# Bulk potential energy by different methods

Sebastian Hütter sebastia... at ovgu.de
Sat Jun 3 18:41:58 UTC 2017

```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.