Why total energy increases during a self-consistent cycle

[Jose Coutinho]

Dear all,

I have been using elk for a few months and often I realized that the total energy increases during the scf cycle. Here is an example:

Total energy of a 64 Ge atom supercell with a substitutional Fe atom.

SCF-related flags are:

reducebf
   0.5                                : reduce mag field every SCF step

mixtype                              : Inter-step mixing
    3                                  : Broyden

 beta0                                : small mixing parameter required. Decrease if unstable
    0.015

 nempty                               : Num empty states/atom.spin
    4

Could some one explain if (and why) this is ok?

Many thanks for your assistance,

/José

[Eike Schwier]

Hello José,

the convergence of the total energy seems fine to me. Depending on the atomic potentials in the first scf loop it may look less monoton, but if the convergence is easily obtained as in your case the energy should move towards this converged vaulue without much oscilations. Wether this is from an initially higher value or as in your case a lower value may depend on the system.

On another note I would like to point out that beta0 (and betamax for that matter) should be related to mixtype 1 (adaptive linear mixer) and for broyden mixer (mixtype 3) the related parameters would be broypm and mixsdb.

best regards,
Eike

[Jose Coutinho]

Dear Eike,

Many thanks for your reply and insight on the Broyden mixer parameters. I am sorry if I am being too presistent on this, but I would like to understand why the energy increases during the SCF cycle. Starting from assumption that the energy is a functional of the density, and that the same energy has a lower bound that corresponds to the ground state density, it is not clear to me why it converges "upwards". Do you have an answer for that?

With kind regards,

/J

[Eike Schwier]

Hi José,

I would argue that since the DFT calculation is an iterative process in which not only the density but also the potential (which in turn is a functional of the density) are calculated and adjusted through the mixer in each step, that the total energy does not give you an indication, if you have found the groundstate of the system. As far as I understant the inner workings of the method, it is rather through the comparison of the density and the potential of loop n with the loop n-1 that we decide at which point we have found the ground state. Only if the potential and densities do not change any more between successive loops (or rather their change is below the convergecne parameters epspot and epsengy) can we talk about the ground state.

best,
Eike

PS: It may also be educational to look at the decomposition of the total energy in the INFO.OUT file to see how different contributions behave over the sycles.

[J. K. Dewhurst]

Dear José and Eike,

The reason that the energy seems to converge 'upwards' in Elk is that the calculation of the density and energy are one cycle out-of-sync. This is just a progamming convenence.

If we had made the potential and energy correspond to the density of the same loop then the energy would constantly decrease throughout the self-consistent cycle.

Nice question though.

Regards,
Kay.