Total energy vs volume

[Axel]

hi all,

a few additional comments...

On Feb 3, 1:25 pm, Teodoro Laino <teodor... at gmail.com> wrote:
> On 3 Feb 2008, at 19:04, xiaoliang wrote:
>
> > I wonder how cp2k calculate the number of grid points? Because If I
> > change the size of reference cell, the number of grid points is

the number of grid points is determined by the density cutoff and
the grids supported by the FFT libraries.

> > changed as well, I think. Then do we need to  make energy vs reference
> > cell size plot to get energy convergece, like the test for energy vs
> > cutoff ?
>
> In principle yes.. but you would discover that to get "full
> convergence" you should reach extremely high cutoff
> (unaffordable for standard calculations).
> However, the nice thing is that the absolute energy is just shifted
> and the shape of the potential energy  does not change
> sensibly. This makes feasible to use a relatively low cutoff (of
> course too small creates problems as well..).

this is a problem that is discussed a lot on mailing lists dedicated
to plane-wave pseudopotential calculations, particularly in
combination
with variable-cell MD. for details, one has to dig out the proper
text books or articles/reviews but in short.

- you do not have to increase the basis set until the total
  energy is converged. most properties converge faster.
- forces converge very fast, stress tensor less so. so one needs
  to have a larger basis set/cutoff for an accuracte stress tensor.
  this has to be tested on a case-by-case basis.
- with variable cell (or using a reference cell) you have the problem,
  that you keep using the same grid for everything, i.e. you are doing
  not a constant cutoff/basis scheme, but a constant plane wave scheme
  which means your effective cutoff changes with the box size.

in my opinion, the best way to get an accurate energy vs. volume plot
(e.g. to fit against an equation of state) is to use an fft library
with many supported grids (FFTW2/3), choose a cutoff so that the jumps
are tolerably 'small' and the calculation is not impossible (i.e.
something
20-50% larger than what you would use for an MD or a geometry
optimization).
if you fix the grid to get a smooth plot, you'll have an unbalanced
result.
for increasing volume your effective density cutoff will decrease
gradually,
it is better if the energy jumps around and you "clean" it with the
EOS fit.

> "Generally speaking" a cutoff of around 300 Ry is most of the time
> enough.. of course the real good number depends on the
> nature of your basis set, pseudo, XC.

nod. one important thing about all these components is, that they are
not completely independent, so one cannot fully test each of them
individually and has to approach "convergence" gradually in several
iterative steps. there are quite a few "rule of thumb" guidelines and
most of them work, but the always have to be verified and there is
always a chance that the particular rule, that you depend on, does not
apply to your specific case.

or shorter: the more flexible and powerful a method or software,
the more options you have to shoot yourself in the foot and the
more it hurts. ;-)

cheers,
    axel.


> Ciao,
> Teo