Finding density functionals with machine learning.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Machine learning

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• Approximating the kinetic energy functional is crucial for DFT accuracy.
• Machine learning offers a novel approach to developing accurate density functionals.

Purpose of the Study:

• To develop and evaluate machine learning models for approximating the kinetic energy density functional.
• To assess the accuracy and data efficiency of the proposed method.
• To explore the applicability of machine learning to real electronic structure problems.

Main Methods:

• Machine learning models were trained to approximate the kinetic energy of noninteracting fermions in one dimension.
• A predictor was developed to identify densities within the training set's interpolation region.
• Principal Component Analysis (PCA) was used to derive a projected functional derivative.

Main Results:

• Mean absolute errors below 1 kcal/mol were achieved on test densities similar to the training set.
• Fewer than 100 training densities were sufficient to reach high accuracy.
• The predictor effectively identified densities within the interpolation region.
• PCA-derived functional derivative yielded highly accurate self-consistent densities.

Conclusions:

• Machine learning provides an effective route to accurate kinetic energy density functionals.
• The method demonstrates high accuracy and data efficiency for model systems.
• Challenges remain for direct application to complex, real electronic structure problems.