Machine learning modeling of Wigner intracule functionals for two electrons in one-dimension

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Machine Learning in Physics

Background:

• Accurate computation of many-electron correlation energy is crucial in quantum chemistry.
• The Wigner distribution function (W) offers a promising alternative to traditional methods.
• A universal functional transformation (F) theoretically links W to correlation energy, but its exact form is unknown.

Purpose of the Study:

• To develop a machine learning model for the unknown functional transformation (F).
• To accurately predict many-electron correlation energies using the Wigner distribution function (W).
• To investigate the application of kernel methods and regularization techniques for this quantum mechanical problem.

Main Methods:

• Utilized a dataset of 923 one-dimensional external potentials with two interacting electrons.
• Applied machine learning, specifically the kernel Ansatz, to model the functional transformation (F).
• Employed a one-step regularization technique to prevent over-fitting to specific phase-space regions.
• Computed reference correlation energies using exact and Hartree-Fock calculations with discrete variable representation.

Main Results:

• Developed machine learning models that require the Wigner distribution function (W) at the Hartree-Fock level as input.
• Achieved monotonous decay in predicted correlation energies for new molecular systems.
• Reached sub-chemical accuracy in the prediction of correlation energies, demonstrating the model's predictive power.

Conclusions:

• Machine learning provides a viable route to model the universal functional transformation (F) for correlation energy.
• The developed models show high accuracy and potential for predicting electronic correlation energies.
• This work advances the use of the Wigner distribution function in quantum chemical calculations.