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. Comments anyone?