# Is total energy difference lower than 1 meV/atom good enough for k-point convergence?

How much energy difference could be considered as tight convergence? Is total energy difference lower than 1 meV/atom good enough for kpoint convergence for total energy calculation?

• This depends on the quantity you are interested in. For example, the energy difference between fcc and hcp Cu is about 8 meV/atom (with the PBE functional). Your precision nearly is on that order of magnitude. But total energies and total energy differences show different convergence behavior. The differences converge faster. The important thing therefore is to also have comparable parameter sets for different calculations. But this example also demonstrates a rather small energy difference. Oct 10, 2020 at 11:23
• – Thomas
Oct 10, 2020 at 12:19

The convergence you are refering to is numerical (i.e. how many $$\mathbf{k}$$-points to include in the numerical approximation of replacing an integral over the Brillouin zone with a discrete sum). In this case, convergence is not something that you can decide on in absolute terms: it depends on what you are interested in. For example, if you are interested in resolving an energy of 100 meV/atom, then converging to below 1 meV/atom is definitely good enough. However, if you want to resolve an energy of 2 meV/atom, then converging below 1 meV/atom may not be sufficient.