Optimizing the Orbital Occupation in the Multiple Minima Problem of Magnetic Materials from the Metaheuristic Firefly Algorithm

We present the use and implementation of the firefly algorithm to help in scanning the multiple metastable minima of orbital occupations in Density Functional Theory (DFT) plus Hubbard $U$ correction and to identify the ground state occupations in strongly correlated materials. We show the application of this implementation with the Abinit code on KCoF$_3$ and UO$_2$ crystals, which are typical $d$ and $f$ electron systems with numerous occupation minima. We demonstrate the validity and performance the method by comparing with previous methodologies. The method is general and can be applied to any code using constrained occupation matrices.