Theoretical Background

The Perdew-Zunger self-interaction correction (PZSIC) is a computationally demanding task. The FLOSIC method attempts to alleviate this computational complexity by parametrizing canonical (KS) orbitals into Fermi orbitals (FOs),

\[F_{i \sigma}(\vec{r})=\frac{\sum_\alpha \psi_{\alpha \sigma}^*\left(\vec{a}_{i \sigma}\right) \psi_{\alpha \sigma}(\vec{r})}{\sqrt{\sum_\alpha\left|\psi_{\alpha \sigma}\left(\vec{a}_{i \sigma}\right)\right|^2}} .\]

where the \(\vec{a}_{i \sigma}\) are the Fermi-orbital descriptors (FODs). The optimal positions are found by minimizing the FOD forces,

\[\frac{d E^{S I C}}{d a_m}=\sum_{k l} \varepsilon_{k l}^k\left\{\left\langle\frac{d \phi_k}{d a_m} \mid \phi_l\right\rangle-\left\langle\frac{d \phi_l}{d a_m} \mid \phi_k\right\rangle\right\} .\]

You can check this paper to learn more about FO derivatives