Kohn-Sham DFT is used for a fictitious system of non-interacting particles.59 Several methods have been tested and developed to model the exchange-correlation energy. The most straightforward approach is the local spin density (LSD), and it yields enough accuracy for equilibrium geometries, lattice constants, vibrational frequencies, and bulk moduli . The generalised gradient approximation (GGA) can explain energy barriers, structural energy differences, and total energies rather than LSD. Semiempirical GGA's are incredibly suitable for small molecules, yet they cannot be used to delocalize the uniform gas or model electrons in metals . The Perdew-Burke-Ernzerhof (PBE) function for exchange-energy correlation is a member of the generalised gradient approximation (GGA) .