Mitigating error cancellation in density functional approximations via machine learning correction

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• Density functional approximations (DFAs) are widely used but limited by system-dependent error cancellation.
• Achieving high accuracy in thermochemical and kinetic energy predictions often relies on this error cancellation, hindering transferability.
• Machine learning (ML) integration offers a path to improve DFA accuracy and reliability.

Purpose of the Study:

• To develop a novel ML-based correction for the B3LYP functional, directly addressing its deviations from the exact exchange-correlation functional.
• To create a transferable and accurate DFA without relying on error cancellation.
• To enhance the predictive power of density functional theory (DFT) for chemical energy calculations.

Main Methods:

• Developed a ML model to correct the B3LYP functional using highly accurate absolute energies as reference data.
• Attributed errors to real-space pointwise contributions for ML model optimization.
• Implemented a double-cycle protocol incorporating self-consistent field (SCF) calculations into the training workflow.

Main Results:

• The ML-corrected B3LYP functional demonstrated improved accuracy in calculated relative energies.
• The ML model, trained exclusively on absolute energies, successfully eliminated the need for error cancellation.
• Comprehensive benchmarks confirmed significant performance improvements over the original B3LYP for thermochemical and kinetic energy calculations.

Conclusions:

• Robust and accurate DFAs can be constructed by directly targeting functional errors, bypassing the limitations of error cancellation.
• The ML-corrected B3LYP functional provides a versatile and superior alternative for various computational chemistry applications.
• This approach offers a promising strategy for developing more accurate and transferable density functional methods.