Application of the Free-Electron Theory to Three-Dimensional Networks

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Abstract
The free‐electron network theory is generalized to permit its application to covalent and metallic crystals. General expressions for the case where the various branches of the network have different lengths and potentials are derived. Delta function discontinuities of potential at the junctions of the branches are introduced to describe the effective field acting on valence electrons. The general equations can be applied to various special cases, such as the Kronig and Penney potential or the behavior of π electrons in planar organic molecules. The free‐electron network theory is used to derive the energy band structure of diamond in the interpolation scheme proposed by Slater. Energy band features are in semiquantitative agreement with those obtained by other methods. Some discrepancies in the sequence of energy levels in different theories are pointed out. The discussion includes the possible application of the free‐electron network theory to more complicated crystals.

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