Bulk potential energy by different methods

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


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 

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,

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