Maximally valent orbitals in systems with non-ideal bond-angles: atomic Wannier orbitals guided by the Mayer bond...

In pursuit of a directed minimal set of basis for systems with non-ideal bond angles, in this work we find the exact orientation of the major overlapping orbitals along the nearest neighbouring coordination segments in a given system such that they maximally represent the covalent interactions throughout the system. We compute Mayer's bond order, akin to Wiberg's bond index, on the basis of atomic Wannier orbitals with customizable non-degenerate hybridization leading to variable orientations, constructed from first principles, in a representative variety of molecules and layered systems. We put such orbitals in perspective with unbiased maximally localized descriptions of bonding and non-bonding orbitals, and energetics to tunneling of electrons through them between nearest neighbours, to describe the different physical aspects of covalent interactions, which are not necessarily represented using a single unique set of atomic or bonding orbitals.