Automated Discovery of Algorithms for Molecular Electronic Structure Calculations Using Physics-Informed Program...

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.