# Re: [Wien] constrain some atoms to minimize the forces

```Dear Stefan,

Resending with a couple of typos corrected:```
```
You will in fact gain very little by artificially constraining the center.

Let me expand upon my first response, with a simplified "toy-model" explanation.

Suppose we transform the complex Pt (111) problem "somehow" to a
simpler one by a transformation of the positions such that the energy
is now a simple quadratic E= E_0 + a*p + b*p*p along some direction p
which is a combination of movements of all the atoms. In such a case
it would take at most two optimization cycles to move to the minimum.
The transformation has reduced the problem to having only one
eigenvalue.

Now suppose that instead of one p, there were two eigenvectors -- it
would take twice as long if their eigenvalues were very different, but
about the same time if they were similar.

Extending this to the general case gives the result I mentioned.
Furthermore if you apply the same thinking to the electronic problem
you will see that the number of iterations to convergence of the SCF
iterations (with fixed atoms) does not scale as the number of density
variables. If it did DFT would be useless! In most cases there are
only a smaller number of eigenvectors of the electronic problem, much
less than the number of density variables, often only 10-30. Some
cases such a systems with d or f electrons have more eigenvectors so
are harder to converge, and
they may also have soft modes.

The same thinking explains why MSR1a is often faster.

Does fixing the center of a slab reduce the number of eigenvectors? It
is not obvious to me that it does.

I would prefer to not fix the center. If the atoms move far from flat
that will tell me that the slab is too thin. Fixing the center does
not make the slab thicker.

On Thu, Jul 14, 2016 at 7:51 AM, Stefaan Cottenier
<stefaan.cotten...@ugent.be> wrote:
>> Your question is based upon a common misunderstanding of minimizing
>> forces. You are thinking that the time to optimize depends upon the
>> number of positions (3*Number of Pt atoms that move) which is wrong.
>> With PORT it scales as the number of clusters of phonon frequencies and
>> weakly with the width of the clusters; with MSR1a it scales as the
>> number of clusters of eigenvalues of the joint electron-phonon problem
>> and their width.
>>
>> You will gain far more by generating a proper symmetric model with P-3m1
>> (maybe P-31m) symmetry rather than what you appear to have, a P1
>> structure. This will reduce the number of uniques phonon etc modes by
>> something like 6-12, and will be much faster and converge better.
>
> Dear Laurence Marks,
>
> When having created the most symmetric slab model that is relevant for
> the case at hand, wouldn't you agree that it still makes sense to fix
> the positions of the middle few layers to their bulk positions? One
> cannot make slabs as thick as to find spontaneously bulk behaviour in
> the center, and therefore imposing the bulk geometry in the slab center
> could be preferred over getting unphysical lattice spacings. Can you
> comment?
>
> Thanks,
> Stefaan
>
>
> --
> Stefaan Cottenier
> Center for Molecular Modeling (CMM) &
> Department of Materials Science and Engineering (DMSE)
> Ghent University
> Tech Lane Ghent Science Park – Campus A
> building 903
> BE-9052 Zwijnaarde
> Belgium
>
--
Professor Laurence Marks
"Research is to see what everybody else has seen, and to think what
nobody else has thought", Albert Szent-Gyorgi
www.numis.northwestern.edu ; Corrosion in 4D: MURI4D.numis.northwestern.edu
Partner of the CFW 100% program for gender equity, www.cfw.org/100-percent
Co-Editor, Acta Cryst A
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