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Semi-empirical quantum chemistry has recently seen a renaissance withapplications in high-throughput virtual screening and machine learning. Thesimplest semi-empirical model still in widespread use in chemistry isH\"uckel's $\pi$-electron molecular orbital theory. In this work, weimplemented a H\"uckel program using differentiable programming with the JAXframework, based on limited modifications of a pre-existing NumPy version. Theauto-differentiable H\"uckel code enabled efficient gradient-based optimizationof model parameters tuned for excitation energies and molecularpolarizabilities, respectively, based on as few as 100 data points from densityfunctional theory simulations. In particular, the facile computation of thepolarizability, a second-order derivative, via auto-differentiation shows thepotential of differentiable programming to bypass the need for numericdifferentiation or derivation of analytical expressions. Finally, we employgradient-based optimization of atom identity for inverse design of organicelectronic materials with targeted orbital energy gaps and polarizabilities.Optimized structures are obtained after as little as 15 iterations, usingstandard gradient-based optimization algorithms.

Inverse molecular design and parameter optimization with H\"uckel theory using automatic differentiation