ADF uses Slater Type Orbitals (STOs). This is different from most other DFT programs, which usually employ Gaussian Type Orbitals (GTOs), for which many standard basis sets are available in the literature. The advantage of the STOs is that fewer of them are needed than with GTOs to get a reasonable description of the molecule. A disadvantage is that not much work has been done to develop balanced STO basis sets. We have attempted to remedy this with the presently available STO basis set database in ADF.
The ADF-BAND program uses Numerical Atomic Orbitals (NAOs) in addition to STOs in order to get an even better description with only a limited number of basis functions.
ET stands for even-tempered. This may apply to the basis and to the fit. In our ET basis sets, only 1s, 2p, 3d, and 4f functions occur. In the fit sets, 5g functions occur in addition to this. [Currently all ADF basis sets are restricted to f functions and fit sets are restricted to g functions as the highest l-value]. The exponents in ET basis sets are given by the simple formula:
ζ = α*βI where I=1,... N
Here ζ is the exponent of the STO, b (which should be larger than 1) defines how far apart two consecutive exponents are, and a determines what the most diffuse exponent is. In principle, each l-value has its own set of α, β, N.
Initially, the only basis sets provided with ADF were those in the directories I, II, III, IV, V, which now have the more intuitive names SZ, DZ, DZP, TZP, and TZ2P, respectively. The increasing numbers point to an increase in size and quality. It is not possible to give a formally correct short general classification for each basis set directory. However, generally speaking we can say that SZ (old name I) is a single-zeta basis set, DZ (old name II) is a double zeta basis set, DZP (old name III) is a double zeta polarized basis, TZP (old name IV) is a core double zeta, valence triple zeta, polarized basis set, and finally TZ2P (old name V) is a core double zeta, valence triple zeta, doubly polarized basis. This explains the more intuitive names that are given for the basis sets. The names have also been changed since some of the basis sets have been modified substantially.
The same is classification is used for the directories ZORA/SZ-TZ2P (old names ZORA/I-V). These were added later because of the special requirements on basis sets for ZORA relativistic calculations, especially in the core region. The ZORA/QZ4P basis set can be loosely described as core triple zeta, valence quadruple zeta, with four sets of polarization functions.
The TZ2P+ basis sets for the transition metals Sc-Zn are nearly identical to TZ2P except for a better description of the d-space (4 d-functions instead of 3). The ZORA/TZ2P+ basis sets for the lanthanides La-Yb are nearly identical to TZ2P except for a better description of the f-space (4 f-functions instead of 3).
AUG stands for augmented. These are augmented standard basis sets with some diffuse STOs are added, especially meant for TDDFT calculations. They are named ASZ, ADZ, ADZP, ATZP, and ATZ2P, which means augmented SZ, augmented DZ, augmented DZP, augmented TZP, and augmented TZ2P, respectively.