where -∇ 2 2 is the one-electron kinetic energy operator, while υ I,σ KS ( r ) and υ I,σ emb ( r ) are the one-electron KS and embedding potential, respectively. The superscript I denotes the subsystem under study and σ = α or β are used as spin labels. The charge-localized states Φ 1 and Φ 2 are then constructed as direct products ,