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Automated Discovery of Algorithms for Molecular Electronic Structure Calculations Using Physics-Informed Program
Kyle Acheson1, Rastislav Turanyi1, Scott Habershon1
1Department of Chemistry, University of Warwick, Coventry CV4 7AL, U.K.
Journal of the American Chemical Society
|March 13, 2026
Summary
We developed a new physics-informed program synthesis (PIPS) method to create algorithms that approximate electronic structure calculations like Hartree-Fock (HF) and density-functional theory (DFT) without iterative self-consistent field steps.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Algorithm Development
Background:
- Electronic structure calculations are crucial for understanding molecular properties.
- Traditional methods like Hartree-Fock (HF) and density-functional theory (DFT) rely on computationally intensive self-consistent field (SCF) iterations.
- Developing faster yet accurate methods is essential for advancing computational chemistry.
Purpose of the Study:
- To introduce a novel physics-informed program synthesis (PIPS) approach.
- To generate algorithms that bypass the need for SCF iterations in electronic structure calculations.
- To achieve accurate approximations of HF and DFT results with significantly reduced computational cost.
Main Methods:
- Exploiting the property that eigenvectors of the Fock matrix (F) are invariant under a class of matrix functions f(F).
- Utilizing PIPS to search for matrices (M) that produce identical molecular orbital coefficients as converged HF or DFT calculations.
- Validating the generated algorithms on heterodiatomic molecules and various hydrocarbon chains.
Main Results:
- Successfully generated new algorithms that accurately predict total energies for small molecules and alkanes.
- Achieved accuracy within 0.1 kcal/mol/atom compared to HF or DFT energies.
- Demonstrated that the new algorithms require only a single matrix diagonalization, eliminating SCF iterations.
- Showcased the transferability and efficiency of the PIPS-generated algorithms on larger alkane systems (C8-C20).
Conclusions:
- PIPS offers a powerful, optimization-based pathway to discover novel, efficient algorithms for molecular quantum chemistry.
- The demonstrated approach can significantly accelerate electronic structure calculations without sacrificing accuracy.
- This method holds potential for application to more complex wave function ansatze, broadening its impact in computational chemistry.
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