The Fermi-Löwdin self-interaction correction for spin transition systems

(Semi)-local density functional approximations underestimate the magnitude of the highest-occupied orbital (HO) eigenvalue, thereby narrowing the HO-LU (lowest-occupied orbital) gap. This inaccuracy can be attributed to self-interaction error (SIE). For spin transition systems like Fe(II) compounds, which show a transition between a low-spin state (S = 0) and a high-spin state (S=2) at a critical temperature, this underestimation can be substantial [1,2], and leads to electron configurations with incorrect energy. In this work we have applied the Fermi-Löwdin self-interaction correction [3], as well as different many-body perturbation approximations, to investigate how SIE affects the transition.