ABINIT Discussion Forums

Hi,
I'm unclear about a small detail in the PAW formalism. As far as I'm concerned the compensation charge \hat{n} is introduced because of a loss of norm during the pseudization process of the wave function. I still can't figure what the details of this norm loss are and how this comes out of the equations. Can anybody give me a hint or refer to some source?
Thank you in advance!

Maxi45

The real experts should correct me if I get this wrong, but here is my understanding--the loss of norm conservation happens in the PAW construction process, basically taking advantage of the fact (just as in ultrasoft pseudopotentials) that it is possible to make much softer pseudopotentials if basis wavefunctions are required only to satisfy a generalized norm condition <phi_i|S|phi_j> = d_ij. This leads to more computational overhead but it is more than offset by the lower energy cutoff required. In this feature, PAW and ultrasoft are very similar. Beyond this, though, the PAW formalism introduces the nhat charge density, which is not physical and is added and subtracted appropriately, and is constructed to ensure that the on-site (that is, within PAW sphere) charge densities between different spheres have no coulomb interaction with each other.

Thank you for the reply. This defininately gives me a hint in the right direction!