5.3.3.8 Which Basis Set Should I Use?
Scores, perhaps hundreds of basis sets have been developed, and new ones appear
yearly, if not monthly. There is something to be said for having a variety of tools in
our armamentarium, but one tends to be not entirely unsympathetic to the descrip-
tion, almost 2 decades ago, of this situation as a “chaotic proliferation” [ 68 ]. There
are books of practical advice [ 1 , 69 ] which help to provide a feel for the appropri-
ateness of various basis sets. By reading the research literature one learns what
approaches, including which basis sets, are being applied to a various problems,
especially those related to the one’s research. This said, one should avoid simply
assuming that the basis used in published work was the most appropriate one: it is
possible that it was either too small or unnecessarily big. Hehre has shown [ 39 ] that
in many cases the use of very large bases is pointless; on the other hand some
problems yield, if at all, only to very large basis sets (see below). A Goldilocks-like
basis can rarely (except for calculations of a cursory or routine nature) be correctly
simply picked; rather, one homes in on it, by experimenting and comparing results
with experimental facts as far as possible. Where egregious deviations from experi-
ment are found at levels that experience suggests should be reliable, one may be
justified in questioning the “facts”. Bachrach places “the first chink in the armor of
the inherent superiority of experiment over computation” in 1970 [ 70 ].
A rational approach in many cases might be to survey the territory first with a
semiempirical method (Chapter 6) or with the STO-3G basis and to use one of these
to create input structures and input Hessians (Section 2.4) for higher-level calcula-
tions) then to move on to the 3–21G()basis or possibly the 6–31G for a reasonable
exploration of the problem. For a novel system for which there is no previous work to
serve as a guide one should move up to larger basis sets and to post-Hartree–Fock
methods (Section 5.4), climbing the latter of sophistication until reasonable conver-
gence of at leastqualitativeresults has been obtained. It is possible for results to
becomeworsewith increasing basis set size [ 71 , 72 ], because of fortuitous cancella-
tion of errors at a lower level. This kind of thing is discussed, albeit with the focus not
directly on basis functions, in several papers with the very apposite words “...the
right answer for the right reason” [ 73 ]. To achieve this happy coincidence of experi-
ment and reality, quite high theoretical levels may be necessary. A somewhat bizarre
phenomenon is that at post Hartree–Fock levels, at least, some fairly large basis sets
predict nonplanar geometries for benzene and similar aromatic hydrocarbons! [ 74 ].
Janoschek has given an excellent survey indicating the reliability of ab initio calcula-
tions and the level at which one might need to work to obtain trustworthy results by
[ 75 ]. After this short litany of warnings, let the reader be reassured that good
geometries, reasonably reliable relative energies, and useful reactivity parameters,
based e.g. on orbital shapes and energies, can often be obtained routinely by standard
methods chosen by comparing their predictions with the experimental facts for a set
of related compounds. Examples of such results are given later in this chapter.
Oxirene (oxacyclopropene) provides a canonical example of a molecule which
even at the highest current levels of theory has declined to reveal its basic secret:
can it exist (“Oxirene: to Be or Not to Be?” [ 53 b])?. Very large basis sets and
5.3 Basis Sets 253