Pure non-local machine-learned density functional theory for electron correlation.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Density-functional theory (DFT) is a cornerstone of computational chemistry for predicting material properties.
• Existing density-functional approximations (DFAs) struggle with electron correlation, leading to inaccuracies like self-interaction errors.
• There is a need for more accurate and efficient methods to describe chemical bonding and interactions.

Purpose of the Study:

• To develop a novel machine-learning based density-functional approximation (DFA).
• To create a pure, non-local, and transferable functional.
• To achieve gold-standard accuracy in predicting chemical interactions and properties.

Main Methods:

• Development of Kernel Density Functional Approximations (KDFAs) using machine learning.
• Training KDFAs with high-accuracy reference methods.
• Applying KDFAs to diverse chemical interactions (non-covalent, ionic, covalent) and system sizes.
• Utilizing KDFAs at mean-field computational cost.

Main Results:

• KDFAs demonstrate high accuracy across various chemical interaction types.
• The developed functionals are transferable across different system sizes.
• Achieved unprecedented accuracy, comparable to coupled cluster methods, for the protonated water dimer's free energy surface.
• Computational cost remains comparable to standard DFAs.

Conclusions:

• KDFAs represent a significant advancement in density-functional theory, bridging accuracy and computational efficiency.
• This machine-learning approach enables accurate calculations of complex systems previously computationally prohibitive.
• KDFAs offer a promising new direction for computational chemistry and materials science research.