The HOMO and LUMO for benzene each consists of degenerate sets of molecular orbitals shown below. Mix the both sets of degenerate r orbitals to generate a total of 8 new molecular orbitals for biphenyl Sketch and and nd label label each ea MO or with respect to to the he new bond formed as shown above. Number the MO ‘s derived from the benzene HOMO’s 3 through 6, and the ones from the LUMO’s 7 through 10. order of increasing energy. Identify the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) for biphenyl.
The Correct Answer and Explanation is :
iphenyl consists of two benzene rings connected by a single bond, allowing for conjugation between the rings.o understand the π molecular orbitals (MOs) of biphenyl, we can combine the π MOs of two benzene molecules.ach benzene molecule has six π MOs: three bonding (π₁, π₂, π₃) and three antibonding (π₄, π₅, π₆), with π₃ and π₄ being degenerate pairs.hen forming biphenyl, these MOs interact to produce new molecular orbitals.
y mixing the degenerate π₃ and π₄* orbitals from each benzene unit, we generate four new molecular orbitals for biphenyl.imilarly, mixing the degenerate π₅ and π₆* orbitals from each benzene unit produces another four molecular orbitals.his results in a total of eight new MOs derived from the degenerate orbitals of the benzene units.
abeling these MOs in order of increasing energy:
- MOs 3 and 4: erived from the in-phase and out-of-phase combinations of the π₃ orbitals of each benzene ring. These are bonding interactions concerning the new C-C bond between the rings.
- MOs 5 and 6: erived from the in-phase and out-of-phase combinations of the π₄* orbitals. These are antibonding interactions concerning the new C-C bond.
- MOs 7 and 8: erived from the in-phase and out-of-phase combinations of the π₅ orbitals. These are higher-energy bonding interactions.
- MOs 9 and 10: erived from the in-phase and out-of-phase combinations of the π₆* orbitals. These are higher-energy antibonding interactions.
n terms of energy ordering, MOs 3 and 4 are lower in energy due to bonding interactions, followed by MOs 5 and 6 (antibonding), then MOs 7 and 8 (higher-energy bonding), and finally MOs 9 and 10 (higher-energy antibonding).
he Highest Occupied Molecular Orbital (HOMO) for biphenyl is MO 6, while the Lowest Unoccupied Molecular Orbital (LUMO) is MO 7.he energy gap between these orbitals influences the chemical properties of biphenyl, including its electronic transitions and reactivity.
nderstanding the formation and energy ordering of these MOs provides insight into the electronic structure of biphenyl and its behavior in various chemical contexts.