Visualization of Orbitals (13) ― How the Orbital Hybridization Accounts for the Structure of Hydrocarbons: σ-bond and π-bond.

Abstract

混成軌道を用いて，ルイスの電子対共有結合の概念にどのようにして同等性(等価性)や方向性を加味できるかを，簡単な分子を例にとって示す．σ電子とπ電子のちがい，π電子が核磁気共鳴スペクトルのケミカルシフトに及ぼす影響についても解説した．

Translated Abstract

When each of the four identical carbon sp³ hybrid orbitals overlaps with the hydrogen 1s orbital, four identical C-H σ bonds are formed and methane (CH₄) results. Because the four sp³ hybrid orbitals have a specific geometry, the angle formed by each H-C-H is 109.47°, the so-called tetrahedral angle. The structure of ethane (C₂H₆) is similarly explained. The bonds in methane and ethane are called single bonds because they result from the sharing of one electron pair between bonded atoms. Carbon atoms can also form double bonds by sharing two electron pairs or triple bonds by sharing three electron pairs. Ethylene (H₂C=CH₂) contains a carbon-carbon double bond. When two carbons with sp² hybrid approach each other, they form a strong σ bond by sp²-sp² overlap. The unhybridized p orbitals interact by sideways overlap to form a π bond, resulting the formation of a carbon-carbon double bond. Four hydrogen atoms form σ bonds with the remaining four sp² orbitals to complete the structure of ethylene. The H-C=C or H-C-H bond angle in ethylene molecule is 121.3°or 117.4°respectively. Acetylene (HC$\equiv$CH) contains a carbon-carbon triple bond. When two carbons with sp hybrid approach each other, they form a strong σ bond by sp-sp overlap. The unhybridized p_y or p_z orbitals interact by sideways overlap to form two π bonds (p_y − p_y and p_z − p_z), resulting the formation of a carbon-carbon triple bond. The two remaining sp hybrid orbitals each form a σ bond with hydrogen to complete the acetylene molecule. Acetylene is a linear molecule with H-C$\equiv$C bond angle of 180°. Difference electron density of HOMO or LUMO in ethylene molecule is visualized. The effect of π electron ring current for the chemical shift measurement in NMR (Nuclear Magnetic Resonance) spectroscopy is also discussed.

Figures

Figure 1.

 The structure of methane; (left): Each sp³ hybrid orbital forms a σ bond by overlap with an H 1s orbital located at the corner of the cube; (right): molecular model of methane.

Figure 2.

 Overlap of carbon sp³ hybrid orbital and hydrogen 1s orbital.

Figure 3.

 The structure of ethane; (left): Each C sp³ hybrid orbital forms a σ bond by overlap with an H 1s orbital or a C sp³ orbital; (right): molecular model of ethane.

Figure 4.

 Overlap of carbon sp³ hybrid orbitals.

Figure 5.

 Five σ bonds (left) and a π bond (right) in an ethylene molecule

Figure 6.

 A π bond image in an ethylene molecule by the overlap of carbon 2p orbitals.

Figure 7.

 A σ bond image by the overlap of carbon 2p orbitals.

Figure 8.

 Examples of conjugated polyene.

Figure 9.

 (left): Two benzene resonance forms; (right): A single circle indicates the equivalence of the carbon-carbon bonds.

Figure 10.

 Three σ bonds (top left) and two π bonds (top right and bottom) in an acetylene molecule

Figure 12.

 (left) LUMO of ethylene; (right) Difference electron density ${\left|{\varphi }_9\right|}^2-\left({\left|\frac{1}{\sqrt{2}}{\chi }_1\right|}^2+{\left|\frac{1}{\sqrt{2}}{\chi }_2\right|}^2\right)$

Figure 11.

 (left) HOMO of ethylene; (right) Difference electron density ${\left|{\varphi }_8\right|}^2-\left({\left|\frac{1}{\sqrt{2}}{\chi }_1\right|}^2+{\left|\frac{1}{\sqrt{2}}{\chi }_2\right|}^2\right)$

Figure 13.

 Regeons of the ¹H NMR spectrum

Figure 16.

 (left and top right) The Probability density distribution in the 3-dimentional distribution of the highest two occupied acetylene orbitals; (bottom right): The electron density in π orbitals has cylindrical symmetry around the internuclear axis.

Figure 15.

 The ring current effects in benzene. Circulating π electrons create a ring current (orange). Induced magnetic field (cyan) reinforces the external magnetic field (H₀) near the protons which are deshielded.

Figure 14.

 Probability density distribution in the 3-dimentional distribution of the highest two occupied benzene orbitals. (left): top view, (center): side view; (right): 18-annulene.

Figure 17.

 Isosurfaces of (left) the squares of hydrogen ${\chi }_{nlm}$ and (center) real functionalized atomic orbitals; (right): Isosurface of the squares of ${\chi }_{211}$.

Figure 18.

 The ring current effects in acetylene. Circulating π electrons create a ring current (orange). The applied (red) and induced (cyan) magnetic fields are opposite and the hydrogen feels weaker net field. This puts the proton in a shielded environment.

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