Bloch Theorem and the Crystal Orbitals

The quantum molecular model under Hiickel approximation is quite general as to allow the enlargement of the discourse from molecules to the crystalline orbitals the present discussion follows (Putz, 2006) 

Firstly, on can formulate the situation of the linear polyenes of type fo which, the string of identical and periodical atoms forms a periodical fiend of nuclei, as protot5q)e for a reticular arrangement (on one line only) of the atoms, as structural points, in a crystal. 

Accordingly, the Hiickel model applied for the general case of the (quasi) linear molecules will produce the orbital eigen-energies with the dependence (Putz, 2006)  

The Eq. (3.16) allows further generalization for molecules with an infinite number of atoms linearly arranged as in a reticular string, or a crystallographic direction in a solid body. 

Quantum Nanochemistry—Volume IV Quantum Solids and Orderability 

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