Machine Learning Optimization of the Collocation Point Set for Solving the Kohn-Sham Equation.

Area of Science:

• Computational Quantum Chemistry
• Materials Science
• Machine Learning Applications

Background:

• The rectangular collocation method offers an alternative to traditional approaches for solving the Schrödinger equation.
• This method allows for basis functions with limited spatial amplitude and avoids issues with potential discontinuities.
• Solving the Kohn-Sham equation is fundamental to density functional theory (DFT) calculations.

Purpose of the Study:

• To investigate the application of machine learning (ML) to reduce the computational cost of the rectangular collocation method.
• To demonstrate the efficacy of ML in optimizing the collocation point set for solving the Kohn-Sham equation.
• To assess the impact of ML-driven point set reduction on the accuracy of DFT calculations.

Main Methods:

• Employed a rectangular collocation approach to solve the Kohn-Sham equation.
• Utilized machine learning, specifically Gaussian process regression and a genetic algorithm, to drastically reduce the number of collocation points.
• Performed calculations for molecular systems CO and H2O, focusing on the effective potential, orbital energies, and orbital shapes.

Main Results:

• Successfully reduced the collocation point set size by over an order of magnitude, from approximately 51,000 to 2,000 points.
• Maintained accuracy at the mHartree level despite the significant reduction in collocation points.
• Demonstrated the feasibility of ML for optimizing basis sets in quantum mechanical calculations.

Conclusions:

• Machine learning techniques can substantially enhance the efficiency of the rectangular collocation method for solving the Kohn-Sham equation.
• This ML-driven optimization allows for faster and more resource-efficient DFT calculations without compromising accuracy.
• The findings pave the way for accelerating complex quantum chemical simulations using intelligent computational strategies.