Outline of the electronic-structure solution in a one-dimensional world

2 Outline of the electronic-structure solution in a one-dimensional world 

The solution of the H atom problem of Chapter 1 provides us with the concept of atomic orbitals. Its extension provides a model for the electronic structure of the heavier atoms which can be developed into an MO model for molecules. Molecular orbitals formed from linear combinations of the same AOs provide a serviceable conceptual model for the electronic structures of molecules. The same AOs provide an approach to the electronic structure of extended systems with periodic geometric structures. It is useful because it avoids the nightmare of 1023 MOs dreamed above. 

1 Crystal orbitals (COs) vs. molecular orbitals (MOs) the example of the H chain 

As emphasized in Section 6.1, to model bulk properties a crystallite must be large enough so that bulk properties dominate over surface properties. So too the H-atom chain here must be long enough so the effects of the two end atoms are 

fine you say. So far we are treating the extended chain like a giant molecule and we are still stuck with drawing in 1023 levels for a mole of H atoms. In the manner of Hoffmann, we would like to have a detailed and informative model that we can use in discussions of the electronic properties of solids without dealing explicitly with all these levels. In addition, we want to emphasize connections between clusters (molecules) and extended systems (solid state). So let s dig around in this band a little bit more and see if we can eliminate the necessity of talking about 1023 orbitals in order to discuss and rationalize properties of extended systems. 

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