Chapter 8, Problem 86P

(a)

Interpretation Introduction

Interpretation:

• The total number of MOs of $\text{1,3,5,7- octatetraene}$ gives has to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

Bonding molecular orbital:

Side-to-side overlap of in-phase p-orbitals produces a pi-bonding molecular orbitals and designated as ${\text{ψ}}_1$.

Anti-bonding molecular orbital:

The side-to-side interaction between out-of-phase p-orbitals produces a ${\text{π}}^{\text{*}}$ anti-bonding molecular orbital.

(b)

Interpretation Introduction

Interpretation:

• The total number of bonding and anti-bonding orbitals of $\text{1,3,5,7- octatetraene}$ have  to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

Bonding molecular orbital:

Side-to-side overlap of in-phase p-orbitals produces a pi-bonding molecular orbitals and designated as ${\text{ψ}}_1$.

Anti-bonding molecular orbital:

The side-to-side interaction between out-of-phase p-orbitals produces a ${\text{π}}^{\text{*}}$ anti-bonding molecular orbital.

(c)

Interpretation Introduction

Interpretation:

• The symmetric and anti-symmetric molecular orbitals of $\text{1,3,5,7- octatetraene}$ have to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

Bonding molecular orbital:

Side-to-side overlap of in-phase p-orbitals produces a pi-bonding molecular orbitals and designated as ${\text{ψ}}_1$.

Anti-bonding molecular orbital:

The side-to-side interaction between out-of-phase p-orbitals produces an ${\text{π}}^{\text{*}}$ anti-bonding molecular orbital.

Symmetric molecular orbitals:

The molecular orbitals that possess a internal plane of symmetry is known as symmetric molecular orbitals and the molecular orbitals that does not possess internal plane of symmetry is known as anti-symmetric molecular orbitals.

(d)

Interpretation Introduction

Interpretation:

• The HOMO and LUMO molecular orbitals of $\text{1,3,5,7- octatetraene}$ in the ground state have to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

HOMO (Highest occupied molecular orbital):

The accommodation of electrons at the highest-energy molecular orbitals is known as HOMO.

LUMO:

The lowest-energy of molecular orbitals that do not contain electrons is known as LUMO.

(e)

Interpretation Introduction

Interpretation:

• The HOMO and LUMO molecular orbitals of $\text{1,3,5,7- octatetraene}$ in the excited state have to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

HOMO (Highest occupied molecular orbital):

The accommodation of electrons at the highest-energy molecular orbitals is known as HOMO.

LUMO:

The lowest-energy of molecular orbitals that do not contain electrons are known as LUMO.

(f)

Interpretation Introduction

Interpretation:

• The relation between HOMO, LUMO and symmetric and antisymmetric orbitals have to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

HOMO (Highest occupied molecular orbital):

The accommodation of electrons at the highest-energy molecular orbitals is known as HOMO.

LUMO:

The lowest-energy of molecular orbitals that do not contain electrons are known as LUMO.

(g)

Interpretation Introduction

Interpretation:

• The number of nodes present in the highest energy MO has to be predicted.

Concept Introduction:

Molecular orbitals:

Linear combination of atomic orbitals leads to the formation of molecular orbital; the number of molecular orbitals produced are equal to the number of atomic orbitals involved.

HOMO (Highest occupied molecular orbital):

The accommodation of electrons at the highest-energy molecular orbitals is known as HOMO.

LUMO:

The lowest-energy of molecular orbitals that do not contain electrons is known as LUMO.

Node: The absence of electron; which means the probability of electrons is zero.