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.

On the specialization of Gaussian basis sets for core-dependent properties.

Despite the fact that most quantum chemistry basis sets are designed for accurately modeling valence chemistry, these general-purpose basis sets continue to be widely used to model core-dependent properties. Core-specialized basis sets are designed with specific features to accurately represent the behavior of the core region. This design typically incorporates Gaussian primitives with higher exponents to capture core behavior effectively, as well as some decontraction of basis functions to provide flexibility in describing the core electronic wave function. The highest Gaussian exponent and the degree of contraction for both s- and p-basis functions effectively characterize these design aspects. In this study, we compare the design and performance of general-purpose basis sets against several literature-based basis sets specifically designed for three core-dependent properties: J coupling constants, hyperfine coupling constants, and magnetic shielding constants (used for calculating chemical shifts). Our findings consistently demonstrate a significant reduction in error when employing core-specialized basis sets, often at a marginal increase in computational cost compared to the popular 6-31G** basis set. Notably, for expedient calculations of J coupling, hyperfine coupling, and magnetic shielding constants, we recommend the use of the pcJ-1, EPR-II, and pcSseg-1 basis sets, respectively. For higher accuracy, the pcJ-2, EPR-III, and pcSseg-2 basis sets are recommended.

Lower Bounds for Nonrelativistic Atomic Energies.

A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory.