Chapter 3, Problem 3.41P

Interpretation Introduction

(a)

Interpretation:

The molecular orbital picture of $\text{propa-1, 2-diene}$ is to be drawn.

Concept introduction:

Orbital picture of a molecule can be built up by first determining which orbitals will overlap and interact effectively. These are generally the orbitals from the valence shell of the atoms forming the bonds; mostly s and p orbitals. The orbital that will overlap end-on and the ones that overlap sideways are then determined on the basis of the electron geometry of the atoms. End on overlap leads to $\text{σ}$ interactions while sideways overlap leads to $\text{π}$ interactions.

Interpretation Introduction

(b)

Interpretation:

The MO energy diagram of $\text{propa-1, 2-diene}$ is to be drawn. The HOMO and LUMO are to be identified.

Concept introduction:

The molecular orbital energy diagram of a molecule is built up by considering the interactions of all the valence shall orbitals from each atom. The total number of MOs produced is the same as the number of interacting AOs.

An end-on overlap of two orbitals produces a pair of MOs of $\text{σ}$ symmetry. One of these, the bonding MO, is considerably lower in energy compared to the contributing AOs. The other, an antibonding MO, is higher in energy compared to the contributing AOs by an almost equal amount.

Interactions between p orbitals produces MOs of two types, one pair with a $\text{σ}$ symmetry and two pairs with $\text{π}$ symmetry. The $\text{σ}$ bonding MO is considerably lower in energy than the two $\text{π}$ bonding MOs. Conversely, the ${\text{σ}}^{*}$ antibonding MO is considerably higher in energy than the two ${\text{π}}^{*}$ antibonding MOs.

The valence electrons of the contributing atoms are then filled in these MOs in increasing order of energy. The MO of highest energy that contains any electrons is called the highest occupied molecular orbital (HOMO), and the empty MO immediately above it is called the lowest unoccupied molecular orbital (LUMO).