Component 2: Which basis set should I use?
Choosing a good functional is not the only major component underlying a
successful DFT calculation. The complementary component is the choice of
a suitable basis set. The basis set issue is somehow even more general,
since it is present not only in DFT, but also in all
wave-function-theory–based methods as well, such as in Hartree-Fock
(HF), and in post-HF treatments. However, the relation between a DFT
calculation and its basis set presents unique aspects that are worth
highlighting in this context. Basis sets are usually collected in the
literature into “families”, with those proposed by Pople and
coworkers,94–102 Dunning and
coworkers,103–106 Weigend and
Ahlrichs,107 and Jensen108–111being the most popular for electronic structure calculations. Navigating
the families of basis sets might be as intimidating as the choice of the
functional, especially for beginners. While in principle the issue of
basis set is solved by the simple axiom “the larger, the better”, in
practice, choosing an appropriate basis set always means striking a
compromise between the accuracy of the results and the computational
cost of the calculations. Large molecules quickly become too expensive
with increasing basis set size, and small basis sets are often the only
option for practitioners who want to study large systems with limited
computational capabilities. At the core of the issue is the fact that
every basis set introduces at least two independent sources of error:
one is called basis set incompleteness error
(BSIE),112–114 and the other is called basis set
superposition error (BSSE).15,115 The magnitude of
both BSIE and BSSE is larger when a small basis set is used (e.g. with
double-ζ basis sets), and diminishes with increasing basis set size. The
BSIE is defined as the difference between the results obtained with (or
extrapolated to) a complete basis set, and those obtained with a small
basis set. We discuss BSIE in experiment 4. The BSSE arises when the
calculated energy of a molecule is