A symmetry-based, nondisplacive mechanism for the first-order B3 reversible arrow B1 phase transition exhibited by many binary semiconductors is proposed. Using a single-molecule R3m unit cell, the energetic and dynamical features of the transformation are disclosed along a transition path characterized by the internal coordinate, the lattice constant, and the rhombohedral angle. First-principles calculations on the wide-gap semiconductor ZnO are performed to illustrate the attainments of the proposed mechanism. Computed potential energy surfaces and Bader analysis of the electronic density are used to describe the atomic rearrangements, the energy profile along the transition coordinate, and the effects of the external pressure on this profile. The geometry and energy of the transition state are determined, and the bonding details of the transformation identified. The proposed mechanism explains the change in coordination from 4 (B3) to 6 (B1), the less covalent Zn-O bond in the B1 structure, and the transformation of ZnO from a direct-gap (B3) to an indirect-gap (B1) material.