where ϵ σ l and f σ l are the atomic eigenvalues and occupation numbers of spin σ. This energy is obtained by variation of the total energy with respect to the MO coefficients using the Hamiltonian, in which µ ∈ A and ν ∈ B and have angular momentum l and l ′ respectively, and the plus and minus sign are for σ = α and σ = β respectively. The α and β Hamiltonians can be later used to define the standard unrestricted, restricted-openshell or constrained unrestricted procedures for defining the secular equation and obtaining the molecular orbital coefficients.