opt-DDAP: Optimizable Density-Derived Atomic Point Charges via Automatic Differentiation

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Accurate long-range electrostatics in interatomic potentials require atom-centered charges.
• The density-derived atomic point (DDAP) method uses density functional theory (DFT) to derive these charges but has limitations with complex systems.
• Existing DDAP methods rely on fixed parameters and can be numerically unstable.

Purpose of the Study:

• To address the limitations of the DDAP method for calculating atom-centered charges.
• To develop a more robust and accurate method for deriving charges for electrostatic modeling.
• To enable optimization of parameters within the DDAP framework.

Main Methods:

• Reformulated the DDAP algorithm as a differentiable computational graph.
• Employed automatic differentiation to optimize Gaussian basis parameters and reciprocal-space cutoff.
• Replaced the Lagrange-multiplier approach with a pseudoinverse solution and charge renormalization for numerical robustness.

Main Results:

• Demonstrated the ability of opt-DDAP to faithfully reconstruct absolute and difference charge densities.
• Validated the framework on NaCl vacancy supercells and MoS₂.
• Achieved numerical stability even with ill-conditioned matrices.

Conclusions:

• The opt-DDAP framework overcomes the limitations of traditional DDAP methods.
• Optimized charges derived from opt-DDAP can serve as improved inputs for machine learning and empirical interatomic potentials.
• This method enhances the accuracy of electrostatic models incorporating long-range interactions.