Benchmarking Basis Sets for Density Functional Theory Thermochemistry Calculations: Why Unpolarized Basis Sets and the Polarized 6‑311G Family Should Be Avoided

Basis
sets are a crucial but often largely overlooked choice in
setting up quantum chemistry calculations. The choice of the basis
set can be critical in determining the accuracy and calculation time
of your quantum chemistry calculations. Clear recommendations based
on thorough benchmarking are essential but not readily available currently.
This study investigates the relative quality of basis sets for general
properties by benchmarking basis set performance for a diverse set
of 139 reactions (from the diet-150-GMTKN55 data set). In our analysis,
we find the distributions of errors are often significantly non-Gaussian,
meaning that the joint consideration of median errors, mean absolute
errors, and outlier statistics is helpful to provide a holistic understanding
of basis set performance. Our direct comparison of performance between
most modern basis sets provides quantitative evidence for basis set
recommendations that broadly align with the established understanding
of basis set experts and is evident in the design of modern basis
sets. For example, while zeta is a good measure of quality, it is
not the only determining factor for an accurate calculation with unpolarized
double- and triple-ζ basis sets (like 6-31G and 6-311G) having
very poor performance. Appropriate use of polarization functions (e.g.,
6-31G*) is essential to obtain the accuracy offered by double- or
triple-ζ basis sets. In our study, the best performances for double- and triple-ζ basis sets
are 6-31++G** and pcseg-2, respectively. However, the performances
of singly polarized double-ζ and doubly polarized triple-ζ
basis sets are quite similar with one key exception: the polarized
6-311G basis set family has poor parametrization, which means its
performance is more like a double-ζ than a triple-ζ basis
set. All versions of the 6-311G basis set family should be avoided
entirely for valence chemistry calculations moving forward.