Accurate Hellmann-Feynman forces from density functional calculations with augmented Gaussian basis sets.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• The Hellmann-Feynman (HF) theorem offers a direct method for calculating forces from electron density.
• Machine learning (ML) models for electron density promise efficient force calculations in large systems.
• A significant barrier to HF theorem adoption with atom-centered basis sets is the Pulay force error.

Purpose of the Study:

• To demonstrate a method for suppressing the Pulay force in HF calculations.
• To enable accurate force calculations for large molecular systems using ML-derived electron densities.
• To facilitate reliable geometry optimization and molecular dynamics simulations with HF forces.

Main Methods:

• Utilizing density functional calculations with suitably augmented Gaussian basis sets.
• Suppressing the Pulay force by careful selection of basis sets.
• Comparing HF forces with analytical forces for accuracy.

Main Results:

• The Pulay force can be effectively suppressed using augmented Gaussian basis sets.
• HF forces computed with this method achieve accuracy comparable to state-of-the-art analytical forces.
• Reliable geometry optimization and molecular dynamics are achievable with HF forces.

Conclusions:

• Augmented basis sets overcome the Pulay force issue, enabling accurate HF force calculations.
• This approach paves the way for efficient and accurate simulations of large systems using ML densities and the HF theorem.
• The findings support the broader application of the HF theorem in computational chemistry and materials science.