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

Eduardo Ariel Menendez Proupin eariel99 at gmail.com
Wed Apr 20 16:02:41 CEST 2011

```Dear Max,
Thanks for your tests. Your  experiments looks nice to be included in a QE
tutorial.
I think your reasoning is correct. Moreover, the energy should always
decrease when you enlarge de basis set (adding G-vectors) because the
calculation is variational (within a given density functional). I am not
sure if the calculation is still variational with ultrasoft
pseudopotentials, or even if the Hohenberg-Kohn lemma is valid with non
local pseudopotentials. With QE I have always seen the energy to decrease
when the cutoffs are increased, but with VASP, I always see an oscillation
in the total energy when the cutoff is incremented. I hope one of our
professors can clarify this point.
Best regards
Eduardo

Eduardo Menendez
Departamento de Fisica
Phone: (56)(2)9787439
URL: http://fisica.ciencias.uchile.cl/~emenendez

From: "Максим Попов" <max.n.popov at gmail.com>
To: PWSCF Forum <pw_forum at pwscf.org>
Date: Wed, 20 Apr 2011 11:25:46 +0200
Subject: Re: [Pw_forum] new bfgs: strange behavior doing vc-relax
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.

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