Is a Pseudo-Wavefunction Really a Mixed State?

[Modey3]

Hello,

I'm studying pseudopotentials right now, and I had an epiphany that the pseudo-wavefunction is really mixed-state of the original Hamiltonian. Has anyone ever thought about a pseudo-wavefunction that way? Just curious.

modey3

 

[kanato]

I'm don't think that's correct. Pseudopotentials remove nodes that are near the core, so a pseudopotential for Nb (say) will have 4d valence states, however the 4d states will not have a node near the core so they really will look like 3d states. I don't think you can accomplish elimination of a node by mixing states with n > 4.

 

[Modey3]

kanato,

If you take the overlap integral between the pseduo-wavefunction and a particular all-electron valence and the core wavefunctions you get non-zero terms. This means that the pseudo wavefunction can be represented as a sum of core-states and the valence states each scaled by their overlaps with the pseduo-wavefunction. The OPW-method does this.

 

[kanato]

Sure, there's non-zero overlap, but I am unconvinced as to whether the all-electron basis is "complete enough" to represent the pseudo-wavefunction.