[Pw_forum] new bfgs: strange behavior doing vc-relax

[Максим Попов]

Dear Eduardo,

thank you very much for expanded answer and sharing the practical tricks.
I've done some computational experiments on bulk Si (cubic conventional
cell) vc-relaxation.

Here is the result (V is volume of initial unit cell, and V0 is equilibrium
volume):

1) starting from V > V0, i.e. 1/V < 1/V0 -> more G-vectors for vc-relax:

G cutoff =  837.7995  ( 101505 G-vectors)     FFT grid: ( 60, 60, 60) -
vc-relax
G cutoff =  837.7995  (  97137 G-vectors)     FFT grid: ( 60, 60, 60)  -
post-scf

!    total energy              =    -372.89634728 Ry - the last energy in
the course of vc-relax
!    total energy              =    -372.89587589 Ry - post-scf energy

NB1: # of G-vectors (vc-relax) > # G-vectors(post-scf), and E(the last point
vc-relax) < E(post-scf).

1) starting from V < V0, i.e. 1/V > 1/V0 -> more G-vectors for post-scf:

G cutoff =  775.1830  (  90447 G-vectors)     FFT grid: ( 60, 60, 60) -
vc-relax
G cutoff =  775.1830  (  97137 G-vectors)     FFT grid: ( 60, 60, 60) -
post-scf

!    total energy              =    -372.89498529 Ry - the last energy in
the course of vc-relax
!    total energy              =    -372.89587142 Ry - post-scf energy

NB2: # of G-vectors(vc-relax) < # G-vectors(post-scf), and E(the last point
vc-relax) > E(post-scf).

Comparing these two experiments, one can make a preliminary conclusion: the
more G-vectors, the lower
the total Energy, provided all other parameters to be fixed.
This is easy to understand: plane-wave basis set is complete, that means 2
things (when dealing with truncated bases):
1) E(N+M) < E(N), where N,M - number of plane waves(G-vectors);
2) lim N->infinity of [ E(N+M)-E(N)] = 0.

Now it seems to be more clear for me :)
Correct me if I'm wrong somewhere.

-- 
Best regards, Max Popov
Ph.D. student
Materials center Leoben (MCL), Leoben, Austria.

2011/4/19 Eduardo Ariel Menendez Proupin <eariel99 at gmail.com>

> >Dear Dr. Giannozzi,
> >thank you for the answer! I could find it myself looking in the output
> file a bit >more carefully...
> >One thing, which is somehow contrary to my expectations, is that the final
> scf >energy is higher
> >than the last one from vc-relax. Could you, please, elaborate a bit on the
> >matter?
>
> Dear Maxim,
>
> I followed this discussion with interest, and thanks to that I learned
> about the new scf calculation with final G-vectors. Concerning your last
> question,
> the energy is higher because the vc-relaxed energy was optimized for a
> different basis set, than the final scf calculation (different G-vectors).
> Hence, the energy of the final scf calculation is is made for a structure
> that is slightly out of the minimum for the new basis set. Remember than the
> G-vectors used in a scf calculation are all the reciprocal lattice vectors
>  contained in a sphere that has a radius determined by the cutoff. These
> vectors are selected at the first step of the vc-relaxation. When the unit
> cell gets deformed, the G-vectors vary accordingly, and the region that the
> G-vectors occupy is a deformation from the initial sphere, maybe an
> elipsoid. When the vc-relax stops, the final scf calculation takes the
> G-vectors contained inside a sphere. Hence, some of the old G-vectors that
> were in the border of the deformed sphere may be eliminated, and some that
> were absent are now included.
> If you had used an (impossible) infinite cutoff, the basis set would be
> complete in both cases (G-vectors contained in an infinite sphere or in an
> infinite elipsoid) and there would be no difference. Usually, I repeat the
> vc-relax procedure starting 'from_scratch' with the last structure
> (coordinates and lattice vectors) in the new input file, until the vc-relax
> procedure performs only one step. In this case there is no difference. If it
> never happens that vc-relax stops at the first step, then I increase the
> cutoffs. In your case, the energy difference of 0.5 mRy may be small enough
> and do not need to do that. It depends on the property that you want. E.g.,
> if you are interested in elastic properties,  you may need that the minimal
> energy structure also gives a stress tensor below 0.1 kbar or so. If you
> cannot get it, increase the cutoff.
>
> The following link may help
>
>
> http://www.quantum-espresso.org/wiki/index.php/Methodological_Background#Stress
>
> Best regards
>
> --
>
>
> Eduardo Menendez
> Departamento de Fisica
> Facultad de Ciencias
> Universidad de Chile
> Phone: (56)(2)9787439
> URL: http://fisica.ciencias.uchile.cl/~emenendez
>
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