# DOS preserving transform

1. Jul 14, 2014

### rigetFrog

To calculate the DOS of a material, the electronic structure typically needs to be calculated first. This requires lots of expertise and the accuracy is questionable.

I'm interested in seeing if there's some shortcut to get some general properties of the DOS:

If I could arbitrarily deform the crystal lattice while preserving the ionic charge density (I can also magically change ionic charge to preserve change density), are there any general statements I could say about the final DOS?

I would like to say the cumulative DOS calculated by integrating from -infinity to a specific energy 'E' would be invariant.

2. Jul 14, 2014

### Dr Transport

I am not aware of any way to calculate the DOS without prior knowledge of the electronic states and I do not think it can be done in the manner you are suggesting.

3. Jul 14, 2014

### rigetFrog

Ok, how bout this.

If we increase the crystal lattice constant, and preserve the ionic charge density (by magically changing the proton and electron charge), then I assert that the density of states would not change. (I'm using units of #states/dE, not #states/(dE*m^3))

Do you agree?

4. Jul 14, 2014

### Dr Transport

Still doesn't seem right, from over 20 years in condensed matter theory, I've never seen the DOS calculated in any other way than using the electronic states via the band structure, matter a fact, that is how it is defined.

5. Jul 14, 2014

### rigetFrog

Ok. I can prove it now.

You've seen that picture plotting the D(E) vs lattice constant, 'a', for the different bands. It shows hows the partial D(E) goes from very sharp at large lattice constant to very broad at small lattice constants.

This process is described by continually splitting of narrow atomic states. No new states are created with decreasing 'a'. Rather, existing degenerate states are split. As long as you're below the upper edge of the band, the total number of states below that energy doesn't change. QED.

Now, any thoughts if I can use this to simplify D(E) calculations?
Can this thought process be generalized to formation of surface states?

(I'm a ~10 year experimentalist whose job description forbids using WIEN2k and am forced to slave away in a lab under threat of lashes. So I spend time dreaming about alternative approaches to the forbidden theory.)