Reducing the Quantum Many-Electron Problem to Two Electrons with Machine Learning.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Machine learning

Background:

• The many-electron problem poses a significant challenge in computational chemistry, with existing methods scaling poorly with system size.
• Calculating molecular energies relies on two-electron wave functions, but determining their occupation distribution (geminal occupations) is complex.
• An extended "aufbau" principle offers a physically elegant approach but requires accurate geminal occupation distributions.

Purpose of the Study:

• To introduce a novel computational paradigm for electronic structure calculations.
• To develop a machine learning model capable of learning geminal occupation distributions.
• To address the challenge of the many-electron problem in computational chemistry.

Main Methods:

• A convolutional neural network was employed to learn approximate geminal-occupation distributions.
• The neural network was trained on hydrocarbon isomers with 2-7 carbon atoms.
• The model was validated by predicting energies for octane isomers and larger hydrocarbons (8-15 carbons).

Main Results:

• The convolutional neural network successfully learned the N-representability conditions, ensuring valid electron distributions.
• The model accurately predicted molecular energies for systems beyond its training set.
• The approach demonstrated the feasibility of reducing the many-electron problem to an effective two-electron problem.

Conclusions:

• Machine learning offers a powerful tool to overcome the limitations of traditional computational chemistry methods.
• This new paradigm enables accurate electronic structure predictions by effectively solving the many-electron problem.
• The developed method opens new avenues for efficient and accurate molecular energy calculations.