[QE-users] Comparison of output from ev.x executable with pressure versus distance obtained from direct numerical derivation

[Nicolas Leconte]

Hi Lorenzo and Paolo,

Thanks for your responses.

Numerical derivation in the sense of deriving the energy with distance to
get the force, and derive by the surface to get the pressure.

For both fit and derivation, between 3.0 and 3.6 Angstrom, I used 1000
points (through interpolation of the DFT data). I further tested it with
1500 points (where I had to change the hard-coded limit for the size of one
of the vectors in ev.f90). It did not change the behavior much.

I would also imagine it to be accidental, but I was surprised to see such a
good agreement. So I was vaguely hoping for some misunderstanding from my
part or even a bug in the code I was not aware of.

Option 2, among the 4 options, Birch-Murnaghan was giving best agreement,
which seems to make sense due to the higher order terms. But maybe by
reducing the range of compression I could get a better agreement. Right
now, compression from 3.4 to 3.0 Ang of my bilayer interlayer distance
requires about 10 GPa.

Maybe that's too much to hope for a good equation of state fitting?

Regards,
Nicolas

On Mon, Apr 1, 2019 at 4:19 AM Paolo Giannozzi <p.giannozzi at gmail.com>
wrote:

> On Sun, Mar 31, 2019 at 4:34 PM Lorenzo Paulatto <paulatz at gmail.com>
> wrote:
>
> My guess is that the chisq (chi squared?)
>>
>
> yes, chi squared, as usually defined: (1/N) \sum_{i=1}^N (E_i^{fit}-E_i)^2
>
> factor is purely accidental.
>>
>
> I cannot but agree
>
> Paolo
>
>>
>> Regards
>>
>> --
>> Lorenzo Paulatto CNRS /SU
>> Written on a virtual keyboard with real fingers
>>
>> On Sun, 31 Mar 2019, 05:23 Nicolas Leconte, <lecontenicolas0 at uos.ac.kr>
>> wrote:
>>
>>> Dear QE users,
>>>
>>> I have recently used the ev.x executable to obtain the equation of state
>>> from my energy versus volume data.
>>>
>>> When I compare the Birch Murnaghan (B-M) 3d order equation of state
>>> results with a direct numerical derivation, I obtain the best matching
>>> between both methods. Yet, there is still some mismatch.
>>>
>>> I tried reducing my data to only include smaller pressures and reduce
>>> the impact of higher order terms, but it doesn't really change much, while
>>> I thought it would.
>>>
>>> Then, while playing with my output data, I noticed that simply
>>> multiplying my pressure curve from B-M with the value of chisq, I get
>>> perfect agreement between both methods.
>>>
>>> Am I missing something as on how to use the output from this script. It
>>> feels like too good a coincidence.
>>>
>>> Now, I wonder what precludes me from using this chisq as a prefactor to
>>> the bulk modulus B0 (
>>> https://en.wikipedia.org/wiki/Birch%E2%80%93Murnaghan_equation_of_state)
>>> to obtain a proper agreement with the numerically derived curve.
>>>
>>> Regards,
>>> Nicolas
>>> _______________________________________________
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>>> users at lists.quantum-espresso.org
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>>
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>
>
> --
> Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
> Phone +39-0432-558216, fax +39-0432-558222
>
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