Woodward-Hoffman Sigmatropic Shift Nomenclature
Sigmatropic rearrangements are concisely described by an order term , which is defined as the migration of a σ-bond adjacent to one or more π systems to a new position (i-1) and (j-1) atoms removed from the original location of the σ-bond. When the sum of i and j is an even number, this is an indication of the involvement of a neutral, all C atom chain. An odd number is an indication of the involvement of a charged C atom or of a heteroatom lone pair replacing a CC double bond. Thus, and shifts become and shifts with heteroatoms, while preserving symmetry considerations. Hydrogens are omitted in the third example for clarity.
A convenient means of determining the order of a given sigmatropic rearrangement is to number the atoms of the bond being broken as atom 1, and then count the atoms in each direction from the broken bond to the atoms that form the new σ-bond in the product, numbering consecutively. The numbers that correspond to the atoms forming the new bond are then separated by a comma and placed within brackets to create the sigmatropic reaction order descriptor.
In the case of hydrogen atom migrations, a similar technique may be applied. When determining the order of a sigmatropic shift involving a hydrogen atom migration it is critical to count across all atoms involved in the reaction rather than only across the closest atoms. For example, the following hydrogen atom migration is of order, attained by counting counterclockwise through the π system, rather than the order designation through the ring CH2 group that would mistakenly result if counted clockwise.
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