Is density mesh cut-off and convergence criterion for energy same?

[hsuya]

I read somewhere that

The total energy was converged to be better than 10meV for a plane wave cutoff of 500eV.
The convergence criterion for energy is chosen to be 104 eV between two consecutive steps...

1. So is the convergence criterion speaking about dE?
 2. Also how do I incorporate the above statements in my ATK script?
 3. And what does the part "...the total energy was converged to be better than 10meV..." mean?

[Petr Khomyakov]

It really depends on what these statements refer to. If it refers to a single SCF calculation, than one should set tolerance to 10 meV, and that would refer to dE in the log file. In this case, however, this would be pretty poorly-converged total energy in a single SCF calculation.

If 10 meV refers to total energy converges with respect to plane-wave basis set, then it does not refer to dE, but rather to the total energy difference for the PW basis set with the cutoff of 500 eV and the PW basis set with much higher cutoff for which one may say the total energy is converged much better than 10 meV - ideally, one should refer to a complete basis set with infinite cutoff, but this kind of calculation is not possible numerically.   

I do not understand the meaning of the second statement, as 104 eV is ridiculously large number, but if it is set to something small, as given with the tolerance parameter in QuantumATK, then it would refer to dE in a single SCF calculation.