Chapter 9, Problem 9.14P

(a)

Interpretation Introduction

Interpretation:

The energy of pi molecular orbitals of benzene and cyclooctatetraene has to be calculated.  Also comment has to be given on the presence or absence of degenerate energy levels.

Concept Introduction:

The energy $\left(E_k\right)$ of pi molecular orbital of monocyclic conjugated polyenes with each of N carbon atoms contributing an electron in a 2p orbital can be calculated using the following equation.

  $\begin{array}{l}{E}_k=\alpha +2\beta \cos \frac{k\pi }{N+1}\\ \\ k=0,\pm 1,\pm 2,\pm 3,\mathrm{...}[\pm \frac{1}{2}N\left(evenN\right),[\pm \frac{1}{2}\left(N-1\right)\left(oddN\right).\end{array}$

(b)

Interpretation Introduction

Interpretation:

The delocalization energies of benzene and hexatriene have to be calculated and compared.

Concept Introduction:

The energy $\left(E_k\right)$ of pi molecular orbital of monocyclic conjugated polyenes with each of N carbon atoms contributing an electron in a 2p orbital can be calculated using the following equation.

  $\begin{array}{l}{E}_k=\alpha +2\beta \cos \frac{k\pi }{N+1}\\ \\ k=0,\pm 1,\pm 2,\pm 3,\mathrm{...}[\pm \frac{1}{2}N\left(evenN\right),[\pm \frac{1}{2}\left(N-1\right)\left(oddN\right).\end{array}$

For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies $E_k$ of the resulting $\pi$ molecular orbitals are given as follows,

  $E_k=\alpha +2\beta \cos \frac{k\pi }{N+1},k=1,2,\mathrm{3...}N$

The pi electron delocalization energy can be calculated using the following equation.

  $E_{deloc}=E_{\pi }-n\left(\alpha +\beta \right)$

Where,

$E_{deloc}=$ delocalization energy

$E_{\pi }=$ total pi electron binding energy

$n=$ total number of pi electron

(c)

Interpretation Introduction

Interpretation:

The delocalization energies for cyclooctatetraene and octatetraene has to be calculated and compared.

Concept Introduction:

The energy $\left(E_k\right)$ of pi molecular orbital of monocyclic conjugated polyenes with each of N carbon atoms contributing an electron in a 2p orbital can be calculated using the following equation.

  $\begin{array}{l}{E}_k=\alpha +2\beta \cos \frac{k\pi }{N+1}\\ \\ k=0,\pm 1,\pm 2,\pm 3,\mathrm{...}[\pm \frac{1}{2}N\left(evenN\right),[\pm \frac{1}{2}\left(N-1\right)\left(oddN\right).\end{array}$

For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies $E_k$ of the resulting $\pi$ molecular orbitals are given as follows,

  $E_k=\alpha +2\beta \cos \frac{k\pi }{N+1},k=1,2,\mathrm{3...}N$

The pi electron delocalization energy can be calculated using the following equation.

  $E_{deloc}=E_{\pi }-n\left(\alpha +\beta \right)$

Where,

$E_{deloc}=$ delocalization energy

$E_{\pi }=$ total pi electron binding energy

$n=$ total number of pi electron