[Pw_forum] Lattice Constant Optimization of Aluminum

[Stefano Baroni]

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)

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