[Q-e-developers] Divergence in PAW UPF

[Andrea Dal Corso]

On Mon, 2016-05-16 at 11:34 +0200, Anton Kozhevnikov wrote: 
> Dear Lorenzo!
> Can you please clarify this statement: "scattering states are not
> normalizable: they always diverge". Are the scattering states differ from
> the unbound states (i.e. plane waves), which are also not normalizable, but
> at least they don't diverge? The scattering states in the UPF files have a
> value of ~10^8 at the end of the radial grid. What's the physics behind the
> states with psi(r)->infinity for r->infinity?
> 

The integration routine computes the scattering states starting from the
origin and integrating outward at the chosen energy. The scattering
state at large r should go as e^{+- \sqrt{-2.0 energy}r} in a.u..
So for positive energies it goes as a plane wave, for negative energies
it diverges except at the eigenvalues for which the diverging
exponential has zero coefficient. 

The important ingredient for the PP generation is the scattering state
before the core radius and this is accurately calculated, while no
effort is done in the atomic code to integrate accurately the scattering
state at large r. This is a quantity that is not used in the PP
generation.

HTH,

Andrea

> With kind regards,
> Anton.
> 
> 
> 
> On Fri, May 13, 2016 at 4:34 PM, Lorenzo Paulatto <
> lorenzo.paulatto at impmc.upmc.fr> wrote:
> 
> > Dear Ilia,
> > when constructing a pseudopotential with multiple projectros, be it PAW,
> > US or
> > normconserving, you build the second projector over a scattering state
> > (which
> > we usually just call wavefunction, for simplicity) of the isolated atom
> > hamiltonian. A scattering state solves the usual Sschroedinger equation:
> > H\psi = e \psi
> > for an energy e which is not an eigenstate of H.
> >
> > Scattering states are not normalizable: they always diverge. The only
> > special
> > thing about PAW, is that these states are solved in the UPF files, while
> > for US
> > and NC they are not.
> >
> > In PAW we rely on the fact the pseudo and all-electron wavefunctions/
> > scattering state are identical after a certain radius, hence instead of
> > integrating up to infinity we stop at the cutoff radius.
> >
> > I see no solution for your problem, I' afraid you'll have to review your
> > definition of the Dij matrix.
> >
> > kind regards
> >
> >
> > On Friday, 13 May 2016 14:49:10 CEST Ilia Sivkov wrote:
> > > Dear All,
> > >
> > > Recently I started to dig a code of Quantum Espresso to compare it with
> > > the developed in our group and found that many PAW UPF files have
> > > divergence in AE and PS radial wave functions. I found that it appears
> > > mostly in 4th P-orbital. Here I post two plots with these AE radial
> > > functions for V and Cu
> > >
> > > Looking at the other files I found such problem in each of them. It
> > > seems that all PAW UPF files have such divergence.
> > >
> > > Interesting point, that Quantum Espresso gives no bad values in density
> > > (variable "rho_lm") and potential (hartree, xc, total), but variable
> > > "pfunc" has such divergense.
> > >
> > > Due to these divergences our developing code gives bad values in Dij
> > > matrix, because it is calculated in a little bit different way.
> > >
> > > I would be very appreciated if you could help me to explain such strange
> > > behavior.
> > >
> > > With best regards,
> > > Ilia Sivkov
> >
> >
> > --
> > Dr. Lorenzo Paulatto
> > IdR @ IMPMC -- CNRS & Université Paris 6
> > +33 (0)1 44 275 084 / skype: paulatz
> > http://www.impmc.upmc.fr/~paulatto/
> > 23-24/4é16 Boîte courrier 115,
> > 4 place Jussieu 75252 Paris Cédex 05
> >
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> >
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-- 
Andrea Dal Corso                    Tel. 0039-040-3787428
SISSA, Via Bonomea 265              Fax. 0039-040-3787249
I-34136 Trieste (Italy)             e-mail: dalcorso at sissa.it