are used to compute molecular orbitals (MOs) ψ I,σ i ( r ) of subsystems A, B, A +• , and B +• as well as their energies I,σ i . In Eq. ( ), -∇ 2 2 is the one-electron kinetic energy operator, υ I,σ KS ( r ) is the one-electron KS potential, and υ I,σ emb ( r ) is the one-electron embedding potential. Subsystems are denoted by the superscript I, whereas σ = α or β are spin labels. Calculated MOs are used to construct Kohn-Sham determinants |A , |B , |A +• , and |B +• . The charge-localized states Φ 1 and Φ 2 are then obtained as direct products of these determinants such that