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Updated: Mar 13, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Computation of indirect nuclear spin-spin couplings with reduced complexity in pure and hybrid density functional
Arne Luenser1, Jörg Kussmann1, Christian Ochsenfeld1
1Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU Munich) and Center for Integrated Protein Science Munich (CIPSM, LMU Munich), Butenandtstr. 5-13, D-81377 Munich, Germany.
Abstract:
We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.
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