Here, 𝐾 𝑥 and 𝐾 𝑦 are exchange operators, 𝐸(𝜙 S ) and 𝐸(𝜙 T ) are the energies of the singlet and triplet excited determinants, while 𝐸(𝜙 1 S ), 𝐸(𝜙 1 T ) and 𝐸(𝜙 2 T ) are the energies of doubly excited determinants. They can be written in terms of the corresponding orbital energies, 𝜖 𝑖 , provided the same orbitals are used for both the singlet and triplet states. 47