text: A [4+2] cycloaddition is exemplified by the Diels-Alder reaction.  The simplest case is the reaction of 1,3-butadiene with ethylene to form cyclohexene.
  One symmetry element is conserved in this transformation – the mirror plane through the center of the reactants as shown to the left.  The molecular orbitals of the reactants are the set {Ψ, Ψ, Ψ, Ψ} of molecular orbitals of 1,3-butadiene shown above, along with π and π of ethylene.  Ψ is symmetric, Ψ is antisymmetric, Ψ is symmetric, and Ψ is antisymmetric with respect to the mirror plane.  Similarly π is symmetric and π is antisymmetric with respect to the mirror plane.
  The molecular orbitals of the product are the symmetric and antisymmetric combinations of the two newly formed σ and σ bonds and the π and π bonds as shown below.
  Correlating the pairs of orbitals in the starting materials and product of the same symmetry and increasing energy gives the correlation diagram to the right.  As this transforms the ground state bonding molecular orbitals of the starting materials into the ground state bonding orbitals of the product in a symmetry conservative manner this is predicted to not have the great energetic barrier present in the ground state [2+2] reaction above.
  To make the analysis precise, one can construct the state correlation diagram for the general [4+2]-cycloaddition.  As before, the ground state is the electronic state depicted in the molecular orbital correlation diagram to the right.  This can be described as ΨπΨ, of total symmetry SS
  A=S.  This correlates with the ground state of the cyclohexene σσπ which is also SSA=S.  As such this ground state reaction is not predicted to have a high symmetry-imposed barrier.
  One can also construct the excited-state correlations as is done above.  Here, there is a high energetic barrier to a photo-induced Diels-Alder reaction under a suprafacial-suprafacial bond topology due to the avoided crossing shown below.