Polarization of core orbitals and computation of nuclear quadrupole coupling constants using Gaussian basis sets

Abstract

Most standard Gaussian basis sets for first row atoms, even large sets designed to converge on a ‘complete basis set’ limit, systematically overestimate the electric field gradient at nuclear sites for first row atoms, resulting in errors of up to 15% in the computation of nuclear quadrupole coupling constants. This error results from a failure to include tight d functions, which permit the core 1s orbitals to distort under the influence of the field of the nuclear quadrupole. Augmentation of standard basis sets with a single set of single-exponent d functions, matched to the reciprocal square of the nominal 1s radius, reduces these errors by up to 90%.

Ion Dynamics in Li2CO3 Studied by Solid-State NMR and First-Principles Calculations

“…Good agreement is observed between the calculated and fitted NMR parameters, although the 7 Li C Q is overestimated by approximately 20%. We note that the overestimation of C Q values by up to 12% has been observed in studies of other oxide materials and may be an inherent error of the DFT method and/or pseudopotential used. , Previous studies have noted that, for first row elements such as Li, polarization of the K shell electrons leads to a small induced K shell quadrupole moment that opposes the nuclear quadrupole moment, and leads to a reduction in the apparent C Q by 12–15% for lithium. , Theoretical approaches will fail to account for this reduction unless a specific spherical pseudopotential combining elements of the nucleus and 1s orbital is used.…”

“…15,32 Previous studies have noted that, for first row elements such as Li, polarization of the K shell electrons leads to a small induced K shell quadrupole moment that opposes the nuclear quadrupole moment, and leads to a reduction in the apparent C Q by 12−15% for lithium. 39,40 Theoretical approaches will fail to account for this reduction unless a specific spherical pseudopotential combining elements of the nucleus and 1s orbital is used. The results of the calculations, together with the symmetry of the structure, show that while there is only a single crystallographic Li site in the structure, there are two magnetically inequivalent Li sites (shown in Supporting Information), which have different relative orientations of the electric field gradient (EFG) tensor relative to the crystal-fixed frame.…”

Fast and Accurate Electric Field Gradient Calculations in Molecular Solids With Density Functional Theory

“…However, this improvement is equal to the average experimental uncertainty of the benchmark set. This result is surprising given previous results employing wave function-based correlation methods that showed improved accuracy in the predicted C q values through the introduction of tight d functions (Harbison, 2015). Extending the GIPAW + MC model to wave function methods with custom Gaussian basis sets is a topic of an ongoing investigation.…”

“…Unlike the CS tensor, comparing predicted EFG tensors (Eqs 2, 3) with experiment does not involve regression and therefore does not benefit from systematic error correction. In addition, previous studies involving GIAO-based EFG tensor predictions demonstrated improved accuracy in the predicted C q values through the introduction of tight d functions (Harbison, 2015). Therefore, care must be taken to ensure the predicted EFG tensor components are well-converged with respect to basis set.…”

“…Specifically, introducing a molecular correction carried out at the PBE0/cc-pCVTZ level reduces the RMS error by 31% and reduced the maximum absolute error by 26%. The choice of density functional and basis set used in the preliminary analysis was motivated by previous studies (Harbison, 2015;Dračínský et al, 2019). In the following sections we thoroughly examine basis set convergence and the relative performance of different hybrid density functionals.…”