# Bulk potential energy by different methods

Matt W mattwa... at gmail.com
Sat Jun 3 20:34:56 UTC 2017

```Hi again,

likely the largest problems are Basis Set Superposition Error (BSSE), using
the LDA approximation for DFT and finite size effects.

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>
).

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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