Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Machine Learning

Background:

• Quantum chemistry calculations are computationally expensive, limiting their application to smaller systems.
• Machine learning (ML) models offer reduced computational cost but often lack interpretability (e.g., deep learning 'black boxes').
• Interpretability is crucial for understanding the physical and chemical basis of predictions.

Purpose of the Study:

• To develop interpretable ML models for quantum chemistry.
• To demonstrate that semiempirical quantum chemical (SEQC) models can be trained on data without sacrificing interpretability.
• To achieve high accuracy comparable to established methods like DFT.

Main Methods:

• Utilized a density-functional-based tight binding (DFTB) model with fixed atomic orbital energies and distance-dependent interactions.
• Trained the SEQC model using data from *ab initio* calculations, similar to deep learning training.
• Validated the model's accuracy against coupled cluster energies with complete basis set extrapolation (CCSD(T)*/CBS).

Main Results:

• The trained SEQC model maintained a physically meaningful functional form.
• Achieved accuracy comparable to density functional theory (DFT) for the tested benchmarks.
• Demonstrated that SEQC models can learn from large datasets with reduced *ab initio* data requirements compared to deep learning.

Conclusions:

• Trained SEQC models offer a low-cost, high-accuracy, and interpretable alternative for quantum chemical studies.
• Physically motivated model forms enhance data efficiency in ML for chemistry.
• This approach bridges the gap between computational efficiency and chemical insight.