the work an additional diffusion pump DMN-20 was used, located near the evaporator nozzle for more effective removal of the vapor of the substance being studied. In recording the electron-diffraction patterns an $s^{2}$ sector was used. From the vapors of $\alpha$-pinene oxide, 15 series of electron-diffraction patterns were obtained at different nozzle—plate distances (188 and 418 mm) and at accelerating electron voltages of 40 and 60 kV. The interpretation of the electron-diffraction patterns was carried out on the basis of visual estimation of intensity by the radial-distribution method and by the method of successive approximations according to the equations*:

$$ rD(r)=\sum sI(s)\exp(-as^{2})\sin sr\,\Delta s, \tag{1} $$

where

$$ s=\frac{4\pi}{\lambda}\sin\frac{\vartheta}{2}, $$

$\lambda$ is the electron wavelength, $\vartheta$ is the scattering angle,

* The calculations were carried out on the M-3 electronic computer by L. F. Shatrukov, to whom we express our gratitude.

\(I(s)\) is the scattering intensity, \(\exp(-a s_{\max}^{2}) = 0.1\); \(\Delta s = 0.2\ \text{\AA}^{-1}\), and

\[ I(s)=\sum_i \sum_j n Z_i Z_j \exp\left(-\frac{1}{2} l_{ij}^{2}s^{2}\right)\frac{\sin s r_{ij}}{s r_{ij}}, \tag{2} \]

where \(Z_i\) and \(Z_j\) are the nuclear charges of atoms \(i\) and \(j\), \(l_{ij}\) is the root-mean-square amplitude of thermal vibrations. The values of \(l_{ij}^{2}/2\) were taken as follows: \(0.0020\ \text{\AA}^{2}\) for C—C and C—O distances between bonded atoms, \(0.0040\ \text{\AA}^{2}\) for C···H distances between nearest nonbonded atoms,

Fig. 2

\(0.0032\ \text{\AA}^{2}\) for C···C and C···O distances between nearest nonbonded atoms, \(0.0040\ \text{\AA}^{2}\) and \(0.0060\ \text{\AA}^{2}\) for C···C, C···O, and C···H distances between nonbonded atoms separated by two and three atoms.

Figure 1 shows the radial distribution curve constructed from the experimental intensity curve with extrapolation of \(I(s)\) in the region \(s = 0\)—\(2.6\ \text{\AA}^{-1}\) by the theoretical intensity curve. The radial distribution curve \(rD(r)\) has five peaks that may be regarded as structural: 1.09, 1.54, 2.16, 2.58, and \(4.09\ \text{\AA}\). The first peak on the \(rD(r)\) curve was assigned to C—H distances, the second to C—O and C—C distances, the third peak at \(r = 2.16\ \text{\AA}\) to C···H and C\(_{3(4)}\)···C\(_{6(5)}\) distances, the fourth—an extremely complex peak—was assigned mainly to C···C and C···O distances separated by one carbon atom. The position of this peak (\(r = 2.58\)) made it possible to estimate the valence angle C—C—C, which was subsequently refined by constructing theoretical curves. The region of the \(rD(r)\) curve from 2.6–3.5 Å corresponds to longer C···C and C···O distances, whose atoms are separated by two and even three carbon atoms. The peak at \(r = 4.09\ \text{\AA}\) was assigned to the distances C\(_6\)···C\(_{10}\), C\(_4\)···C\(_{10}\), C\(_7\)···C\(_{10}\), C\(_8\)···C\(_{10}\) (see Fig. 2a).

Fig. 3

Formally, the model of the molecule of \(\alpha\)-pinene oxide may be represented as a combination of a dimethylcyclobutane ring and 2:3-epoxybutylene. It is known from literature data\({}^{(4–7)}\) that the carbon atoms of cyclobutane do not lie in one plane. The angle between two planes in the cyclobutane molecule and its derivatives is 150–160°. Taking the angles C\(_1\)—C\(_2\)—C\(_3\), C\(_1\)—C\(_7\)—C\(_6\), C\(_7\)—C\(_1\)—C\(_2\), C\(_8\)—C\(_4\)—C\(_9\), C\(_{10}\)—C\(_2\)—C\(_8\), and C\(_1\)—C\(_2\)—C\(_{10}\)

equal to 112–114° (from the data of the radial-distribution curve), theoretical intensity curves were calculated for various angles α and β (α is the angle between the planes C₃C₄C₆ and C₃C₅C₆; β is the angle between the planes C₁OC₂ and C₁C₂C₇). The best agreement with the experimental intensity curve is given by theoretical curve i (model a, Fig. 2, Fig. 3, and Table 1), the parameters of which are given in Table 2. For comparison, Fig. 1 gives the theoretical radial-distribution curve calculated from the curve \(I(s)\) for model i. From the comparison it is seen that, on the whole, both curves agree satisfactorily. The section of the curve \(rD(r)\) in the region 2.0–2.2 was calculated without the exponential term in equation (1), in order to determine the position of the peak in this region.

Table 1

Comparison of the experimental and theoretical intensity curves
(curve i)

It is interesting to note the following. The carbon atom C₁₀ is in an approximately equatorial position. If the angle β is increased to 180° and more, then the oxygen atom and the methyl group will become “crowded,” and as a result the CH₃ group will tend to move into an axial position. But then it will be “crowded” because of the position of the gem-dimethyl group. It is sufficient to point out that the distance C₈⋯C₁₀ in this case will be about 1.9 Å, and the molecule will experience additional steric strain.

Construction of theoretical intensity curves for models in which the angle β is 116, 130, 150°, etc., confirmed this supposition. None of the theoretical curves (for example, curves a, b, c, and g in Fig. 3) agrees with the experimental one.

A model was also tested (model b, Fig. 2) in which the atoms C₁, C₂, C₃ and C₆ and C₇ are coplanar, but the theoretical intensity curve for this model (curve d, Fig. 3) does not agree with the experimental curve. In paper (2) there is an indication that the bonds C₁—C₇, C₁—C₂, C₂—C₃ in cyclohexene oxide lie in one plane, the atom C₅ is below, and the atom C₆ above this plane. One might suppose that such a motif would also be retained in the α-pinene oxide molecule. However, construction of such a model (model c, Fig. 2) showed that the distances C₂⋯C₄ and C₅⋯C₇ would be approximately equal to 2.3 Å (a considerable shortening of the C⋯C distance compared with the value 2.58 Å). If these distances are taken

Table 2

Parameters of the theoretical curves*

* For all the curves listed in the table, the values are
\(r(\mathrm{C—H}) = 1.08\) Å, \(r(\mathrm{C—C}) = 1.55\) Å, \(r(\mathrm{C—O}) = 1.44\) Å. Shortest distances C⋯H = 2.16 Å, ∠C₁₀—C₂—C₁ = ∠C₁₀—C₂—C₃ = 112.

** Table 2 and Fig. 3 give some of the calculated curves.

*** Atoms C₁, C₂, C₃, C₆, and C₇ are coplanar.

equal to \(\sim 2.5\) Å (this corresponds to a \(C—C—C\) angle of \(\sim 109^\circ\)), then the \(C_4 \ldots C_5\) distance will be less than 2.0 Å, which is unlikely. And indeed, the theoretical intensity curve (curve \(e\) in Fig. 3) agrees poorly with the experimental curve.

Thus, as a result of the electron-diffraction study of the structure of the molecule of \(\alpha\)-pinene oxide, the configuration of the molecule was determined (model \(a\), Fig. 2) with the following parameters: \(r(C—H)=1.09\) Å (assumed), \(r(C—C)=1.56 \pm 0.02\) Å, \(r(C—O)=1.45\) Å (assumed),

\[ \angle C_1—C_2—C_3 = \angle C_1—C_7—C_6 = \angle C_7—C_1—C_2 = \angle C_{10}—C_2—C_1 = \]
\[ = \angle C_{10}—C_2—C_3 = 112 \pm 3^\circ,\quad \angle C_3—C_4—C_6 = \angle C_3—C_5—C_6 = 87^\circ, \]
\[ \angle C_8—C_4—C_9 = 114 \pm 3^\circ,\quad \alpha = 146 \pm 8^\circ,\quad \beta = 103 \pm 10^\circ,\quad \angle C—C—H = 109^\circ \]

(assumed).

It is interesting to note that in the molecule of \(\alpha\)-pinene oxide there are no large deviations of the \(C—C—C\) valence angles from the tetrahedral value, except in the cyclobutane ring (incidentally, in octachloro- and octafluorocyclobutane the \(C—C—C\) angles are \(87—89^\circ\)); i.e., the configuration of the molecule found has the minimum spatial hindrance among those tested. The magnitude of the angle \(\beta = 103^\circ\) agrees well with the corresponding angle (\(98.1^\circ\)) in the molecule of cyclopentene oxide \((^8)\).

Institute of Organic Chemistry
Academy of Sciences of the USSR
Kazan

Institute of Organoelement Compounds
Academy of Sciences of the USSR

Received
17 XII 1963

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