A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn–Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0–3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work.
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21 December 2022
Research Article|
December 15 2022
Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes
Andreas Hesselmann
;
Andreas Hesselmann
a)
(Investigation, Methodology, Software, Writing – original draft, Writing – review & editing)
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
a)Author to whom correspondence should be addressed: hesselmann@theochem.uni-stuttgart.de
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Hans-Joachim Werner
;
Hans-Joachim Werner
b)
(Investigation, Methodology, Validation, Writing – review & editing)
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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Peter J. Knowles
Peter J. Knowles
c)
(Investigation, Methodology, Software, Writing – review & editing)
2
School of Chemistry, Cardiff University
, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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a)Author to whom correspondence should be addressed: hesselmann@theochem.uni-stuttgart.de
b)
Electronic mail: werner@theochem.uni-stuttgart.de
c)
Electronic mail: KnowlesPJ@cardiff.ac.uk
J. Chem. Phys. 157, 234106 (2022)
Article history
Received:
August 09 2022
Accepted:
November 22 2022
Citation
Andreas Hesselmann, Hans-Joachim Werner, Peter J. Knowles; Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes. J. Chem. Phys. 21 December 2022; 157 (23): 234106. https://doi.org/10.1063/5.0119622
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