Leveraging Normalizing Flows for Orbital-Free Density Functional Theory

Abstract

Orbital-free density functional theory (OF-DFT) for real-space systems has historically depended on Lagrange optimization techniques, primarily due to the inability of previously proposed electron density approaches to ensure the normalization constraint. This study illustrates how leveraging contemporary generative models, notably normalizing flows (NFs), can surmount this challenge. We develop a Lagrangian-free optimization framework by employing these machine learning models for the electron density. This diverse approach also integrates cutting-edge variational inference techniques and equivariant deep learning models, offering an innovative reformulation to the OF-DFT problem. We demonstrate the versatility of our framework by simulating a one-dimensional diatomic system, LiH, and comprehensive simulations of hydrogen, lithium hydride, water, and four hydrocarbon molecules. The inherent flexibility of NFs facilitates initialization with promolecular densities, markedly enhancing the efficiency of the optimization process.

7 pages, 5 Figures, (SI: 17 pages, 6 figures)

References in corpus (13)

• Learning the exchange-correlation functional from nature with fully differentiable density functional theory
• Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression
• Evolving symbolic density functionals
• Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond
• Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning
• Grad DFT: a software library for machine learning enhanced density functional theory
• Automatic Differentiation for Orbital-Free Density Functional Theory
• Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation
• Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional
• Kinetic Energy Density Functionals by Axiomatic Approach
• Deep learning density functionals for gradient descent optimization
• Orbital-Free Quasi-Density Functional Theory
• Efficient single-grid and multi-grid solvers for real-space orbital-free density functional theory

Cited by in corpus (1)

• MOLPIPx: an end-to-end differentiable package for permutationally invariant polynomials in Python and Rust