Benchmark of approximate quantum chemical and machine learning potentials for biochemical proton transfer reactions

Proton transfer reactions are among the most common chemical transformations and are central to enzymatic catalysis and bioenergetic processes. Their mechanisms are often investigated using DFT or approximate quantum chemical methods, whose accuracy directly impacts the reliability of the simulations. Here, a comprehensive set of semiempirical molecular-orbital and tight-binding DFT approaches, along with recently developed machine learning (ML) potentials, are benchmarked against high-level MP2 reference data for a curated set of proton transfer reactions representative of biochemical systems. Relative energies, geometries and dipole moments are evaluated for isolated reactions. Microsolvated reactions are also simulated using a hybrid QM/MM partition. Traditional DFT methods offer high accuracy in general but show markedly larger deviations for proton transfers involving nitrogen-containing groups. Among approximate models, RM1, PM6, PM7, DFTB2-NH, DFTB3 and GFN2-xTB show reasonable accuracy across properties, though their performance varies by chemical group. Strikingly, the ML-corrected ($\Delta$-learning) model PM6-ML improves accuracy for all properties and chemical groups, and transfers well to QM/MM simulations. Conversely, standalone ML potentials perform poorly for most reactions. These results provide a basis for evaluating approximate methods and selecting potentials for proton transfer simulations in complex environments.