Essentials of Computational Chemistry

180 6 AB INITIO HARTREE–FOCK MO THEORY
triple-ζ contractions are provided, (ii) polarization functions of increasingly higher angular
momentum are included for the triple-ζ case, and (iii) diffuse functions were optimized for
negative ions at a correlated level of electronic structure theory.
6.2.8 Sources
Most electronic structure programs come with a library of built-in basis sets, to include
many if not all of those mentioned above. A tremendously useful electronic resource is the
Environmental Molecular Sciences Laboratory Gaussian Basis Set Order Form, a website that
permits the download of a very large number of different basis sets formatted for a variety
of different software packages. Moreover, the site has reference information that typically
includes values for test calculations as published by the original authors. Since different
software packages may have different conventions for how to deal with certain aspects of
the basis set (e.g., five spherical vs. six Cartesian d functions), it is always a good idea to
carry out such test calculations to ensure that the basis set is being used in a manner consistent
with its definition and, hopefully, with previously reported calculations in the literature.
So, how to choose the ‘best’ basis set for the problem at hand? Obviously a fair rule of
thumb is that bigger is better, keeping in mind issues of balance between valence decontraction
and presence of polarization functions. As noted above, diffuse functions are warranted
in certain specific situations, but in the absence of those situations, there tends to be no
strong reason to include them.
Additionally, access to particular software packages may play some role in motivating the
choice of basis set. Some packages are equipped to take advantage of efficiencies possible
for such features as combined s and p exponents, or general contractions, while others are
not, and there may thus be significant timing issues differentiating basis sets.
Finally, and perhaps most important for the vast majority of chemical problems where
saturation of the basis set is not a practical possibility, the choice should consider the degree
to which other results from that particular basis set at that particular level of theory are
available for comparison. For instance, to the extent that there are an enormous number
of HF/6-31G(d) results published, and thus a reasonably firm understanding of the specific
successes and failures of the model, this can assist in the interpretation of new results – Pople
has referred to the collection of all data from a given theoretical prescription as comprising
a ‘model chemistry’ and emphasized the utility of analyzing theoretical performance (and
future model development efforts) within such a framework.
6.3 Key Technical and Practical Points of Hartree–Fock Theory
A deep understanding of the underlying theory is, alas, of only limited value in successfully
carrying out a HF calculation with any given software package. This section is not designed
to supplant program users’ manuals, the utility of reading which cannot be overemphasized,
but discusses aspects of practical HF calculations that are often glossed over in formal
presentations of the theory.