Molecular orbitals of linear polyenes

an array of p-orbitals Schematic, qualitatively correct π molecular orbitals can be easily generated from a linear array of n p atomic orbitals by following a few simple rules.
  1. The lowest-energy MO always has all p orbitals in phase, making it symmetric with respect to end-for-end reflection:
    an array of in-phase p-orbitals
    This MO has no "vertical" nodes, that is, points along the chain at which neighboring p-orbitals are out of phase.
  2. asymmetric MO of ethylene, and the result of end-for-end reflection
    The next MO has a single vertical node, and one half of the MO is the "anti-mirror image" of the other half; that is, the MO is antisymmetric with respect to end-for-end reflection. An example is the π* MO of ethylene, shown above.
  3. symmetric antibonding MO of butadiene
    The third MO has two vertical nodes, and is symmetric. To find the position of the vertical nodes, remember that half of the p-orbitals need to reflect the other half. An example is the third MO of butadiene, shown above.
  4. Molecular orbitals continue to add vertical nodes and alternate symmetric/antisymmetric until the highest-energy MO is reached, which has a vertical node between each atom. When combining n p orbitals, the highest-energy π MO will have n-1 vertical nodes.

Some examples of π MO diagrams are linked below. "S" is "symmetric", "A" is "antisymmetric" to end-for-end reflection (useful for thinking about disrotatory pericylic processes). Symmetries with respect to 180° rotation (useful for thinking about conrotatory processes) are the opposite.

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