Several simple reactions are used in the first three activities to show
that we cannot rely on chemical intuition alone to guide us in the
choice of a good xc functional approximation. Every chemist is
familiar with the concept of conformational barriers, orcis -trans isomerizations. These reactions are “easy” in
the sense that almost all the functionals that we tried (see SI) get
quantitative results. The reason of such great across-the-board
performance is because the electron densities of the molecules do not
change much throughout the reaction. Even if a functional provides
quantitatively inaccurate densities, it can still provide good results,
as long as it is consistent in the description of the (minimal) changes.
This compensation is called “error cancellation”. In some cases, such
as these simple reactions, error cancellation works to our
advantage—making the results better than expected—but other times it
might work against us. Unfortunately, error cancellation is not
systematic, and there is no way to understand its behavior a
priori . Looking at databases of accurate data can be diagnostic in this
sense, as it can help understanding whether some results are affected or
not.
The second group includes mainly Diels–Alder and isomerizations
reactions. The results for these reactions reveal that some functionals
might be quite inaccurate, even for simple organic reactions. In such
cases, the electron density of the products can be drastically different
than the density of the reactants. Therefore, error cancellation is not
as beneficial as for the molecules of the previous case, and results
must be evaluated carefully.83 Other problematic
reactions include molecules that are bound through non-covalent
interactions. As it has been repeatedly
shown,21,25,26,84–86 most functionals (especially
older ones) are not capable of describing van der Waals interactions. In
2012, the accurate description of non‑covalent interactions was still
listed as a major challenge for DFT.87 Many experts in
the field25,26,88,89 have recently recommended to use
functionals in conjunction with some form of “dispersion correction”
to substantially alleviate this issue. The two most popular corrections
are the -D of Grimme and coworkers,74,76,90,91 and the
VV10 functional of Vydrov and Van Voorhis.75 The -D
approach (in its four different flavors) is very popular, and it comes
at essentially no additional cost. While some functionals—such as the
Minnesota family—have been specifically designed to properly account
for the bonding in the van der Waals region, and therefore they do not
require additional corrections for the majority of cases, adding
dispersion correction to any other functional is in general always
strongly recommended,25,26,88,92 and we align with
this recommendation.a
The last group of reactions shows that seemingly simple molecules like
O3 or CaO can be very challenging for many functionals.
In such situations, we suggest seeking experts’ advice for guidance on
what to do. Before concluding this section, we want to underline one
more time that it is not the aim of this tutorial to provide answers on
how to solve all the issues that might arise in DFT calculations, nor it
is our intention to endorse the usage of newer functionals or to
discourage the usage of older approximations. We have shown (see SI for
numerical results) that for several simple cases 30- or 40-year-oldxc functionals—such as the popular B3LYP
approximation31–34—are perfectly capable of
providing accurate answers. However, it is our purpose to show that
these older xc functionals sometimes fail to provide reliable
results, and newer and more advanced methods are indeed available.
Moreover, for relatively unknown systems, we simply cannot predict in
advance whether older xc functionals are going to be reliable or
not. In conclusion, the question used as title for this section, “which
functional should I use?”, is probably the most difficult to
answer.93
Our final suggestion: Avoid underestimating the difficulty of
choosing a functional, since currently there is still no valid answer to
the question of which functional works best. Do not pick a functional
just because it is the most readily available and rely on recently
published studies and suggestions from experts.