Chapter 9, Problem 9.1IA

Interpretation Introduction

Interpretation:

The molecular orbital energy level diagrams of ethene on the basis that the molecule is formed from the appropriately hybridized ${\text{CH}}_{\text{2}}$ or $\text{CH}$ fragments has to be constructed.

Concept introduction:

Huckel molecular orbital theory is used for the determination of the energies of molecular orbitals of $\pi$ electrons of conjugated systems.  In Huckel molecular orbital theory, molecular orbitals are formed by a linear combination of atomic orbitals.

Molecular orbital diagrams are used for determining the bonding in molecules using a linear combination of atomic orbitals.  The number of molecular orbitals formed is equal to the number of atomic orbitals that combine with each other.  The energy of the molecular orbital is given by the expression shown below.

  ${\text{E}}_{\text{±}}\text{=}\frac{\text{1}}{\text{2}}{\text{(α}}_{\text{A}}{\text{+α}}_{\text{B}}\text{)±}\frac{\text{1}}{\text{2}}{\text{(α}}_{\text{A}}{\text{-α}}_{\text{B}}\text{)}{\left\{\text{1+}{\left(\frac{\text{2β}}{{\text{α}}_{\text{A}}{\text{-α}}_{\text{B}}}\right)}^{\text{2}}\right\}}^{\frac{\text{1}}{\text{2}}}$