Multi-Objective Optimization of Molecular Hyperpolarizability via NSGA-II with Hierarchical Quantum Chemical Screening

The design of organic molecules with large first hyperpolarizabilities (β) is important for developing nonlinear optical (NLO) materials for applications in optical switching, frequency conversion, and photonic devices. However, the vast chemical space and computational expense of accurate quantum mechanical calculations present significant challenges for molecular discovery. We present the multi-objective evolutionary algorithm Non-dominated Sorting Genetic Algorithm II (NSGA-II) with a hierarchical computational screening approach to efficiently identify molecules with optimal trade-offs between hyperpolarizability and molecular complexity.

Our approach employs GFN2-xTB, a semi-empirical tight-binding method, as a rapid surrogate model to evaluate thousands of candidate molecules during the evolutionary optimization. The NSGA-II algorithm simultaneously optimizes for maximum hyperpolarizability while minimizing molecular size, generating Pareto-optimal solutions with the best compromises between these competing objectives. The molecular design space is constrained to organic molecules containing only C, N, O, and H atoms with single and double bonds, ensuring synthetic accessibility while maintaining chemical diversity through mutation operators.

Promising candidates from the Pareto front undergo validation through a hierarchical screening process using MOPAC PM7 semi-empirical calculations for refined estimates of hyperpolarizability. This multi-scale approach balances computational efficiency with prediction accuracy, enabling exploration of chemical space at scales impractical for ab initio methods alone. Final validation of the solution molecules is conducted using B3LYP density functional theory calculations with appropriate basis sets.

Initial results demonstrate the framework's ability to discover diverse molecular scaffolds with enhanced NLO properties. The methodology provides a computationally efficient pathway for the rational design of NLO materials.