  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.
