[Wien] k-point and "closed shell atoms" in atomic energy calculation

[Stefaan Cottenier]

>    According to the FAQ, when we calculate atomic energy within FLAPW, we
should use only 1 k-point. I just can't understand this. I think if we
calculate total bulk energy with 1000 k-points (for example), we should use
identical k points for the calculation of atomic energy.

k-points for atoms are meaningless: they have no k-dispersion (=in a
spaghetti plot, all band would be perfectly flat). That means that in a
single k-point there is as much information as in 1000 k-points, and there
is no need to take more than 1.

Another way to understand this: with bigger cells in real space, the
reciprocal unit cell shrinks. Therefore, you can use less k-points for big
cells, because they give you the same effective sampling of reciprocal space
(the number of k-point per reciprocal volume should stay constant). Now, a
free atom has a unit cell of infinite volume, such that the reciprocal cell
is infinitesimally small. Any number of k-points -- including just 1 -- will
give you a perfect sampling for this 'reciprocal cell'.


>    The FAQ also told us for non-closed shell atoms, we should use
spinpolarization. I wonder if the "closed shell atoms" is just confined to
Inert atoms such as Ne, Ar etc?

No, it is relevant also for all atoms with closed subshells, such as Ca or
Cd.

Stefaan