[Pw_forum] Lattice Constant Optimization of Aluminum

[Paul M. Grant]

Wow!  Thanks for thinking so hard about my predicament!

 

OK, let’s see.  I follow your points about the code.  As usual, my blunder
was not looking at the source behind “relax.”  It would be great if there
were a “guide to the source” a la the way PW_INPUT serves for the namelists,
that is, which “*.f90” does what?  Under the covers, I find the PWscf source
well commented, though, when I can find it.  

 

Now, it’s well known that a linear, infinite, periodic metallic chain is
unstable to dimerization (Peiels-Froehlich or static CDW instability)
inasmuch as gapping the planar Fermi surface by commensurate nesting with
respect to the 1D Brillouin zone boundary lowers the ground state energy of
the system.  That is, all (quasi)-1D metals sit on top of a metastable hill
in the local configurational ground state space and will fall into an
insulating state under an infinitesimal change in lattice constant, even if
the new equilibrium is a quasiperiodic chain (e.g., “Fibonacci sequence”),
if indeed such a thing can exist.  On the other hand, in 2D or 3D metals,
we’re saved by the fact that most Fermi surfaces have a high overall degree
of curvature with respect to their polygonal BZs, thus suppressing a
tendency to nest (the A15 compounds are somewhat an exception
that’s why
they’re strong-coupled superconductors).  At the end of the day, at T = 0,
all Landau-Fermi metals are “gapped” by some arbitrarily weak
electron-electron interaction
only superconductors, antiferromagnets, and
possibly ferromagnets can exist (John Hubbard once told me he didn’t think
itinerant ferromagnets were “real metals.”).

 

So, what you’re telling me is that pw.x with “relax” will not find the
Peierls state of a periodic chain of, say, sodium atoms, or polyacetylene
with equal carbon-carbon bond lengths, but presumably “vc-relax” will?  (I
tried playing with vc-relax last night on Al, but fell asleep on my keyboard
before I could get it to work
I’ll try again this evening).  Naturally, I
“manually optimized” Al with trial “scf” runs before all of this (I should
have thought about using Paolo’s equation of state fit, but I’d didn’t know
it existed within PCscf), and believed “relax” sort of worked the same way.
Up at Stanford I use the CASTEP geometry optimization package which on
simple structures “jiggles” all atoms in a symmetry preserving way (i.e.,
cubic cells stay cubic) in its search for local configurational total energy
minima.  I see now that PWscf separates this task into “relax” and
“vc-relax.”  By the way, PWscf is a MUCH better computational tool than
CASTEP, moreover it’s free, but what’s most important, as any reader of
pw_forum can see, encompasses a far more collegial user support community.

 

Sorry for the above polemic, Stefano, but I spent a good deal of my life
trying to turn quasi-1D metals into superconductors!

 

Ciao, -Paul

 

Paul M. Grant, PhD

Principal, W2AGZ Technologies

Visiting Scholar, Applied Physics, Stanford University

EPRI Science Fellow (Retired)

IBM Research Staff Member Emeritus

 <mailto:w2agz at pacbell.net> w2agz at pacbell.net

 <http://www.w2agz.com/> http://www.w2agz.com

 

 

 

  _____  

From: pw_forum-admin at pwscf.org [mailto:pw_forum-admin at pwscf.org] On Behalf
Of Stefano Baroni
Sent: Thursday, April 26, 2007 12:00 PM
To: pw_forum at pwscf.org
Subject: Re: [Pw_forum] Lattice Constant Optimization of Aluminum

 

Dear Paul: you are not doing anything wrong, but expecting something the
code cannot do (not even if it was a Perfect Schrödinger Solver). Let me
make a simple example that may convince you of what is missing. Take a
monoatomic, periodic, linear chain out of equilibrium: what would the force
acting on each atom be? 0, of course, by symmetry! How can it be, for a
non-equilibrium configuration? Forces are zero by symmetry because you are
considering (the code is considering) an infinite system. If the system was
finite instead, forces on atoms near the surfaces would be nonvanishing, and
the relaxation would (slowly) propagate from near the surface to deep into
the bulk. The point is, in an infinite system vanishing forces are a
necessary condition for equilibrium, but not a sufficient one. Vanishing
forces AND stresses are both necessary and sufficient conditions for
equilibrium to occur. If forces are already zero (by symmetry in your Al
case, because each atomic site has cubic symmetry: notice that they are zero
to machine precision, not just small) then you have to search for a
configuration of zero pressure (which is large for your non-equilibrium
configuration). This is achieved by vc-relax, or by fitting the E vs. volume
relation to some equation of state, as suggested by somebody else in this
forum recently. The latter is actually the preferred method for very simple
systems (i.e. for systems whith very few degrees of freedom). Hope I did not
misunderstood your question and that this clarifies. Yours - Stefano

  

On Apr 26, 2007, at 4:41 AM, Paul M. Grant wrote:





To All: 

(BTW: PG: My last note on the “default” value of npk should have been termed
“default maximum.”  Sorry, but we Americans haven’t spoken English since
1776.  Anyway, thanks for pointing me to the right Fortran routine.)

I’m trying to do a very simple homework problem with PWscf
the optimization
of the lattice constant of aluminum.

Even with a wildly wrong first estimate of celldm(1) of 7.2 (the
experimental value at RT is 7.665 au), I get zero net individual atomic
forces and thus no optimization.  I’ve gotten “relax” in PWscf to work with
a lot more complex polymer monoclinic unit cell containing eight atoms and
two different elements.  So, I must be doing something really dumb
(stupid)
maybe I should be using vc-relax instead?  Anyway, here’s the I/O
(scusi e grazie):

---

Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste

[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

 

Please, if possible, don't  send me MS Word or PowerPoint attachments

Why? See:   <http://www.gnu.org/philosophy/no-word-attachments.html>
http://www.gnu.org/philosophy/no-word-attachments.html

 





 

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