Visualization of Orbitals (12) ― Carbon sp³, sp² and sp Hybrid Orbitals

Abstract

炭素原子をはじめとする多電子原子を原子価結合法で取り扱い，原子価状態の軌道関数を表す方法である混成軌道が，原子軌道の線形結合によってどのような数式で表され，それらの数式を可視化するいろいろな方法によってどのように描かれるかを紹介した．

Translated Abstract

Mathematical expressions of carbon sp³, sp² and sp hybrid orbitals were visualized by various techniques such as orbital picture, real 3-dimensional probability density picture in a glass block, and isosurface representation. Orbital picture and probability density picture were especially useful for recognizing equivalency and directional characteristics of the chemical bonds. Isosurface representation uniquely showed the difference of s or p characters between these three hybrid orbitals.

Figures

Figure 1.

 Lewis structures (electron-dot structures) of H₂, HF, CH₄ and NH₃ molecules.

Figure 2.

 Diagrams showing how the shapes of molecules predicted when the valence shell of the central atom contains 4, 3 or 2 electron pairs.

Figure 3.

 (left): Probability density distribution in the 3-dimentional distribution of carbon ${\chi }_{{\text{sp}}^{\text{3}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{3}}}^{\text{2}},{\chi }_{{\text{sp}}^{\text{3}}}^{\text{3}}$, and${\chi }_{{\text{sp}}^{\text{3}}}^{\text{4}}$orbitals looking through Z axis (top) and looking through Y axis (bottom); (right): An image of a sphere looking through X axis。

Figure 4.

 (left): Probability density distribution in the 3-dimentional distribution of carbon ${\chi }_{{\text{sp}}^{\text{3}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{3}}}^{\text{2}},{\chi }_{{\text{sp}}^{\text{3}}}^{\text{3}}$, and${\chi }_{{\text{sp}}^{\text{3}}}^{\text{4}}$orbitals; (right): Diagrams showing how the shapes of molecules predicted when the valence shell of the central atom contains 4 electron pairs:

Figure 5.

 Probability density distribution in the 3-dimentional distribution of Carbon ${\chi }_{{\text{sp}}^{\text{2}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{2}}}^{\text{2}},{\chi }_{{\text{sp}}^{\text{2}}}^{\text{3}}$, and${\chi }_{2{\text{p}}_z}$orbitals.

Figure 6.

 Probability density distribution in the 3-dimentional distribution of carbon ${\chi }_{\text{sp}}^{\text{1}},{\chi }_{\text{sp}}^{\text{2}},{\chi }_{2{\text{p}}_y}$and${\chi }_{2{\text{p}}_z}$orbitals.

Figure 7.

 Carbon ${\chi }_{{\text{sp}}^{\text{3}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{2}}}^{\text{1}}$and ${\chi }_{\text{sp}}^{\text{1}}$orbitals.

Figure 8.

 Probability density distribution in the 3-dimentional distribution of carbon ${\chi }_{{\text{sp}}^{\text{3}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{2}}}^{\text{1}}$and ${\chi }_{\text{sp}}^{\text{1}}$orbitals.

Figure 9.

 Isosurface representation of carbon ${\chi }_{{\text{sp}}^{\text{3}}}^{\text{1}},{\chi }_{{\text{sp}}^{\text{2}}}^{\text{1}}$and ${\chi }_{\text{sp}}^{\text{1}}$orbitals.

参考文献

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