These points are discussed quite a lot in the literature ("our" basis sets are not unique to ATK). You can find a lot of good information by searching on e.g. Google for "basis set zeta". Note that most of those discussions pertain to Gaussian (GTO) or Slater (STO) type orbitals, however; ATK uses localized orbitals, which work a bit differently, although they have many features in common.
It would be hard to sum it up in a few words in a Forum discussion, but very generally speaking, the localized basis set used in ATK have the following features (non-exhaustive list):
- SIESTA numerical orbitals
- Closely resemble atomic orbitals, which is a very nice thing, esp. for localized properties like dopants
- Angular part described by solid (not spherical) harmonics, which is more suitable for solid state systems
- Finite range, which gives sparse matrices (and a cheap description of vacuum)
- Generally much fewer basis orbitals needed than for plane waves = smaller matrices = less memory for large systems
- Non-variational, no simple way to extend it systematically to converge in basis set size
- Not as precise as plane waves (primarily for the reason above)
I encourage anyone with input on the topic to share their experiences with the community here!
Some useful links, mostly about the SIESTA method:
http://iopscience.iop.org/0953-8984/14/11/302/http://www.mcc.uiuc.edu/summerschool/2005/week_one_lectures/miguel_pruneda/
