[Pw_forum] Semicore states and Spin-orbit coupling

W2AGZ w2agz at w2agz.com
Fri Feb 25 05:57:24 CET 2011

To All:

I noted the thorough and extensive response by Nicola to the subject
question.  Where were professors like him when I was a graduate student?
Speaking of which...

Many, many, many...years ago, while I was a PhD candidate in the group of
Harvey Brooks and Bill Paul at Harvard, a burning question at the time was,
"What's the energy gap of grey tin (the diamond structure of Sn)?"  It was
thought tin could not be made pure enough so that it could be detected
optically or through transport.  Bill and his student, Steve Groves
(deceased about four years ago), came up with the brilliant idea that the
"conduction band" might "sink" below the valence band (the reversal from Si
and Ge), and thus, by "k dot p" perturbation, undergo a "reflection of the
upper branch" of the lower s-p split valence band, resulting in a "zero-gap"
band gap with Ef passing through the gamma point degeneracy.  It is now
known as the "Groves-Paul" model for the electronic structure of grey tin,
and is the forerunner of the now famous "Dirac singularity" in graphene.

So...for some time, I've wondered if, given the appopriate pseudopotential,
would quantum-espresso be able to yield the Groves-Paul bandstructure?
Alas, after a very cursory search, I've not been able to find an appropriate
PP which includes the required spin-orbit interaction...at least as far as I
can see from the two that are in the QE database.  I haven't looked further,
but is the QE community aware of such?  Does the ld1.x tool in QE provide
the necessary resource and ability, should I want to "make one?"

Sorry for the long post.  I think this exercise would provide a great class
lecture presentation or assignment.

Ciao, -Paul
IBM Research Staff Member Emeritus

-----Original Message-----
From: pw_forum-bounces at pwscf.org [mailto:pw_forum-bounces at pwscf.org] On
Behalf Of Nicola Marzari
Sent: Wednesday, February 23, 2011 7:39 PM
To: PWSCF Forum
Subject: Re: [Pw_forum] Semicore states and Spin-orbit coupling

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

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

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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