Machine learned Hückel theory: Interfacing physics and deep neural networks.

Area of Science:

• Computational Chemistry
• Materials Science
• Machine Learning in Physics

Background:

• The Hückel Hamiltonian is a fundamental tight-binding model for understanding electron behavior in molecules and materials.
• Its simplicity relies on empirical parameters for orbital energies and interatomic interactions, limiting its quantitative accuracy.
• Accurate modeling of electron interactions is crucial for predicting material properties and chemical reactivity.

Purpose of the Study:

• To improve the accuracy of the extended Hückel model using machine learning.
• To develop a dynamically parameterized physics model that retains interpretability.
• To explore the synergy between deep neural networks and simplified physical models.

Main Methods:

• Developed a deep neural network to generate dynamic parameters for the Hückel Hamiltonian.
• Trained the neural network on orbital energies and densities from density functional theory (DFT) calculations.
• Replaced the empirical parameters of the extended Hückel model with machine-learned, dynamic values.

Main Results:

• The machine-learned extended Hückel model demonstrated significantly increased accuracy compared to the original empirical model.
• The deep neural network parameterization proved to be smooth, accurate, and captured key physical insights.
• The enhanced model successfully retained the interpretability inherent in the original Hückel framework.

Conclusions:

• Machine learning offers a powerful approach to enhance the accuracy of simplified physics models like the extended Hückel Hamiltonian.
• Dynamically parameterized models generated by deep neural networks can bridge the gap between qualitative and quantitative predictions.
• This work highlights the potential of integrating machine learning with established physics models for advancing computational science.