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

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Semiempirical quantum chemistry, particularly Hückel's π-electron theory, is experiencing a resurgence.
• Applications include high-throughput virtual screening and machine learning in chemistry.

Purpose of the Study:

• Implement a Hückel molecular orbital theory program using differentiable programming (JAX).
• Enable efficient gradient-based optimization of model parameters for excitation energies and polarizabilities.
• Demonstrate inverse design of organic electronic materials with specific properties.

Main Methods:

• Modified a pre-existing NumPy Hückel code using the JAX framework for auto-differentiation.
• Tuned model parameters using gradient-based optimization with data from density functional theory (DFT) simulations.
• Employed gradient-based optimization of atom identity for inverse material design.

Main Results:

• Achieved efficient gradient-based optimization of Hückel parameters for excitation energies and polarizabilities.
• Demonstrated facile computation of polarizability (a second-order derivative) via auto-differentiation.
• Successfully performed inverse design of organic electronic materials, achieving target orbital energy gaps and polarizabilities within 15 iterations.

Conclusions:

• Differentiable programming offers a powerful approach to optimize semiempirical quantum chemistry models.
• Auto-differentiation simplifies the calculation of higher-order derivatives, avoiding numerical differentiation or complex analytical derivations.
• This method facilitates efficient inverse design of novel organic electronic materials.