Symmetry, Bonding, and Wannier Function Construction in the PF− 6 Molecule: A First-Principles Case Study

Paul M. Masanja^1*Esther J. Tarimo¹P.V. Kanaka Rao¹Vijay Singh¹Bernard Mwankemwa¹Javier Junquera²

• ¹The University of Dodoma, Dodoma, Tanzania
• ²Universidad de Cantabria, Santander, Spain

We present a comprehensive analysis of the electronic structure of the PF6−anion, a prototypical octahedral molecular system with high Oh symmetry. Using symmetry-adapted linear combinations of atomic orbitals and group theoretical techniques, we construct molecular orbitals and provide a systematic classification according to irreducible representations of the Oh point group. The role of the P-centered 3s, 3p, and 3d orbitals, together with the symmetry-adapted 2s and 2p orbitals of the six surrounding fluorine atoms, is explicitly analyzed. The electronic structure is described both within the theory of molecular orbitals and with the picture based on sp3d2 hybridization. Maximally localized Wannier functions derived from first-principles density functional theory calculations using the siesta and wannier90 codes are computed. The constructed Wannier functions accurately reflect the expected molecular symmetries and provide a natural minimal basis for tight-binding and second-principles modeling. A detailed comparison is made between bonding, nonbonding, and antibonding orbitals, as well as their energetic ordering. Our results demonstrate the interplay between symmetry, bonding, and electronic structure in molecular systems with high cubic symmetry and set the stage for the development of accurate minimal models for such systems.