3a. In Molecular orbital (MO) theory, for a pentadienyl cation in strong acid, which of the three lowest orbitals is the HOMO and which the LUMO?
3b. A pentadienyl cation is really a delocalized carbocation readily attacked by nucleophiles in an SN1-type process. Which Carbon atoms of the pentadienyl cation (# 1, 2, 3, 4 and/or 5) would the nucleophile attack?
HINT: A nucleophile will always attack the LUMO; it cannot attack the HOMO because the HOMO is filled.
[Please see attached image for question Number 3 and related diagrams.]
Molecular orbital theory treats electrons in molecular structure as moving under the influence of the nuclei of the entire molecule. In sigma covalent bonds, the bonding interaction is between discrete atoms. Conversely, pi bonds can be formed between overlapping orbitals of like symmetries to create multiple bonds. Pi bonds are different from sigma bonds in that, while sigma bonds are between atoms situated between the bonding molecules' nuclei, pi bonds are delocalized in regions above and below the nuclei of the bonding molecules.
Quantum mechanics fixes electrons in atoms to form orbitals that contain these electrons. Molecular orbitals--which are different from atomic orbitals--contain valence electrons between atoms since molecular orbitals surround a number of atoms in a molecule. Molecular orbital theory approximates the positions of the molecular orbitals, which are the bonded electrons. In MO theory, electrons are no longer deterministically are given defined coordinates but the application of wavelike behavior of electrons allows probable locations (delocalized locations) according to the mathematical wavefunctions defining all the possible positions of the electrons. These wavefunctions are called electron eigenstates and they quantitatively describe the atomic orbital basis in which an electron can temporarily reside ("Molecular Orbital Theory," Wikipedia).
A molecular orbital diagram displays the "resulting molecular orbitals stemming from atomic interaction based on their relative energies and assigns bonding, nonbonding and/or antibonding character to each molecular orbital" (Wikipedia). The HOMO is the Highest Occupied Molecular Orbital, and the LUMO is the Lowest Unoccupied Molecular Orbital. A significant difference between HOMO and LUMO is that the HOMO is occupied and contains electrons while the LUMO is unoccupied and contains no electrons. The HOMO and LUMO are determined from the values assigned resulting from a molecular orbital diagram. HOMOs and LUMOs are also called frontier orbitals. Nucleophiles are a chemical species that contribute electrons in chemical bonding reactions. LUMOs may react with nucleophiles by accepting an electron pair from the nucleophile.