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

Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel’s π-electron molecular orbital theory. In this work, we implemented a Hückel pr...

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Bibliographic Details
Published in:	The Journal of chemical physics 2023-03, Vol.158 (10), p.104801-104801
Main Authors:	Vargas–Hernández, Rodrigo A., Jorner, Kjell, Pollice, Robert, Aspuru–Guzik, Alán
Format:	Article
Language:	eng
Subjects:	Algorithms Data points Density functional theory Design optimization Design parameters Differentiation Electronic materials Energy gap Inverse design Machine learning Mathematical models Molecular orbitals Optimization Physics Pi-electrons Quantum chemistry
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Summary:	Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel’s π-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.
ISSN:	0021-9606 1089-7690 1089-7690