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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Wow! Thanks for thinking so hard about my
predicament!<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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.”).<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Sorry for the above polemic, Stefano, but
I spent a good deal of my life trying to turn quasi-1D metals into
superconductors!<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Ciao, -Paul<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<div>
<p class=MsoNormal><strong><b><i><font size=4 color=navy face="Comic Sans MS"><span
style='font-size:13.5pt;font-family:"Comic Sans MS";color:navy;font-style:italic'>Paul
M. Grant, PhD</span></font></i></b></strong><font color=navy><span
style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><strong><b><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>Principal, W2AGZ
Technologies</span></font></b></strong><font color=navy><span style='color:
navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><strong><b><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>Visiting Scholar, Applied
Physics, <st1:place w:st="on"><st1:PlaceName w:st="on">Stanford</st1:PlaceName>
<st1:PlaceType w:st="on">University</st1:PlaceType></st1:place></span></font></b></strong><font
color=navy><span style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><strong><b><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>EPRI Science Fellow
(Retired)</span></font></b></strong><font color=navy><span style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><strong><b><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>IBM Research Staff Member
Emeritus</span></font></b></strong><font color=navy><span style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><a href="mailto:w2agz@pacbell.net"><strong><b><font
color=navy face=Arial><span style='font-family:Arial;color:navy;text-decoration:
none'>w2agz@pacbell.net</span></font></b></strong></a></span></font><font
color=navy><span style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><a href="http://www.w2agz.com/"><strong><b><font
color=navy face=Arial><span style='font-family:Arial;color:navy;text-decoration:
none'>http://www.w2agz.com</span></font></b></strong></a></span></font><font
color=navy><span style='color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
style='font-size:12.0pt;color:navy'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=navy face="Times New Roman"><span
style='font-size:12.0pt;color:navy'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
pw_forum-admin@pwscf.org [mailto:pw_forum-admin@pwscf.org] <b><span
style='font-weight:bold'>On Behalf Of </span></b>Stefano Baroni<br>
<b><span style='font-weight:bold'>Sent:</span></b> Thursday, April 26, 2007
12:00 PM<br>
<b><span style='font-weight:bold'>To:</span></b> <st1:PersonName w:st="on">pw_forum@pwscf.org</st1:PersonName><br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Pw_forum] Lattice
Constant Optimization of Aluminum</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>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<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>On Apr 26, 2007, at 4:41 AM, Paul M. Grant wrote:<o:p></o:p></span></font></p>
</div>
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<br>
<o:p></o:p></span></font></p>
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<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
class=apple-style-span><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PlaceType"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PlaceName"><O:SMARTTAGTYPE namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="place"><font
size=2 color=black face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:black'><span style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'>To All: <O:P style="font-family: Arial; font-size: 13.3333px; "></O:P></span></font></span><font
color=black><span style='color:black'><o:p></o:p></span></font></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
class=apple-style-span><font size=2 color=black face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:black'>(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.)<O:P style="font-family: Arial; font-size: 13.3333px; "></O:P></span></font></span><font
color=black><span style='color:black'><o:p></o:p></span></font></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
class=apple-style-span><font size=2 color=black face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:black'>I’m trying to do a
very simple homework problem with PWscf…the optimization of the lattice
constant of aluminum.<O:P style="font-family: Arial; font-size: 13.3333px; "></O:P></span></font></span><font
color=black><span style='color:black'><o:p></o:p></span></font></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
class=apple-style-span><font size=2 color=black face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:black'>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):</span></font></span><font
color=black><span style='color:black'><o:p></o:p></span></font></p>
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</O:SMARTTAGTYPE></O:SMARTTAGTYPE></O:SMARTTAGTYPE></span>
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<p class=MsoNormal><span class=apple-style-span><span style='border-spacing: 0px 0px;
text-align:auto;-khtml-text-decorations-in-effect: none;-apple-text-size-adjust: auto;
orphans: 2;widows: 2;word-spacing:0px'><font size=1 color=black face=Helvetica><span
style='font-size:9.0pt;font-family:Helvetica;color:black'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'><span
style='border-spacing: 0px 0px;text-align:auto;-khtml-text-decorations-in-effect: none;
-apple-text-size-adjust: auto;orphans: 2;widows: 2;word-spacing:0px'>---</span></font></span><font
size=2 color=black face=Helvetica><span style='font-size:10.5pt;font-family:
Helvetica;color:black'><o:p></o:p></span></font></p>
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<p class=MsoNormal><span class=apple-style-span><font size=1 color=black
face=Helvetica><span style='font-size:9.0pt;font-family:Helvetica;color:black'>Stefano
Baroni - <st1:PlaceName w:st="on">SISSA & DEMOCRITOS</st1:PlaceName>
<st1:PlaceName w:st="on">National</st1:PlaceName> <st1:PlaceName w:st="on">Simulation</st1:PlaceName>
<st1:PlaceType w:st="on">Center</st1:PlaceType> - <st1:City w:st="on"><st1:place
w:st="on">Trieste</st1:place></st1:City></span></font></span><font size=2
color=black face=Helvetica><span style='font-size:10.5pt;font-family:Helvetica;
color:black'><o:p></o:p></span></font></p>
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<div>
<p class=MsoNormal><span class=apple-style-span><font size=1 color=black
face=Helvetica><span style='font-size:9.0pt;font-family:Helvetica;color:black'>[+39]
040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</span></font></span><font
size=2 color=black face=Helvetica><span style='font-size:10.5pt;font-family:
Helvetica;color:black'><o:p></o:p></span></font></p>
</div>
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<p class=MsoNormal><font size=2 color=black face=Helvetica><span
style='font-size:10.5pt;font-family:Helvetica;color:black'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><span class=apple-style-span><font size=1 color=black
face=Helvetica><span style='font-size:9.0pt;font-family:Helvetica;color:black'>Please,
if possible, don't send me MS Word or PowerPoint attachments</span></font></span><font
size=2 color=black face=Helvetica><span style='font-size:10.5pt;font-family:
Helvetica;color:black'><o:p></o:p></span></font></p>
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<p class=MsoNormal><span class=apple-style-span><font size=1 color=black
face=Helvetica><span style='font-size:9.0pt;font-family:Helvetica;color:black'>Why?
See: </span></font></span><font size=2 color=black face=Helvetica><span
style='font-size:10.5pt;font-family:Helvetica;color:black'><a
href="http://www.gnu.org/philosophy/no-word-attachments.html"><span
class=apple-style-span><span style='-khtml-text-decorations-in-effect: underline'><font
size=1 color="#0023e9"><span style='-khtml-text-decorations-in-effect: underline'><span
style='-khtml-text-decorations-in-effect: underline'><span style='font-size:
9.0pt;color:#0023E9'><span style='-khtml-text-decorations-in-effect: underline'><span
style='-khtml-text-decorations-in-effect: underline'><span style='-khtml-text-decorations-in-effect: underline'><span
style='-khtml-text-decorations-in-effect: underline'><span style='-khtml-text-decorations-in-effect: underline'><span
style='-khtml-text-decorations-in-effect: underline'>http://www.gnu.org/philosophy/no-word-attachments.html</span></span></span></font></span></span></span></span></a></span></span></span></span><o:p></o:p></span></font></p>
</div>
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<p class=MsoNormal><font size=2 color=black face=Helvetica><span
style='font-size:10.5pt;font-family:Helvetica;color:black'><o:p> </o:p></span></font></p>
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style='font-size:10.5pt;font-family:Helvetica;color:black'><br>
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