Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

Buccheri, Alexander; Li, Rui; Deustua, J. Emiliano; Moosavi, S. Mohamad; Bygrave, Peter J.; Manby, Frederick R.

doi:10.1021/acs.jctc.4c01234

Title: Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

Journal Article · 04 February 2025 · Journal of Chemical Theory and Computation

DOI: https://doi.org/10.1021/acs.jctc.4c01234 · OSTI ID:2523658

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^[4]; Bygrave, Peter J. ^[5]; Manby, Frederick R. ^[5]

University of Bristol (United Kingdom); Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany)
California Institute of Technology, Pasadena, CA (United States)
California Institute of Technology, Pasadena, CA (United States); Examol Corporation, Pittsburgh, PA (United States)
University of Toronto, ON (Canada)
University of Bristol (United Kingdom); Iambic Therapeutics, San Diego, CA (United States)

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.

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Research Organization:: Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019390

OSTI ID:: 2523658

Journal Information:: Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 4 Vol. 21; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Periodic GFN1-xTB Tight Binding: A Generalized Ewald Partitioning Scheme for the Klopman–Ohno Function

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