Stereo chemistry
Note in the above suprafacial shift the new stereocentre has the same configuration as in the reactant.
Note in the above antarafacial shift the new stereocentre has the opposite configuration as in the reactant.
Sigmatropic alkyl shift
When a chiral alkyl group shifts there is an additional stereochemical feature to be considered. The shift can occur with retention or inversion in configuration at the migration centre.
[1,3]-suprafacial migration of the group proceeds with inversion in configuration at the stereo centre
[1,5]-suprafacial migration of the group proceeds with retention in configuration at the stereo centre.
Note: All these reactions including the stereochemistry can be explained using FMO theory.(Frontier Molecular Orbital theory)