Noise-Tolerant Force Calculations in Density Functional Theory: A Surface Integral Approach for Wavelet-Based...

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Traditional force calculations in Density Functional Theory (DFT) using the Hellmann-Feynman theorem can suffer from inaccuracies, particularly with advanced basis set representations like wavelets.
• Accurate computation of forces is crucial for molecular dynamics simulations and predicting material properties.

Purpose of the Study:

• To introduce and validate a new method for computing quantum mechanical forces in DFT.
• To address the limitations of the Hellmann-Feynman theorem in specific computational contexts.
• To provide accurate force data for training machine-learned potentials.

Main Methods:

• Developed a method for calculating forces via surface integrals of the quantum mechanical stress tensor.
• Applied the method to systems utilizing multiresolution wavelet representations of orbitals.
• Integrated the force calculation method with machine learning techniques for potential training.

Main Results:

• The surface integral method yields highly accurate forces, showing superior consistency with the potential energy surface compared to the Hellmann-Feynman theorem.
• The approach demonstrates robustness and reliability, particularly for DFT with discontinuous basis sets and wavelet methods.
• Forces computed using surface integrals are accurate enough for training machine-learned potentials, unlike those from the Hellmann-Feynman theorem.

Conclusions:

• Surface integrals over the stress tensor provide a more accurate and reliable alternative for force computations in DFT, especially with wavelet-based methods.
• This method overcomes key limitations of the Hellmann-Feynman theorem for specific basis sets.
• The high accuracy of forces from surface integrals enables their effective use in developing advanced machine-learned potentials.