Bloch function of an infinite, 1-D linear chain of dz2 orbitals.

[Dekoy]

Homework Statement

Consider an infinite, one-dimensional linear chain of dz2 orbitals separated at a distance a. Write an expression of the BLOCH FUNCTION that describes this chain.

Homework Equations

ψk=Ʃexp(ikna)χn

The Attempt at a Solution

I read this http://onlinelibrary.wiley.com/doi/10.1002/anie.198708461/pdf and from here I gt the idea that the Bloch function should just be Ʃexp(ikna) times the radial part of the dz2 wavefunction but I don't think this is correct. Could anyone please explain how I can do this I've already looked all over the web and books and couldn't find anything.
Thank You.

 

[mark726]

Hello,

You are definitely on the right track with your understanding of the Bloch function in this scenario. The Bloch function for an infinite, one-dimensional linear chain of dz2 orbitals separated by a distance a can be written as:

ψk(x) = Ʃexp(ikna)χn(x)

Where χn(x) is the radial part of the dz2 wavefunction and n is the index for the individual orbitals in the chain. The term exp(ikna) represents the phase shift between neighboring orbitals and is dependent on the wavevector k and the distance between orbitals a.

One thing to note is that the Bloch function is a periodic function, meaning that it repeats itself every a units. This is due to the periodic nature of the lattice structure in this scenario.

I hope this helps clarify things for you. Good luck with your research!