杂化轨道成键能力及夹角计算公式的简洁推导

doi:10.3866/PKU.DXHX202208064

University Chemistry ›› 2023, Vol. 38 ›› Issue (8): 312-317.doi: 10.3866/PKU.DXHX202208064

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Concise Derivation of Formulas for Calculating the Bonding Ability of Hybrid Orbitals and the Angle between Hybrid Orbitals

Dongju Zhang(), Yanhong Liu

School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China

Received:2022-08-10 Accepted:2022-09-19 Published:2022-09-30
Contact: Dongju Zhang E-mail:zhangdj@sdu.edu.cn

Abstract

Abstract:

Hybrid orbital theory is an important part of the chemical bond theory. The bonding ability of hybrid orbitals and the angle between two hybrid orbitals are the most important and difficult topics in the teaching and learning of hybrid orbital theory. Most textbooks usually give the relevant formulas directly and ignore their derivation, which does not meet the needs for the advanced learning of some students. This paper provides a simple derivation of these formulas to dispel students' doubts and deepen their understanding of hybrid orbital theory.

Key words: Hybrid orbital theory, Maximum bonding capacity, Angle between two hybrid orbitals

Dongju Zhang, Yanhong Liu. Concise Derivation of Formulas for Calculating the Bonding Ability of Hybrid Orbitals and the Angle between Hybrid Orbitals[J].University Chemistry, 2023, 38(8): 312-317.

Figures/Tables 1

References 17

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轨道	$ Y(\theta , \varphi ) $	$ Y(x, y, z) $	$ \left\| {Y{{(\theta , \varphi )}_{\max /\min }}} \right\| $	成键能力(F)
s	$ \sqrt {\frac{1}{{4\pi }}} $	$ \sqrt {\frac{1}{{4\pi }}} $	$ \sqrt {\frac{1}{{4\pi }}} $	1
p_x	$ \sqrt {\frac{3}{{4\pi }}} \sin \theta \cos \varphi $	$ \sqrt {\frac{3}{{4\pi }}} x $	$ \sqrt {\frac{3}{{4\pi }}} $	$ \sqrt 3 $
p_y	$ \sqrt {\frac{3}{{4\pi }}} \sin \theta \sin \varphi {\text{ }} $	$ \sqrt {\frac{3}{{4\pi }}} y $	$ \sqrt {\frac{3}{{4\pi }}} $	$ \sqrt 3 $
p	$ \sqrt {\frac{3}{{4\pi }}} \cos \theta $	$ \sqrt {\frac{3}{{4\pi }}} z $	$ \sqrt {\frac{3}{{4\pi }}} $	$ \sqrt 3 $
d_z2	$ \sqrt {\frac{5}{{16\pi }}} (3{\cos ^2}\theta - 1) $	$ \sqrt {\frac{5}{{16\pi }}} (3{z^2} - 1) $	$ \sqrt {\frac{5}{{4\pi }}} $	$ \sqrt 5 $
d_x2−y2	$ \sqrt {\frac{{15}}{{16\pi }}} {\sin ^2}\theta \cos 2\varphi $	$ \sqrt {\frac{{15}}{{16\pi }}} ({x^2} - {y^2}) $	$ \sqrt {\frac{{15}}{{16\pi }}} $	$ 0.866\sqrt 5 $
d_xz	$ \sqrt {\frac{{15}}{{16\pi }}} \sin 2\theta \cos \varphi $	$ \sqrt {\frac{{15}}{{4\pi }}} xz $	$ \sqrt {\frac{{15}}{{16\pi }}} $	$ 0.866\sqrt 5 $
d_yz	$ \sqrt {\frac{{15}}{{16\pi }}} \sin 2\theta \sin \varphi {\text{ }} $	$ \sqrt {\frac{{15}}{{4\pi }}} yz $	$ \sqrt {\frac{{15}}{{16\pi }}} $	$ 0.866\sqrt 5 $
d_xy	$ \sqrt {\frac{{15}}{{16\pi }}} {\sin ^2}\theta \sin 2\varphi $	$ \sqrt {\frac{{15}}{{4\pi }}} xy $	$ \sqrt {\frac{{15}}{{16\pi }}} $	$ 0.866\sqrt 5 $

Concise Derivation of Formulas for Calculating the Bonding Ability of Hybrid Orbitals and the Angle between Hybrid Orbitals

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