https://doi.org/10.1351/goldbook.08157
Feature of a concerted transformation in which the primary changes in bonding occur within a cyclic array of atoms but in which two nonbonding atomic orbitals on an atom interchange roles with two bonding orbitals.
Example: Epoxidation with dimethyldioxirane

Note: Because the atomic orbitals that interchange roles are orthogonal, such a reaction does not proceed through a fully conjugated transition state and is thus not a pericyclic reaction. It is therefore not governed by the rules that express orbital symmetry restrictions applicable to pericyclic reactions.