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Maximally valent orbitals in systems with non-ideal bond-angles

In pursuit of a minimal basis for systems with non-ideal bond angles, in this work we try to pinpoint 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 through out the system. We compute Mayer's bond order, akin to the Wiberg's bond index, in the basis of atomic Wannier orbitals with customizable non-degenerate hybridization constructed from first principles, in a representative variety of molecules and layered systems. We put them 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 by a single unique set of atomic or bonding orbitals.