[Pw_forum] Semicore states and Spin-orbit coupling

Nicola Marzari nicola.marzari at materials.ox.ac.uk
Thu Feb 24 04:38:44 CET 2011

Dear Paul,

> 1.) What kind of influence a semicore state in the pseudopotential has on the calculation.  I found some general information of
>         the comparison of norm-conserving and non norm-conserving (ultrasoft) pseudopotentials but I don't find any good
>         written description of the influence of semicore states. Which properties are altered the
>         most if using semicore states and what are the advantages and disadvantages?

in general you can have semicore states both in the norm-conserving
(nc) and ultrasoft approaches (us). The only disadvantage of including
them is the additional computational cost (more electrons, and more
structured orbitals that require a higher cutoff). sometimes the
"non-linear core correction" can be used (e.g. in group I/II) to account
for core/valance overlap - see the 1982 Louie PRB, or

Let's take Fe: 4s2 3d6 are the valence, while 3s2 3p6 are the semicore.
8-electron pseudos are probably good to describe metallic iron, but not
much else - but only a comparison of calculations done with or without
semicore can tell you if they are needed (if they make a difference, 
they are needed).

Adding 3p6 (at the cost of 6 more electrons) is probably a very good 
thing, while adding 3s2 (although customarily done) probably doesn't 
help that much (they are too low in energy). A critical difference here
emerges between us and nc pseudo - nc pseudo have one projector
per angular momentum, while us have typically two - hence if you use the
3s semi-core, with us you can have a s projector at 3s energies, and a
s projector at 4s energies, while with nc you are forced to have one
projector that acts in the same way on the 3s and 4s (a bad idea - 
better to drop the 3s back in the core).

> 2.) Since the systems I have to deal with contain heavy elements the question arises what kind of influence the spin orbit
>        coupling has on structural and electronic properties. I found one paper and the two corresponding potentials for gold
>        and platinum which incorporate a full relativistic treatment and enable a calculation including spin-orbit coupling for
>        the LDA functional. Perhaps I havn't found the example of tutorial but is there a general procedure to incorporate
>        SO effects on a GGA or a meta-GGA level yet?

I'd look at Andrea Dal Corso papers on phonons - probably the effects on 
structural properties are small, and on electronic properties, ahem,
relevant for all properties that are not there without spin-orbit :-).

Do keep in mind, though, that the pseudopotentials themselves have been 
generated with a relativistic calculation for the all electron atom, so
a lot of the key effects have been captured there already.
> A third question is dealing with the density cutoff.
> 3.) In the QEwiki is written that a higher density cutoff should be used in the case of ultrasoft pseudopotentials and it should
>         be checked that all setting have converged. I have done some calculations and changed first of all the Ecutoff and after
>         that the Rhocutoff from four to ten times the Ecutoff. There was no big influence of the Rhocutoff on the structure and energy
>         in my particular case. Just to avoid a problem in the future. What properties are altered the most by using a insufficent Rhocutoff?

Best way to think at this is not that a higher density cutoff is needed
(density cutoff is fixed by the true physics of the charge density),
but a lowe wavefunction cutoff can be used. The end result is the same.
8 times is a good ballpark, and 6 to 12 the common range. Of course, if 
your Ecutoff is very high, then 4 will work - but the point is that you
want to use for both the minimum value that is sufficient.

A good check can be optical phonons - do them with energy cutoffs of
10-12-14....-38-40 Ry, using a rhocutoff of 4, 6, 8, 12 times ,
and compare these curves.


> Best wishes
> Paul

Prof Nicola Marzari    Department of Materials    University of Oxford
Chair of Materials Modelling  Director, Materials Modelling Laboratory
nicola.marzari at materials.ox.ac.uk     http://mml.materials.ox.ac.uk/NM

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