Bulk potential energy by different methods

[Sebastian Hütter]

Hi,

16 calculations with different parameter combinations later, I think this 
works now.

LDA is known to overbind (as a general rule), first paper I found in a 
search gives 24% overbinding (Al_cohesive 
<https://spiral.imperial.ac.uk/bitstream/10044/1/871/1/Ab%20initio%20calculations%20of%20the%20cohesive.pdf>). 

That turned out to be true here, as well. Switching from a PADE to PBE 
functional basically solved the problem, regardless of the other changes 
tried.

DZVP understimates the cohesive energy, TZVP hits it a bit better. The 
difference is only a 1-2% though.

Using &MGRIDS in real space (with the supercell size as in the file above) 
and k-points (reasonably converged around 15x15x15 MP grid, ran with 
25x25x25 for good measure) gives almost identical results. Only important 
thing: the wavefunctions appear to be complex valued, I had by chance 
copy-pasted a "WAVEFUNCTIONS REAL" keyword, that gives wildly wrong results.

The isolated atom's energy is unsurprisigly not affected by any of that.

I learned a lot here, thank you! Can this be taken as a general rule? I 
mean, it's easier here to see what works and what doesn't because we known 
the expected results, but if we didn't?


Regards,

Sebastian


Am Samstag, 3. Juni 2017 22:34:56 UTC+2 schrieb Matt W:
>
> Hi again,
>
> likely the largest problems are Basis Set Superposition Error (BSSE), 
> using the LDA approximation for DFT and finite size effects.
>
>
>
> I would have expected your number to be too large, as the BSSE also 
> overbinds, but this is due to the incomplete basis set, rather than level 
> of theory. This suggests that your cell is not large enough to converge 
> energies (as Matthias suggests).
>
> Try using the bigger TZVP basis set (in MOLOPT_UCL) and see how that 
> changes things. Then see if you can increase supercell size, or try running 
> with k-points.
>
> Matt
>
> On Saturday, June 3, 2017 at 7:41:58 PM UTC+1, Sebastian Hütter wrote:
>>
>> Hi,
>>
>> Is should be - cohesive energies, structural relaxations do not use a 
>>> 'total energy' but you subtract one or more total energies and work with a 
>>> difference. That should be well defined and comparable between methods (and 
>>> to experiment).
>>>
>> Okay, now some things make more sense. I have checked some of my memories 
>> with literature, please correct me if/where I got something wrong...
>>
>> In genereal, E_coh = E_total - Sum(Atoms, E_iso(atom)).
>>
>> For classical potentials such EAM, a single atom in vacuum is taken to 
>> have E_iso=0, so E_coh = E_total. This is what i.e. LAMMPS prints as total 
>> potential energy, so here we get the cohesive energy directly.
>> For our DFT case, an isolated atom in vacuum *has* a nonzero energy, 
>> namely that of its spin-paired, neutral, and spherically symmetric state. 
>> We can find that by placing one atom in a (non-periodic) large cell, and 
>> calculating the energy: because there is no bonding anywhere, E_coh is 0 
>> and the individual atom's energy is the system energy. Subtracting that 
>> from the bulk total energy yields the cohesive energy, which should now 
>> agree with that found with classical potentials as well as experiments. 
>> Additionally, for the same applied cell distortion, we should get the same 
>> change in energy from both methods (assuming same relaxed lattice 
>> parameter) - if this wasn't the case, calculating B = V d²E/dV² wouldn't 
>> work.
>>
>> However, for the Al bulk case using the basis set and potential from 
>> before (a=4.05A), I find:
>> E_tot = -288.01 eV / unit cell
>> E_iso,al = 52.9318 eV / atom
>> -> E_coh = E_tot - 4*E_iso,al = -16.285 eV or -4.07 eV / atom
>>
>> This is quite far off from the known value - even if we optimize closer 
>> to the lowest-energy lattice parameter, it only gets even more wrong.
>>
>>
>>
>> Thank you for your patience,
>>
>> Sebastian
>>
>
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