Multi-objective evolutionary strategy for improving semiempirical Hamiltonians in the study of enzymatic reactions at the QM/MM level of theory

Quantum mechanics/molecular mechanics (QM/MM) simulations are crucial for understanding enzymatic reactions, but their accuracy depends heavily on the quantum-mechanical method used. Semiempirical methods offer computational efficiency but often struggle with accuracy in complex systems. This work presents a novel multi-objective evolutionary strategy for optimizing semiempirical Hamiltonians, specifically designed to enhance their performance in enzymatic QM/MM simulations while remaining broadly applicable to condensed-phase systems. Our methodology combines automated parameter optimization, targeting \textit{ab initio} or density functional theory (DFT)-reference potential energy surfaces, atomic charges, and gradients, with comprehensive validation through minimum free energy path (MFEP) calculations. To demonstrate its effectiveness, we applied our approach to improve the GFN2-xTB Hamiltonian using two enzymatic systems that involve hydride transfer reactions where the activation energy barrier is severely underestimated: Crotonyl-CoA carboxylase/reductase (CCR) and dihydrofolate reductase (DHFR). The optimized parameters showed significant improvements in reproducing potential and free energy surfaces, closely matching higher-level DFT calculations. Through an efficient two-stage optimization process, we first developed parameters for CCR using reaction path data, then refined these parameters for DHFR by incorporating a targeted set of additional training geometries. This strategic approach minimized the computational cost while achieving accurate descriptions of both systems, as validated through QM/MM simulations using the Adaptive String Method (ASM). Our method represents an efficient approach for optimizing semiempirical methods to study larger systems and longer timescales, with potential applications in enzymatic reaction mechanisms studies, drug design, and enzyme engineering.