Answer the following questions for the MOs of 1,3-butadiene:
d. Which MO is the HOMO and which is the LUMO in the excited state?
e. What is the relationship between the HOMO and the LUMO and symmetric and antisymmetric orbitals?

Verified step by step guidance

1. Identify the molecular orbitals (MOs) of 1,3-butadiene. There are four π molecular orbitals, which can be labeled as ψ1, ψ2, ψ3, and ψ4, in order of increasing energy.
2. Understand that in the ground state, the electrons fill the lowest energy MOs first. For 1,3-butadiene, there are four π electrons, which will fill ψ1 and ψ2, making ψ2 the highest occupied molecular orbital (HOMO) and ψ3 the lowest unoccupied molecular orbital (LUMO).
3. In the excited state, an electron is promoted from the HOMO to the LUMO. Therefore, in the excited state, ψ3 becomes the HOMO and ψ4 becomes the LUMO.
4. Recognize that molecular orbitals can be classified as symmetric or antisymmetric with respect to a plane of symmetry. Symmetric orbitals remain unchanged upon reflection, while antisymmetric orbitals change sign.
5. Determine the symmetry of the MOs: ψ1 and ψ3 are symmetric, while ψ2 and ψ4 are antisymmetric. In the excited state, the HOMO (ψ3) is symmetric, and the LUMO (ψ4) is antisymmetric.

Key Concepts

Molecular Orbitals (MOs)

Molecular orbitals are formed by the combination of atomic orbitals when atoms bond together. In 1,3-butadiene, the MOs can be classified as bonding, non-bonding, or antibonding. The highest occupied molecular orbital (HOMO) is the highest energy orbital that contains electrons, while the lowest unoccupied molecular orbital (LUMO) is the lowest energy orbital that does not contain electrons. Understanding these orbitals is crucial for predicting the electronic transitions in molecules.

HOMO and LUMO

The HOMO and LUMO play a critical role in determining a molecule's reactivity and electronic properties. The HOMO is the orbital from which an electron can be excited to the LUMO, which is essential for understanding processes like absorption of light and chemical reactions. In the excited state of 1,3-butadiene, the HOMO and LUMO can be identified based on their energy levels, influencing the molecule's behavior in various chemical contexts.

Symmetric and Antisymmetric Orbitals

Symmetric and antisymmetric orbitals refer to the spatial distribution of electron density in molecular orbitals. Symmetric orbitals have electron density that is evenly distributed around the molecular axis, while antisymmetric orbitals have a nodal plane where the electron density changes sign. The relationship between HOMO and LUMO can often be understood in terms of their symmetry properties, as transitions between these orbitals can be influenced by the symmetry of the molecular system.