Total Energy

[fabella]

I have been using several codes. Does anyone know how Wien2k, PWscf interpret their total energy values. For example, in VASP the total energy is intuitively just the cohesive energy (eV/atom) of crystal. In Wien2k these values are on order of 580Ry/atom for Silicon. Is anyone familiar with these definitions of total energy?

Thank You
W

[tjf]

I'd suggest that it's rarely a good idea to rely on such definitions, with the possible exception of atom-centred basis set codes such as ADF. Generally you should consider your energies to be with respect to some arbitrary zero point. I think I'd take some convincing that VASP doesn't fall into this catagory too.

[fabella]

However, this "arbitrary zero point" obeys the Birch Murnaghan equation of states. There must be some 'real' physical reasoning for defining such an energy? I agree, across the board there is some method (which varies) for 'defining' the value for total energy.

[tjf]

Well, when you solve the Kohn-Sham equations you get the energy with respect to (I think -- it's not that important) infinitely seperated electrons and nuclii. Replace the Coulomb external potential with a pseudopotential and that zero of energy becomes something completely different, effectively arbitrary, depending entirely on the PSP. But remember it's shifted, not scaled. PAW does something very similar: it shifts the defined zero of energy. The energy calculated internally in VASP is this shifted energy. VASP then adds the energies calculated on this shifted energy scale for the atoms, resulting in an approximate extrinsic cohesive energy (or bond energy for us chemists).

The energy is just shifted, no scaled. So all the energy derivatives remain unaltered, unless you squeeze things enough to start overlapping core regions. Thus generally all the moduii remain unaltered. Hence the equations of state remain unaltered.

As an aside, the reason I don't think that the energy reported by VASP is reliably the true cohesive energy (but feel free to argue) is that in general the basis sets for the atomic and bulk calculations differ significantly. There's no convenient cancellation of errors.

[fabella]

You are right about KS eqts. and total energy. The total energy represents the amount of energy to bring electrons and nuclei from infinity. (Thank you for the insight on PP shift in zero energy.) I was searching in the Wien2k forum and it seems that you can calculate the 'true' cohesive energy if you make an fcc unit cell with lattice parameter 30bohr (~16A) & place the atom at (0,0,0) then calculate using 1kpt. I have not tried this but it seems this is not very helpful for larger systems. I think it takes some tinkering and free computer time.
Furthermore, in regards to your comment about the arbitrary shift, my guess is this is all we need to calculate accurate forces. Oh, but then we would need to know this approx. 'shift'. hmm.

W

[tjf]

There's no such thing as an absolute zero of energy. All energies are always relative to some arbitrarily defined energy zero.

But the scale doesn't change. When you shift your zero, derivatives don't change. Thus forces, modulii and the like don't change. [d(E+c)/dx=dE/dx, remember?]

[cdt9f]

tjf is right. The shift is irrelevant to the forces.

Chris