text: A general sigmatropic rearrangement can be classified as order [i,j], meaning that a σ bond originally between atoms denoted 1 and 1, adjacent to one or more π systems, is shifted to between atoms i and j.  Thus it migrates (i − 1), (j' − 1) atoms away from its original position.
  A formal symmetry analysis via correlation diagrams is of no use in the study of sigmatropic rearrangements as there are, in general, only symmetry elements present in the transition state.  Except in special cases (e.g. [3,3]-rearrangements), there are no symmetry elements that are conserved as the reaction coordinate is traversed.  Nevertheless, orbital correlations between starting materials and products can still be analyzed, and correlations of starting material orbitals with high energy product orbitals will, as usual, result in "symmetry-forbidden" processes.  However, an FMO based approach (or the Dewar-Zimmerman analysis) is more straightforward to apply.
  One of the most prevalent classes of sigmatropic shifts is classified as [1,j], where j is odd.  That means one terminus of the σ-bond migrates (j − 1) bonds away across a π-system while the other terminus does not migrate.  It is a reaction involving j + 1 electrons: j − 1 from the π-system and 2 from σ-bond.  Using FMO analysis, [1,j]-sigmatropic rearrangements are allowed if the transition state has constructive overlap between the migrating group and the accepting p orbital of the HOMO.  In [1,j]-sigmatropic rearrangements if j + 1 = 4n, then supra/antara is thermally allowed, and if j + 1 = 4n + 2, then supra/supra or antara/antara is thermally allowed.
  The other prevalent class of sigmatropic rearrangements are [3,3], notably the Cope and Claisen rearrangements.  Here, the constructive interactions must be between the HOMOs of the two allyl radical fragments in the transition state.  The ground state HOMO Ψ of the allyl fragment is shown below.  As the terminal p-orbitals are of opposite sign, this reaction can either take place in a supra/supra topology, or an antara/antara topology.
  The selection rules for an [i,j]-sigmatropic rearrangement are as follows:
  * For supra/supra or antara/antara [i,j]-sigmatropic shifts, if i + j = 4n + 2 they are thermally allowed and if i + j = 4n they are photochemically allowed
  * For supra/antara [i,j]-sigmatropic shifts, if i + j = 4n they are thermally allowed, and if i + j = 4n + 2 they are photochemically allowed
  This is summarized in the following table: