Large or small molecule?

In general it is advisable to use the best basis set that you can afford to use in terms of CPU time and memory. If you want to optimize the geometry or calculate the atomization energy of a diatomic molecule there is little reason not to use the very large ZORA/QZ4P basis, or (for light elements) a similarly large ET basis (we recommend the ET-pVQZ basis). If you are studying a molecule with 100 atoms or more, the use of such large basis sets does not only become prohibitive because of the required CPU time and memory, but it also is much less needed than for smaller systems. In medium-sized or large molecules even the moderately large basis sets will prove to be quite adequate because of the effect of basis set sharing. Each atom profits from the basis functions on its many neighbors. Additionally, if a large basis contains diffuse functions, linear dependency problems may occur. See also the input key DEPENDENCY in the ADF User Guide. In many cases basis DZ or DZP will give acceptable accuracy for calculations on large systems. If you are inexperienced it may be prudent to test a few different basis sets to get a feel for the size of basis set effects. To get a rough idea for the size of various basis sets, we mention here the number of functions for all-electron basis sets from the directories ZORA/SZ up to ZORA/QZ4P. For carbon, the number of functions is 5 (basis ZORA/SZ,I), 10 (DZ,II), 15 (DZP,III), 19 (TZP,IV), 26 (TZ2P,V), 43 (QZ4P). The same numbers for hydrogen are: 1 (SZ,I), 2 (DZ,II), 5 (DZP,III), 6 (TZP,IV), 11(TZ2P,V), 21(QZ4P). These numbers arise because ADF uses 'pure' d and f functions. In other words, 5 instead of 6 d functions are used and 7 instead of 10 f functions. Note that especially the jump from TZ2P (old name V) to QZ4P is quite steep.

In an overgeneralizing fashion we can state that the single zeta basis SZ (old name I) is hardly ever sufficient to get more than a qualitative picture and should be used only when larger basis sets are not affordable. The double zeta basis DZ (old name II) performs already much better and may give quite reasonable results, for example in geometry optimizations on large molecules. However, in more subtle situations, for example if hydrogen bonds are important, it is advisable to use at least one set of polarization functions. This is the double zeta polarized DZP basis set (old name III). Basis set TZP (old name IV) extends the valence space (but not the core space which remains double zeta) to triple zeta. In basis TZ2P (old name V) an additional polarization function is added. For example, hydrogen gets a d polarization function in addition to its p polarization function and carbon gets an f polarization function on top of a d polarization function. Several tests have shown that often the second polarization function is of more use when it has an l value one higher than the first polarization function. This is reflected in the choice just described. If another polarization function is needed it is usually best to add another one of the lowest l-value (2p+1d for hydrogen, 2d+1f for carbon). This choice has been made in the ET basis VI. There, sometimes even three d polarization functions were added, for example 3 p functions for Be, and 3 d functions for S. The reason for this is that S can occur in hypervalent species such as SF₆, which put special demands on the basis set. In the case of Be, the unoccupied p level is so close in energy to the occupied ones that it is sometimes called a valence level. Symantics aside, it is clear that a proper description of the p level of Be is very important and it is therefore not strange to add a third p function. In general, the unoccupied levels for the atoms on the left side of the periodic table are close to the occupied ones. This makes it necessary to add a few extra functions for the lowest unoccupied levels in order to get a description which corresponds to the general level of accuracy one expects from the hierarchical basis set names SZ-TZ2P (old names I-V). This fact was insufficiently recognized in the previous ADF basis sets. In our tests this led to higher errors in the energy for the diatomics containing for example Li, Be, K, Ca and so on. By adding appropriate functions we have corrected this. As a consequence, the basis set quality for a particular subdirectory is now more uniform throughout the periodic system. At the same time we have attempted to increase the number of functions in a systematic fashion so that each element is described by at least as many functions of a particular l value as its predecessor.

The ZORA/QZ4P basis sets might be roughly described as core triple zeta, valence quadruple zeta, with 4 polarization functions (2 d and 2 f functions for C, 2 p and 2 d for H). The fit sets corresponding to these basis sets are also much larger than the fit sets found in basis sets SZ-TZ2P (old names I-V). If one has doubts about the adequacy of a fit set for a certain element, this can be tested by replacing its fit set by the large one from the QZ4P directory. In the ZORA/QZ4P basis sets, the choice for the exponents of the polarization functions was done in a systematic, but somewhat hand-waving manner. For this reason the exponents were always rounded to half integers. Also the geometric mean of the exponents usually does not coincide with the choices made in directories SZ-TZ2P (old names I-V) and the ET basis sets. However, the fact that two polarization functions (with reasonable exponents) are present instead of a single one is far more important. A reasonable intermediate basis set, in size between V and QZ4P might be envisaged in which a single polarization function is added, as described above. This is roughly the choice for the polarization functions made in the ET directory VI.