Level-shifting was initially introduced by Saunders and Hillier to address oscillatory SCF iterations caused by rapid mixing between the occupied (occ.) and virtual (virt.) space. The algorithm shifts up the virtual-space diagonal elements of the Hamiltonian represented in the previous iteration's MO basis by a constant value λ (typically around 0.2 Hartree), and therefore limits vigorous occupied-virtual mixture upon diagonalization, making the SCF iterations more stable. Mathematically, level-shifting for a closed-shell molecule can be expressed as: