where E k l = a † kα a lα + a † kβ a lβ is the spin-free unitary group generator and v ln km denotes the 4-center Coulomb integral expressed in the molecular orbital basis. From now on the labels k,l(m,n) stand for orbitals of A (B) monomer, α(β) labels denote occupied spinorbitals, while ρ(σ) denote virtual spinorbitals of monomer A (B, respectively). Let us now define the following operator, acting in the Hilbert space