Assessment of basis sets for density functional theory-based calculations of core-electron spectroscopies

Abstract

The performance of Gaussian basis sets for density functional theory-based calculations of core-electron spectroscopies is assessed. The convergence of core-electron binding energies and core-excitation energies using a range of basis sets including split-valence, correlation-consistent, polarisation-consistent and individual gauge for localised orbitals basis sets is studied. For self-consistent field calculations of core-electron binding energies and core-excitation energies of first-row elements, relatively small basis sets can accurately reproduce the values of much larger basis sets, with the IGLO basis sets performing particularly well. Calculations for the K-edge of second-row elements are more challenging, and of the smaller basis sets, pcSseg-2 has the best performance. For the correlation-consistent basis sets, inclusion of core-valence correlation functions is important, with the cc-pCVTZ basis set giving accurate results. Time-dependent density functional theory-based calculations of core-excitation energies show less sensitivity to the basis set with relatively small basis sets, such as pcSseg-1 or pcSseg-2, reproducing the values for much larger basis sets accurately. In contrast, time-dependent density functional theory calculations of X-ray emission energies are highly dependent on the basis set, but the IGLO-II, IGLO-III and pcSseg-2 basis sets provide a good level of accuracy.

Efficient simulation of near-edge x-ray absorption fine structure (NEXAFS) in density-functional theory: Comparison of core-level constraining approaches

“…In contrast and also at the GGA level, van Meer et al report that a large basis set introduced a clustering of many spurious states with low oscillator strengths in the virtual space at an energy of -ǫ HOMO , above which the states do not correspond well to excitation energies anymore 108 . Similarly, when using hybrid DFT functionals in another study 58 , the authors also experienced that including too many diffuse basis functions can lead to a decrease in accuracy -a behavior we also observe for many variants in the nitrogen transition energies.…”

“…As particularly the class of explicit variants requires an adequate description of the (typically more diffuse) unoccupied KS states, a number of studies have assessed the numerical convergence of correspondingly simulated spectra for more common localized (Gaussian) basis sets. 47,55,[58][59][60][61][62][63] In contrast, much less is known on the basis set requirements of the latter class of implicit variants (intuitively deemed less demanding) and gener-ally for numeric atomic orbital (NAO) type basis sets. 64 Aiming to establish a numerically most efficient, yet robust protocol for large-scale NEXAFS simulations with NAO basis sets as for instance implemented in the fullpotential DFT code FHI-aims 64,65 , we, therefore, present a systematic investigation using a test set of nitrogenand carbon-containing compounds.…”

Improving the predictive quality of time‐dependent density functional theory calculations of the X‐ray emission spectroscopy of organic molecules

“…The cc-pCVQZ basis set is large and has been shown to give emission energies that are converged with respect to the basis set. [26] The computed spectra reproduce the experimental spectra remarkably well. For all of the molecules, the computed spectra predict the peak heights and their relative energy spacing with a high degree of accuracy.…”

“…The magnitude of these shifts is given in the figure caption, and these shifts are in addition to the energy correction due to relativistic effects. The cc‐pCVQZ basis set is large and has been shown to give emission energies that are converged with respect to the basis set . The computed spectra reproduce the experimental spectra remarkably well.…”

“…This is consistent with the findings of previous studies. [26] It is of interest to have small basis sets that are able to replicate the results of the much larger basis sets at a vastly reduced computational cost.…”