Chapter 14, Problem 14.31P

Interpretation Introduction

Interpretation:

The $\text{π}$ MOs and the MO energy diagram for $\text{penta-1, 3-dienyl}$ cation are to be drawn similar to the ones shown in Figure 14-5 and 14-6. Each MO is to be identified as bonding, nonbonding, or antibonding. The HOMO and LUMO are to be labeled.

Concept introduction:

The hybridization of carbon atoms determines the number and nature of the $\text{σ}$ and $\text{π}$ MOs in the molecule or molecular ion. The number of contributing AOs and the total number of MOs formed is equal. The valence electrons of the molecule or the molecular ion are then distributed in the MOs, starting with the lowest energy orbitals. The $\text{σ}$ bonding MOs are the lowest energy orbitals and are filled first. They are completely filled up. The next in energy are the $\text{π}$ bonding MOs, which are also completely filled up in the ground state. The highest energy MO from this set is generally the HOMO. If the number of contributing p AOs is odd, there may also be one nonbonding MO, which generally will be the LUMO. These are generally empty.

The $\text{π}$ MOs on adjacent atoms interact constructively or destructively, depending on their phases. If they are of the same phase, the interaction is constructive and results in a bonding MO. If the phases are different, the interaction is destructive and results in an antibonding MO. This overlap shows a nodal plane in the center, where the electron density is zero. The phases of the orbitals on either side of the nodal plane are different.