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

Area of Science:

• Computational chemistry
• Materials science
• Solid-state physics

Background:

• The periodic GFN1-xTB tight-binding model faces challenges with its second-order electrostatic functional form.
• This functional form exhibits Coulombic behavior only at large distances and lacks a closed-form Fourier transform solution.

Purpose of the Study:

• To develop a novel formulation for treating electrostatics within the periodic GFN1-xTB model.
• To overcome the limitations of the existing electrostatic functional form for improved accuracy.

Main Methods:

• Introduced a binomial expansion of the Klopman-Ohno function to partition short- and long-range interactions.
• Applied a generalized Ewald summation to solve the electrostatic energy for damped potentials of the form |R^n + c|^−m.

Main Results:

• Eliminated unphysical behavior in equation of state curves for molecular crystals and bulk semiconductors.
• Achieved a mean absolute energy error of 35 meV/atom in bulk systems, comparable to M3GNet.
• Demonstrated sufficient precision for accurate structure relaxation.

Conclusions:

• The developed electrostatic treatment significantly improves the periodic GFN1-xTB model.
• GFN1-xTB shows strong potential as a universal tight-binding parametrization for materials simulations.