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[Pio Baettig <baettigp@gmx.net>]

Dear Jess,

thank you very much for your e-mail.
In principle, you should send your questions to the mailing-list, as it 
might also be interesting for others...


If you are just interested in the equilibrium lattice-constant (and not 
the angles), you can calculate several points with different lattice 
constants around the equilibrium and then fit the energies to a 
Birch-Murnaghan equation of state, cf. 
http://en.wikipedia.org/wiki/Birch%E2%80%93Murnaghan_Equation
and references therein.

This book:
http://www.univie.ac.at/Mineralogie/EMU/notvol4.htm
has also a good introduction, maybe your institute has it?

I googled a bit and found the following, which might help you too:
http://www.tcm.phy.cam.ac.uk/castep/CASTEP_talks/refson2.pdf

In a very basic approximation, you could also fit a parabola to the 
Energy vs a-curve and take the minimum lattice constant.
I don't think, you would be too far off, close to the minimum the 
anharmonicity should not yet be too big.

Alternatively, if you are also interested in the angles between the 
unit-cell vectors, you can also calculate the energies for a combination 
of a and alpha, plot them in a 3d-plotting-program and estimate the 
lowest energy.

(For Bi, the data from Pearsons Handbook are as follows:
R-3m, a=4.7236 Angst, alpha=57.3476 degrees
Bi 0.23407 0.23407 0.23407
Bi 0.76593 0.76593 0.76593)

so you would for calculate the energies for matrix (for example) like this:

    alpha
a   55 55.5 56 56.5 57 57.5 58 58.5 59
4.4
4.5
4.6
4.7
4.8
4.9
5.0

find the minimum and maybe iterate more until you are at a sufficient 
precision. (A 3d-plotting-program could help you in finding the minimum)

After you found your minimum, you should optimize the positions to 
minimize the forces and restart with a/alpha, until you obtained your 
results with a sufficient precision.


Best regards,

Pio Baettig





Jess Kondor wrote:
> Dear Pio Baettig,
>
>  I have seen your thread in abinit forum about Bi PAW pseudopotential. I 
> have a question for you (if don't mind). You tested your PAW 
> pseudopotential very carefully. Did you calculate the cohesive energy 
> using PAW and abinit? I try to test a pseudo for Bismuth but for LCAO 
> code (openmx) and different basis sets give different cohesive energies. 
> And do you know how to find equilibrium lattice constant of Bismuth 
> (using equation of state) if there is no automatic variable cell 
> relaxation?
>
>  thank you for you help,
>    jess