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Published February 25, 2025 | Published
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Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

Buccheri, Alexander1, 2 ORCID icon
Li, Rui3 ORCID icon
Deustua, J. Emiliano3 ORCID icon
Moosavi, S. Mohamad4 ORCID icon
Bygrave, Peter J.1
Manby, Frederick R.1
  • 1. ROR icon University of Bristol
  • 2. ROR icon Max Planck Institute for the Structure and Dynamics of Matter
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon University of Toronto
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Abstract

A novel formulation is presented for the treatment of electrostatics in the periodic GFN1-xTB tight-binding model. Periodic GFN1-xTB is hindered by the functional form of the second-order electrostatics, which only recovers Coulombic behavior at large interatomic distances and lacks a closed-form solution for its Fourier transform. We address this by introducing a binomial expansion of the Klopman-Ohno function to partition short- and long-range interactions, enabling the use of a generalized Ewald summation for the solution of the electrostatic energy. This approach is general and is applicable to any damped potential of the form |Rn + c|-m. Benchmarks on the X23 molecular crystal dataset and a range of prototypical bulk semiconductors demonstrate that this systematic treatment of the electrostatics eliminates unphysical behavior in the equation of state curves. In the bulk systems studied, we observe a mean absolute error in total energy of 35 meV/atom, comparable to the machine-learned universal force field, M3GNet, and sufficiently precise for structure relaxation. These results highlight the promising potential of GFN1-xTB as a universal tight-binding parametrization.

Copyright and License

© 2025 The Authors. Published by American Chemical Society. This publication is licensed under CC-BY 4.0.

Acknowledgement

The authors thank Neil Allan and Thomas Miller for insightful converations, and the developers of both DFTB+ and TBLite for their robust, open-source packages. A.B. thanks Miguel Marques for dicussions on universal force fields, and Nicolas Tancogne-Dejean for reading an early draft of the manuscript.

Funding

This material is based upon work supported by the U.K. EPSRC grant EP/P022308/1, and the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0019390. Open access funded by Max Planck Society.

Contributions

A.B., R.L., and E.D. contributed equally to this work. A.B implemented the periodic GFN1-xTB model, derived the expansion of the KO γ-potential in terms of the binomial theorem, wrote the python workflows for performing and processing calculations, and performed the calculations. R.L implemented the periodic GFN1-xTB model, derived the k = 0 term for S3, derived the gradient theory and implemented the forces, and performed the QCore calculations. J.E.D resolved several blocking issues in the periodic GFN1-xTB implementation, and performed DFT MOF calculations. S.M.M. performed MOF calculations with QCore. P.J.B. supervised and contributed to both the molecular and periodic implementations of the GFN1-xTB model. F.R.M. conceived and supervised the project. All authors discussed the results of the manuscript before submission.

Supplemental Material

  • Materials Project IDs, calculation settings and EOS plots for all systems studied, as well as additional details on the asymptotic expansion of the hypergeometric function, and a full derivation of the gradient theory for periodic GFN1-xTB (PDF)

Files

buccheri-et-al-2025-periodic-gfn1-xtb-tight-binding-a-generalized-ewald-partitioning-scheme-for-the-klopman-ohno.pdf

Additional details

Funding Dates Caltech Custom Metadata
Created:
March 17, 2025
Modified:
March 17, 2025