Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation

Abstract

Semi-empirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semi-empirical model still in widespread use in chemistry is Hückel's $\pi$-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework, based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations, using standard gradient-based optimization algorithms.

31 pages, 16 Figures

References in corpus (9)

• Array Programming with NumPy
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Bayesian optimization with known experimental and design constraints for chemistry applications
• Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization
• Differentiable quantum chemistry with PySCF for molecules and materials at the mean-field level and beyond
• Automatic Differentiation for the Direct Minimization Approach to the Hartree-Fock Method
• Differentiable Physics: A Position Piece
• Inverse design of dissipative quantum steady-states with implicit differentiation
• Automatic differentiation for coupled cluster methods

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