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

Abstract

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.

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

“…In practice, the “3” basis function behaves more like a core basis function rather than a valence basis function, suggesting that 6-311G is better characterized as a double core-zeta, double valence-zeta basis set rather than a true triple valence-zeta. Although this basis set design may lead to unexpectedly strong performance in modeling core-dependent properties like NMR spectroscopy, it is recommended that property-specific specialized basis sets be used for the calculation of core-dependent properties • Diffuse functions are very important to reducing errors for double-ζ basis sets in this data set (e.g., 6-31G* at 8.9 kJ mol –1 vs 6-31+G* at 5 kJ mol –1 ).…”

“…Although this basis set design may lead to unexpectedly strong performance in modeling core-dependent properties like NMR spectroscopy, it is recommended that property-specific specialized basis sets be used for the calculation of core-dependent properties. 12 • Diffuse functions are very important to reducing errors for double-ζ basis sets in this data set (e.g., 6-31G* at 8.9 kJ mol −1 vs 6-31+G* at 5 kJ mol −1 ). It is likely these errors are caused by a small number of large outliers in molecules (e.g., anions) where diffuse functions are critical for describing the larger electron distribution.…”

“…The generalizability of these conclusions to other calculation types needs to be considered carefully, and there are certainly some known cases where they will not hold as the basis set requirements are very different. Most strikingly, for core properties such as NMR chemical shifts and coupling constants, the basis set requirements are very different and so a separate benchmarking study has been conducted . For excited states, especially very highly excited states, diffuse functions are likely to be important as the electronic wave function is significantly larger than the ground state wave function.…”

“…Most strikingly, for core properties such as NMR chemical shifts and coupling constants, the basis set requirements are very different and so a separate benchmarking study has been conducted. 12 For excited states, especially very highly excited states, diffuse functions are likely to be important as the electronic wave function is significantly larger than the ground state wave function. Diffuse functions are also known to be important when modeling dipole moments 94 which depend on good descriptions of electron densities further from the nucleus.…”

“…Experts on basis set design can typically advise on the strengths and limitations of particular basis sets; for example, that anions need diffuse functions, − the 6-311G family are not valence-triple-ζ basis sets, and property-specialized basis sets should be used for properties which have unusual basis set demands such as NMR parameters, − EPR parameters, − and X-ray − calculations, to name but a few. Such recommendations are based on a detailed understanding of basis sets design and being able to read and understand the composition of basis sets in terms of primitive exponents and contraction schemes.…”