# Can one infer that covalent bonds are directional from the band structure?

I've recently learnt about Wannier functions and changing basis from wave-like 'Bloch functions' to seemingly more localised 'Wannier functions' and how one can think of electrons equally as delocalised waves in solids or as in more localised bonds.

To complete these equality, I was wondering if there is any obvious in the band structure of a covalent substance that causes the Wannier functions to be so directional like covalent bonds are?

There is no direct correlation between the band structure of a covalent material and the directional character of the corresponding Wannier functions. The reason is quite general. There is no direct relation between the spectrum of the eigenvalues and the spatial properties of the eigenfunctions. The only thing which is possible to establish easily is how much the band structure differs from that of a free electron gas. However, it is enough to have a look at the band structure of a few insulators, semiconductors, $$s-p$$-bonded, and transition metals, to realize how difficult may be to establish a robust connection between band structure and spatial properties of wavefunctions, Wannier functions included.