[gpaw-users] Questions on EquationofStates in pw mode

[Ole Holm Nielsen]

Dear Jun,

I think you will save a lot of work by using constant kinetic energy 
cutoff in your plane wave calculations.  You will have to do a least 
squares fit of the EOS (probably you should use the Rose-Vinet EOS) 
because there will be jumps in the E_total curve.

One way to check plane wave convergence (using of course constant 
kinetic energy cutoff) is to compare the fitted EOS parameters from both 
the E_total and the Pressure (stress) curves. If the lattice constant, 
bulk modulus etc. agree well, then the calculation is converged well 
enough.  Another way to view the same thing is to take the derivative of 
the fitted E_total curve: It must be identical to the fitted curve for 
the Pressure.

I can send you a copy of my 1986 paper off-line.

Best regards,
Ole

On 01/11/2013 03:38 AM, jun yan wrote:
> Dear Ole,
>
>     Thanks a lot for the detail instructions. You definitely points out the several potential problems existed currently in the GPAW on getting reliable EOS. Its strange I can't access this paper through stanford. Currently I probably don't have a lot time digging this further. I think I will keep this in mind and run EOS at enough high energy cutoff…. Thanks again for your input.
>
> All the best,
> Jun
>
> On Jan 10, 2013, at 1:05 AM, Ole Holm Nielsen wrote:
>
>> jun yan <junyan at stanford.edu> wrote:
>>>      When one performs the EOS in pw mode, the number of plane waves are forced to be the same with different volumes of cells (let's say the lattice parameters are scaled from 0.95 to 1.05) by using the command PW(ecut, cell=cell_at_scale_1.0). Using this way, the EOS fitting curve looks perfect. It however means that, with increasing cell volume, the effective plane wave cutoff energy is decreasing since the number of plane waves is fixed. In my calculations, the decreasing of plane wave cutoff energy results in increasing of the total energy. The consequence is thus the lattice parameters shift to smaller values using fixed number of plane waves compared to using fixed plane wave cutoff energy. My question is, which one is physically meaningful : fixing the number of plane waves or the effective plane wave energy cutoff ? I will think its the latter. However, the EOS based on using the same plane wave cutoff energy looks much worse than fixing the number of plane wave!
 s.!
>>   I!
>>>   appreciate if anyone has any insights on this. Thanks !
>>
>> This is probably a FAQ. Conventional wisdom in the field of plane wave
>> DFT calculations states that for varying unit cell volumes you *must*
>> keep the plane wave *kinetic energy* cutoff constant in order to ensure
>> a constant, unbiased real-space resolution of your plane wave basis set.
>>   Probably every textbook dealing with the plane wave method will agree
>> with this.
>>
>> If you (wrongly) vary the volume and keep the *number* of plane waves
>> constant (i.e., the basis set is unchanged), you'll have a finer real
>> space resolution at smaller volumes, and hence lower total energies at
>> those volumes than if you (correctly) kept the cutoff energy constant.
>> The calculated equation of state (EOS), lattice constant, and bulk
>> modulus will consequently be quite wrong.  The exception is if you have
>> an unnecessarily high number of plane waves so that the calculation is
>> equally well converged with respect to the basis set at all volumes.
>>
>> I wrote a paper with two colleagues on this particular aspect: P. Gomes
>> Dacosta et al., J. Phys. C: Solid State Phys. vol. 19 (1986), 3163-3172.
>> We discussed the jumps in E_total as the basis set changes, and show how
>> the pressure (stress theorem) can be used to improve the numbers, and
>> even a correction formula Eq.(5) for E_total due to non-fully converged
>> basis sets.  Hopefully this old paper may clarify the issue that you are
>> asking about.
>>
>> For the EOS it also makes a difference *which* mathematical formula you
>> choose.  I don't know the current status in this field (high pressure
>> physics), but many years ago we discussed whether the Birch EOS was more
>> physically correct than the Murnaghan EOS for determining the bulk
>> modulus (probably yes).  There may be newer EOS formulas which perform
>> even better.  Please take a look at Wikipedia:
>> http://en.wikipedia.org/wiki/Birch%E2%80%93Murnaghan_equation_of_state
>> and
>> http://www.sklogwiki.org/SklogWiki/index.php/Rose-Vinet_%28Universal%29_equation_of_state
>>
>> Best regards,
>> Ole
>>
>> --
>> Ole Holm Nielsen
>> Department of Physics, Technical University of Denmark
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>

-- 
Ole Holm Nielsen
Department of Physics, Technical University of Denmark,
Building 307, DK-2800 Kongens Lyngby, Denmark
E-mail: Ole.H.Nielsen at fysik.dtu.dk
Homepage: http://www.fysik.dtu.dk/~ohnielse/
Tel: (+45) 4525 3187 / Mobile (+45) 5180 1620 / Fax: (+45) 4593 2399