# [Wien] What is the E-cut

Jorissen Kevin Kevin.Jorissen at ua.ac.be
Sun Mar 20 01:57:59 CET 2005

```Sorry Saeid for repeating much you have already said, I'm just getting a bit confused here.

* Wien basically finds eigenstates of the Hamiltonian of the structure in your case.struct.
These eigenstates are expanded into a basis set (and we calculate the coefficients).  This basis set consists of (L)APW functions, which have a wave vector .  Your calculation will consider all (L)APW functions with a wave vector of magnitude less than kmax, where kmax equals RKM / (smallest muffin tin in the unit cell).  RKM is the number in the top of case.in1.  The number E_cut is basically the square of kmax.  There is no different cutoff for s, p, d ... functions.  Typical values for RKM (=RKmax) are 5-8.
In addition, we augment the basis with localized functions (the so-called local orbitals), which are attributed to particular states (s, p, ...) and have a particular 'energy', which may be different for each localized function, and has nothing to do with E_cut or kmax.
* The Hamiltonian has really a lot of solutions, and we don't need all of them.  We solve only for those states with eigenenergy in a particular window.  This window is the Emin and Emax that you find on the last line of case.in1.  It has nothing at all to do with the basis set.  (Except, of course, that your basis set should be able to describe the solutions you will get ;)).
If we do spin-orbit calculations, we first calculate all 'up' states (x lapw1 -up), then all 'down'-states (x lapw1 -dn), and then we mix them by introducing the spin-orbit interaction (x lapwso).  If we want to do this mixing correctly, we need some states that were unoccupied before mixing.  That's why the emax (upper limit of the energy window) has to be increased from the default 1.5 (which simply means : just above the Fermi level) to a (much) higher value.

* There is another cutoff in wien : the density (and the potential) are also expanded in plane-wave-like functions, and for these, too, a cutoff has to be defined.  This is the parameter Gmax on the bottom of case.in2.  Common sense requires that Gmax >= 2 * kmax (as density equals wave function squared).  Sometimes, we want an even better accuracy here (eg. to evaluate derivatives of the density correctly for GGA - that's why we always take gmax 14 or better for GGA calculations).

Perhaps I've been a bit too much time on too basic stuff here, but it's 2 am here and everything is slower at that hour of the night ;).

May I recommend the excellent manuscript by S. Cottenier that you will find on the regular users page of www.wien2k.at ?  (It describes how to estimate the number of basis functions before the calculation - afterwards it's easy, just do grep :RKM case.scf).
And of course the wien2k UG.

Kevin Jorissen

EMAT - Electron Microscopy for Materials Science   (http://webhost.ua.ac.be/emat/)
Dept. of Physics

UA - Universiteit Antwerpen
Groenenborgerlaan 171
B-2020 Antwerpen
Belgium

tel  +32 3 2653249
fax + 32 3 2653257
e-mail kevin.jorissen at ua.ac.be

________________________________

Van: wien-admin at zeus.theochem.tuwien.ac.at namens saeid jalali
Verzonden: za 19-3-2005 18:31
Aan: wien at zeus.theochem.tuwien.ac.at
Onderwerp: Re: [Wien] What is the E-cut

> You mean the E_cut is the Emax in case.in1?
Yes, exactly.
Indeed we are looking into the band structre of
material from [Emin, Emax] window, interval, energy.

> How do we know the number of basis functions from
> E_cut?

I am sure you must know that we can transform a
function from real space to momentum, wave vector, or
energy space and vice versa.

If you expand a wave function in terms of a complete
basis set in the energy space, then the expansion
coefficients, wave functions in energy space, will be
a function of energy, and the last coefficient will be
determined by the E_cut where you truncate the
expansion.

Your,
Saeid.

> Thanks
>
>
> >The E_cut as it comes from its name is a cut off
> for
> >energy to expand the wave functions.
> >In principle the number of Fourier expansion
> >coefficients must be infinite, however, in practice
> it
> >is impossible to sum numerically many numbers.
> >Thus numerically one needs to set essentially an
> >energy cut off to truncate the infinite sum
> somewhere
> >that the order of magnitude of the coefficients is
> >reducing so that adding the truncated coefficients
> >could not affect the result any more in our desired
> >accuracy.
> >For the most cases Fermi energy is less than 1Ry
> >(around 0.5Ry), so If you would not add spin-orbit
> >interaction 1.5 Ry could be a good choice for
> E_cut,
> >see the end of case.in1 file.
> >However, in the case of taking spin-orbit (SO)
> >coupling into account one must increase the E_cut
> from
> >1.5Ry to something more or less between 7Ry to 10Ry
> >considering a suitable convergence on some
> parameters.
> >This is due to the fact that adding SO is a
> >relativistic effect that makes further splitting
> the
> >orbitlas. For example (switching on SO) p will be
> >splitted to p1/2 and p3/2. The wave function of
> p1/2
> >like s (and as opposed to the other orbitals with
> >l<>0) can penetrate into the nuclear. This means
> that
> >the value of the wave function of p1/2 in the
> vicinity
> >of origin colud not be neglected. The variations of
> >wave functions near the nuclear are so large that
> >could not be expanded by a few expansion
> coefficients,
> >and one should take a large E_cut to reproduce the
> >behavior of the wave function correctly as we are
> >using a full-potential method (and not a
> >pseudopotential one).
> >
> >
> >Your,
> >Saeid.
> >
> >--- Chur Allen <anin1996 at hotmail.com> wrote:
> > > Dear wien users:
> > > calculations. I dont
> > > understand the E-cut.
> > > It is said to be the size of the basis
> > > functions.There are E-cut for s,p,d
> > > and the E-cut for spin orbit.They range from 0
> to
> > > 150 ev.My question is what
> > > is E-cut , how to find it after a
> calculation,and
> > > how we make use of it?
> > > Can you give me a explanation?
> > >
> > >
>
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