Chapter 28.2, Problem 2P

(a)

Interpretation Introduction

Interpretation: Bonding and anti-bonding molecular orbitals has to be determined for the molecular orbitals of $\text{1,3,5-hexatriene}$.

Concept introduction:

Molecular orbital theory suggests that atomic orbitals of different atoms combines to create molecular orbitals.

Molecular orbitals can be constructed from linear combination of atomic orbitals.

Bonding orbotals are formed by the additive combination of atomic orbitals and the antibonding orbitals are formed by the substractive combination of atomic orbitals.

Antibonding orbital is a molecular orbital that results when two parallel atomic orbitals with opposite phases interact.

Antibonding orbitals have higher energy than the bonding molecular orbitals.

HOMO is a molecular orbital which is the abbrevation of Highest Occupied Molecular Orbital.

LUMO is also a molecular orbital which is the short form of Lowest Unoccupied Molecular Orbital.

If the lobes at the ends of the MO are in phase, then the MO is symmetric.

If the two lobes are out phase then the MO is antisymmetric.

(b)

Interpretation Introduction

Interpretation: HOMO and LUMO molecular orbitals in the ground state has to be determined for the molecular orbitals of $\text{1,3,5-hexatriene}$.

Concept introduction:

Molecular orbital theory suggests that atomic orbitals of different atoms combines to create molecular orbitals.

Molecular orbitals can be constructed from linear combination of atomic orbitals.

Bonding orbotals are formed by the additive combination of atomic orbitals and the antibonding orbitals are formed by the substractive combination of atomic orbitals.

Antibonding orbital is a molecular orbital that results when two parallel atomic orbitals with opposite phases interact.

Antibonding orbitals have higher energy than the bonding molecular orbitals.

Ground state and and exited states are the positions with lower and higher energy respectively.

HOMO is a molecular orbital which is the abbrevation of Highest Occupied Molecular Orbital.

LUMO is also a molecular orbital which is the short form of Lowest Unoccupied Molecular Orbital.

If the lobes at the ends of the MO are in phase, then the MO is symmetric.

If the two lobes are out phase then the MO is antisymmetric.

(c)

Interpretation Introduction

Interpretation: HOMO and LUMO molecular orbitals in the existed state has to be determined for the molecular orbitals of $\text{1,3,5-hexatriene}$.

Concept introduction:

Molecular orbital theory suggests that atomic orbitals of different atoms combines to create molecular orbitals.

Molecular orbitals can be constructed from linear combination of atomic orbitals.

Bonding orbotals are formed by the additive combination of atomic orbitals and the antibonding orbitals are formed by the substractive combination of atomic orbitals.

Antibonding orbital is a molecular orbital that results when two parallel atomic orbitals with opposite phases interact.

Antibonding orbitals have higher energy than the bonding molecular orbitals.

Ground state and and exited states are the positions with lower and higher energy respectively.

HOMO is a molecular orbital which is the abbrevation of Highest Occupied Molecular Orbital.

LUMO is also a molecular orbital which is the short form of Lowest Unoccupied Molecular Orbital.

If the lobes at the ends of the MO are in phase, then the MO is symmetric.

If the two lobes are out phase then the MO is antisymmetric.

(d)

Interpretation Introduction

Interpretation: Symmetric and anti-symmetric MOs has to be determined for the molecular orbitals of $\text{1,3,5-hexatriene}$.

Concept introduction:

Molecular orbital theory suggests that atomic orbitals of different atoms combines to create molecular orbitals.

Molecular orbitals can be constructed from linear combination of atomic orbitals.

Bonding orbotals are formed by the additive combination of atomic orbitals and the antibonding orbitals are formed by the substractive combination of atomic orbitals.

Antibonding orbital is a molecular orbital that results when two parallel atomic orbitals with opposite phases interact.

Antibonding orbitals have higher energy than the bonding molecular orbitals.

Ground state and and exited states are the positions with lower and higher energy respectively.

HOMO is a molecular orbital which is the abbrevation of Highest Occupied Molecular Orbital.

LUMO is also a molecular orbital which is the short form of Lowest Unoccupied Molecular Orbital.

If the lobes at the ends of the MO are in phase, then the MO is symmetric.

If the two lobes are out phase then the MO is antisymmetric.

(e)

Interpretation Introduction

Interpretation: The relationship between HOMO and LUMO and symmetric and antisymmetric molecular orbitals has to be determined.

Concept introduction:

Molecular orbital theory suggests that atomic orbitals of different atoms combines to create molecular orbitals.

Molecular orbitals can be constructed from linear combination of atomic orbitals.

Bonding orbotals are formed by the additive combination of atomic orbitals and the antibonding orbitals are formed by the substractive combination of atomic orbitals.

Antibonding orbital is a molecular orbital that results when two parallel atomic orbitals with opposite phases interact.

Antibonding orbitals have higher energy than the bonding molecular orbitals.

Ground state and and exited states are the positions with lower and higher energy respectively.

HOMO is a molecular orbital which is the abbrevation of Highest Occupied Molecular Orbital.

LUMO is also a molecular orbital which is the short form of Lowest Unoccupied Molecular Orbital.

If the lobes at the ends of the MO are in phase, then the MO is symmetric.

If the two lobes are out phase then the MO is antisymmetric.