[Pw_forum] Lattice Constant Optimization of Aluminum

[Stefano Baroni]

On Apr 27, 2007, at 2:41 AM, Paul M. Grant wrote:

> ...

> 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).
NO, I was not saying this. In order to find dimerization (to have the  
code find it) you have to double the unit cell and slightly displace  
the atoms from their mono-atomic chain equilibrium positions. In  
order to relax to the equilibrium lattice constant, you have to allow  
the latter to vary (which "cv-relax" does, while "relax" does not).  
If you do "relax" on a stable monoatomic chain off equilibrium or on  
a Peierls-unstable chain, atoms would not move from their positions,  
but for two different reasons (at least, different in my understanding).
> 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.
We do appreciate your praise, thanks.
>  Sorry for the above polemic, Stefano, but I spent a good deal of  
> my life trying to turn quasi-1D metals into superconductors!
I know, Paul. I was, how to say? a bit too pedagogic? too prolix? not  
for your sake, but the kids' sake. Hope I was not too wrong!

Ciao - Stefano

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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