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. The ML-corrected (Δ-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.

Institute of Organic Chemistry and Biochemistry Czech Academy of Sciences Prague 160 00 Czech Republic

Instituto de Estudos Avançados Universidade de São Paulo Rua da Praça do Relógio 109 São Paulo SP 05508 050 Brazil

Instituto de Química Universidade de São Paulo Av Prof Lineu Prestes 748 São Paulo SP 05508 900 Brazil

Zobrazit více v PubMed

Nicholls, D. G. ; Ferguson, S. J. . Bioenergetics, 4th ed.; Academic Press: Boston, 2013.

Field, M. J. A Pratical Introduction to the Simulation of Molecular Systems, 2nd ed.; Cambridge University Press: Cambridge, 2007.

Arantes G. M.. Free Energy Profiles for Catalysis by Dual-Specificity Phosphatases. Biochem. J. 2006;399:343–350. doi: 10.1042/BJ20060637. PubMed DOI PMC

Kubar T., Elstner M., Cui Q.. Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines. Annu. Rev. Biophys. 2023;52:525–551. doi: 10.1146/annurev-biophys-111622-091140. PubMed DOI PMC

König P., Ghosh N., Hoffmann M., Elstner M., Tajkhorshid E., Frauenheim T., Cui Q.. Toward theoretical analyis of long-range proton transfer kinetics in biomolecular pumps. J. Phys. Chem. A. 2006;110:548–563. doi: 10.1021/jp052328q. PubMed DOI PMC

Li C., Voth G. A.. A quantitative paradigm for water-assisted proton transport through proteins and other confined spaces. Proc. Natl. Acad. Sci. U. S. A. 2021;118(49):e2113141118. doi: 10.1073/pnas.2113141118. PubMed DOI PMC

Dral, P. O. ; Řezáč, J. . Quantum Chemistry in the Age of Machine Learning, Dral, P. O. , Eds.; Elsevier, 2023, pp. 67–92.

Åqvist J., Warshel A.. Simulation of Enzyme Reactions Using Valence-Bond Force Fields and Other Hybrid Quantum-Classical Approaches. Chem. Rev. 1993;93:2523–2544. doi: 10.1021/cr00023a010. DOI

Porezag D., Frauenheim T., Köhler T., Seifert G., Kaschner R.. Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. Phys. Rev. B. 1995;51:12947–12957. doi: 10.1103/PhysRevB.51.12947. PubMed DOI

Elstner M., Porezag D., Jungnickel G., Elsner J., Haugk M., Frauenheim T., Suhai S., Seifert G.. Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B. 1998;58:7260–7268. doi: 10.1103/PhysRevB.58.7260. DOI

Smith J. S., Nebgen B. T., Zubatyuk R., Lubbers N., Devereux C., Barros K., Tretiak S., Isayev O., Roitberg A. E.. Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning. Nat. Commun. 2019;10(1):2903. doi: 10.1038/s41467-019-10827-4. PubMed DOI PMC

Zheng P., Zubatyuk R., Wu W., Isayev O., Dral P. O.. Artificial intelligence-enhanced quantum chemical method with broad applicability. Nat. Commun. 2021;12(1):7022. doi: 10.1038/s41467-021-27340-2. PubMed DOI PMC

Zhang S., Makoś M. Z., Jadrich R. B., Kraka E., Barros K., Nebgen B. T., Tretiak S., Isayev O., Lubbers N., Messerly R. A., Smith J. S.. Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential. Nat. Chem. 2024;16:727–734. doi: 10.1038/s41557-023-01427-3. PubMed DOI PMC

Arantes G. M., Loos M.. Specific Parametrisation of a Hybrid Potential to Simulate Reactions in Phosphatases. Phys. Chem. Chem. Phys. 2006;8:347–353. doi: 10.1039/B511805K. PubMed DOI

Arantes G. M., Ribeiro M. C. C.. A Microscopic View of Substitution Reactions Solvated by Ionic Liquids. J. Chem. Phys. 2008;128(11):114503. doi: 10.1063/1.2890042. PubMed DOI

Arantes G. M., Field M. J.. Ferric-Thiolate Bond Dissociation Studied with Electronic Structure Calculations. J. Phys. Chem. A. 2015;119:10084–10090. doi: 10.1021/acs.jpca.5b05658. PubMed DOI

Teixeira M. H., Curtolo F., Camilo S. R. G., Field M. J., Zheng P., Li H., Arantes G. M.. Modeling the Hydrolysis of Iron-Sulfur Clusters. J. Chem. Inf. Model. 2020;60:653–660. doi: 10.1021/acs.jcim.9b00881. PubMed DOI

Welborn M., Chen J., Wang L.-P., Van Voorhis T.. Why many semiempirical molecular orbital theories fail for liquid water and how to fix them. J. Comput. Chem. 2015;36:934–939. doi: 10.1002/jcc.23887. PubMed DOI

Hennemann M., Clark T.. A specific MNDO parameterization for water. J. Chem. Phys. 2023;158(3):034106. doi: 10.1063/5.0132863. PubMed DOI

Deng B., Zhong P., Jun K., Riebesell J., Han K., Bartel C. J., Ceder G.. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nat. Mach. Intell. 2023;5:1031–1041. doi: 10.1038/s42256-023-00716-3. DOI

Gaus M., Cui Q., Elstner M.. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB) J. Chem. Theory Comput. 2011;7:931–948. doi: 10.1021/ct100684s. PubMed DOI PMC

Mangiatordi G. F., Brémond E., Adamo C.. DFT and Proton Transfer Reactions: A Benchmark Study on Structure and Kinetics. J. Chem. Theory Comput. 2012;8:3082–3088. doi: 10.1021/ct300338y. PubMed DOI

Nachimuthu S., Gao J., Truhlar D. G.. A benchmark test suite for proton transfer energies and its use to test electronic structure model chemistries. Chem. Phys. 2012;400:8–12. doi: 10.1016/j.chemphys.2012.01.014. PubMed DOI PMC

Kitheka M. M., Redington M., Zhang J., Yao Y., Goyal P.. Benchmarks of the density functional tight-binding method for redox, protonation and electronic properties of quinones. Phys. Chem. Chem. Phys. 2022;24:6742–6756. doi: 10.1039/D1CP05333G. PubMed DOI

Stewart J. J. P.. Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters. J. Mol. Model. 2013;19:1–32. doi: 10.1007/s00894-012-1667-x. PubMed DOI PMC

Stewart J. J. P., Stewart A. C.. A semiempirical method optimized for modeling proteins. J. Mol. Model. 2023;29(9):284. doi: 10.1007/s00894-023-05695-1. PubMed DOI PMC

Grimme S., Bannwarth C., Shushkov P.. A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1–86) J. Chem. Theory Comput. 2017;13:1989–2009. doi: 10.1021/acs.jctc.7b00118. PubMed DOI

Bannwarth C., Ehlert S., Grimme S.. GFN2-xTB: An Accurate and Broadly Parametrized Self-Consistent Tight-Binding Quantum Chemical Method with Multipole Electrostatics and Density-Dependent Dispersion Contributions. J. Chem. Theory Comput. 2019;15:1652–1671. doi: 10.1021/acs.jctc.8b01176. PubMed DOI

Helgaker, T. ; Jørgensen, P. ; Olsen, J. . Molecular Electronic-Structure Theory, 1st ed.; Wiley: New York, 2000.

Weigend F., Ahlrichs R.. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005;7:3297–3305. doi: 10.1039/b508541a. PubMed DOI

Dewar M. J., Thiel W.. Ground States of Molecules. 38. The MNDO Method. Approximation and Parameters. J. Am. Chem. Soc. 1977;99:4899–4907. doi: 10.1021/ja00457a004. DOI

Dewar M. J., Zoebisch E. G., Healy H. F., Stewart J. P. P.. AM1: A New General Purpose Quantum Mechanical Molecular Model. J. Am. Chem. Soc. 1985;107:3902–3909. doi: 10.1021/ja00299a024. DOI

Stewart J. J. P.. Optimization of Parameters for Semiempirical Methods 0.1. Method. J. Comput. Chem. 1989;10:209–220. doi: 10.1002/jcc.540100208. DOI

Rocha G. B., Freire R. O., Simas A. M., Stewart J. J. P.. RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I. J. Comput. Chem. 2006;27:1101–1111. doi: 10.1002/jcc.20425. PubMed DOI

Repasky M. P., Chandrasekhar J., Jorgensen W. L.. PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods. J. Comput. Chem. 2002;23:1601–1622. doi: 10.1002/jcc.10162. PubMed DOI

Stewart J. J. P.. Optimization of Parameters for Semiempirical Methods V: Modification of NDDO Approximations and Application to 70 Elements. J. Mol. Model. 2007;13:1173–1213. doi: 10.1007/s00894-007-0233-4. PubMed DOI PMC

Rezac J., Hobza P.. Advanced corrections of hydrogen bonding and dispersion for semiempirical quantum mechanical methods. J. Chem. Inf. Model. 2012;8:141–151. doi: 10.1021/ct200751e. PubMed DOI

Niehaus T., Elstner M., Frauenheim T., Suhai S.. Application of an approximate density-functional method to sulfur containing compounds. J. Mol. Struct.:THEOCHEM. 2001;541:185–194. doi: 10.1016/S0166-1280(00)00762-4. DOI

Riccardi D., Schaefer P., Yang, Yu H., Ghosh N., Prat-Resina X., König P., Li G., Xu D., Guo H., Elstner M., Cui Q.. Development of Effective Quantum Mechanical/Molecular Mechanical (QM/MM) Methods for Complex Biological Processes. J. Phys. Chem. B. 2006;110:6458–6469. doi: 10.1021/jp056361o. PubMed DOI

Gaus M., Goez A., Elstner M.. Parametrization and Benchmark of DFTB3 for Organic Molecules. J. Chem. Theory Comput. 2013;9:338–354. doi: 10.1021/ct300849w. PubMed DOI

Gaus M., Lu X., Elstner M., Cui Q.. Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications. J. Chem. Theory Comput. 2014;10:1518–1537. doi: 10.1021/ct401002w. PubMed DOI PMC

Smith J. S., Nebgen B., Lubbers N., Isayev O., Roitberg A. E.. Less is more: Sampling chemical space with active learning. J. Chem. Phys. 2018;148(24):241733. doi: 10.1063/1.5023802. PubMed DOI

Devereux C., Smith J. S., Huddleston K. K., Barros K., Zubatyuk R., Isayev O., Roitberg A. E.. Extending the Applicability of the ANI Deep Learning Molecular Potential to Sulfur and Halogens. J. Chem. Theory Comput. 2020;16:4192–4202. doi: 10.1021/acs.jctc.0c00121. PubMed DOI

Grimme S., Antony J., Ehrlich S., Krieg H.. A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010;132(15):154104. doi: 10.1063/1.3382344. PubMed DOI

Kovács D. P., Moore J. H., Browning N. J., Batatia I., Horton J. T., Pu Y., Kapil V., Witt W. C., Magdău I.-B., Cole D. J., Csányi G.. MACE-OFF: Short-Range Transferable Machine Learning Force Fields for Organic Molecules. J. Am. Chem. Soc. 2025;147:17598–17611. doi: 10.1021/jacs.4c07099. PubMed DOI PMC

Neumann, M. ; Gin, J. ; Rhodes, B. ; Bennett, S. ; Li, Z. ; Choubisa, H. ; Hussey, A. ; Godwin, J. . Orb: A Fast, Scalable Neural Network Potential. arXiv, 2024. 10.48550/arXiv.2410.22570. DOI

Rhodes, B. ; Vandenhaute, S. ; Šimkus, V. ; Gin, J. ; Godwin, J. ; Duignan, T. ; Neumann, M. . Orb-v3: atomistic simulation at scale. arXiv, 2025. 10.48550/arXiv.2504.06231. DOI

Chen, Y. ; Hou, Y.-F. ; Isayev, O. ; Dral, P. O. . Universal and Updatable Artificial Intelligence-Enhanced Quantum Chemical Foundational Models. ChemRxiv, 2024. 10.26434/chemrxiv-2024-604wb. DOI

Nováček M., Řezáč J.. PM6-ML: The Synergy of Semiempirical Quantum Chemistry and Machine Learning Transformed into a Practical Computational Method. J. Chem. Theory Comput. 2025;21:678–690. doi: 10.1021/acs.jctc.4c01330. PubMed DOI PMC

Pelaez R. P., Simeon G., Galvelis R., Mirarchi A., Eastman P., Doerr S., Thölke P., Markland T. E., De Fabritiis G.. TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations. J. Chem. Theory Comput. 2024;20(10):4076–4087. doi: 10.1021/acs.jctc.4c00253. PubMed DOI

Becke A. D.. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A. 1988;38:3098–3100. doi: 10.1103/PhysRevA.38.3098. PubMed DOI

Lee C., Yang W., Parr R.. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B. 1988;37:785–789. doi: 10.1103/PhysRevB.37.785. PubMed DOI

Perdew J. P., Burke K., Ernzerhof M.. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996;77:3865–3868. doi: 10.1103/PhysRevLett.77.3865. PubMed DOI

Zhao Y., Truhlar D. G.. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006;125(19):194101. doi: 10.1063/1.2370993. PubMed DOI

Becke A. D.. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993;98:5648. doi: 10.1063/1.464913. DOI

Chai J.-D., Head-Gordon M.. Systematic Optimization of Long-Range Corrected Hybrid Density Functionals. J. Chem. Phys. 2008;128(8):084106. doi: 10.1063/1.2834918. PubMed DOI

Lin Y. S., Li G. D., Mao S. P., Chai J. D.. Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. J. Chem. Theory Comput. 2013;9:263–722. doi: 10.1021/ct300715s. PubMed DOI

Ditchfield R., Hehre W., Pople J. A.. Self-Consistent Molecular-Orbital Methods IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules. J. Chem. Phys. 1971;54:724–728. doi: 10.1063/1.1674902. DOI

Arantes G. M.. The Catalytic Acid in the Dephosphorylation of the Cdk2-pTpY/CycA Protein Complex by Cdc25B Phosphatase. J. Phys. Chem. B. 2008;112:15244–15247. doi: 10.1021/jp8070019. PubMed DOI

Huang J., Rauscher S., Nawrocki G., Ran T., Feig M., de Groot B. L., Grubmuller H., mackerell Jr A. D.. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods. 2017;14:71–73. doi: 10.1038/nmeth.4067. PubMed DOI PMC

Jorgensen W. L., Chandrasekhar J., Madura J. D., Impey R. W., Klein M. L.. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983;79:926–935. doi: 10.1063/1.445869. DOI

Neese F.. Software update: The ORCA program systemVersion 5.0. Wiley Interdiscip. Rev.: comput. Mol. Sci. 2022;12(5):e1606. doi: 10.1002/wcms.1606. DOI

Hourahine B., Aradi B., Blum V., Bonafé F., Buccheri A., Camacho C., Cevallos C., Deshaye M. Y., Dumitrică T., Dominguez A.. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. J. Chem. Phys. 2020;152(12):124101. doi: 10.1063/1.5143190. PubMed DOI

Moussa, J. E. ; Stewart, J. J. P. . MOPAC version 23.0.3; Zenodo, 2024. 10.5281/zenodo.6511958, Accessed: 2024-12-26. DOI

Field M. J.. pDynamo3Molecular Modeling and Simulation Program. J. Chem. Inf. Model. 2022;62:5849–5854. doi: 10.1021/acs.jcim.2c01239. PubMed DOI

The D3 dispersion model. https://github.com/dftd3/simple-dftd3, Accessed 2025–April–25.

Larsen A. H., Mortensen J. J., Blomqvist J., Castelli I. E., Christensen R., Dułak M., Friis J., Groves M. N., Hammer B.. et al. The atomic simulation environmenta Python library for working with atoms. J. Phys.: Condens. Matter. 2017;29(27):273002. doi: 10.1088/1361-648X/aa680e. PubMed DOI

Dral P. O.. et al. MLatom 3: A Platform for Machine Learning-Enhanced Computational Chemistry Simulations and Workflows. J. Chem. Theory Comput. 2024;20:1193–1213. doi: 10.1021/acs.jctc.3c01203. PubMed DOI PMC

Bitzek E., Koskinen P., Gähler F., Moseler M., Gumbsch P.. Structural Relaxation Made Simple. Phys. Rev. Lett. 2006;97:170201. doi: 10.1103/PhysRevLett.97.170201. PubMed DOI

Boyd, S. ; Vandenberghe, L. . Convex Optimization, 1st ed.; Cambridge University Press: Cambridge, UK, 2004.

Wang L.-P., Martinez T. J., Pande V. S.. Building Force Fields: An Automatic, Systematic, and Reproducible Approach. J. Phys. Chem. Lett. 2014;5:1885–1891. doi: 10.1021/jz500737m. PubMed DOI PMC

Arantes G. M.. Redox-Activated Proton Transfer through a Redundant Network in the Qo Site of Cytochrome bc1. J. Chem. Inf. Model. 2025;65:2660–2669. doi: 10.1021/acs.jcim.4c02361. PubMed DOI PMC

Arantes, G. M. Dataset: Benchmark of approximate quantum chemical and machine learning potentials for biochemical proton transfer reactions; Zenodo, 2025. 10.5281/zenodo.15304677, Accessed: 2025-04-29. PubMed DOI PMC

Trung N. Q., Mechler A., Hoa N. T., Vo Q. V.. Calculating bond dissociation energies of X-H (X = C, N, O, S) bonds of aromatic systems via density functional theory: a detailed comparison of methods. R. Soc. Open Sci. 2022;9:220177. doi: 10.1098/rsos.220177. PubMed DOI PMC

Nam K., Cui Q., Gao J., York D. M.. Specific Reaction Parametrization of the AM1-d Hamiltonian for Phosphoryl Transfer Reactions: H, O and P Atoms. J. Chem. Theory Comput. 2007;3:486–504. doi: 10.1021/ct6002466. PubMed DOI

Plotnikov N. V., Warshel A.. Exploring, Refining, and Validating the Paradynamics QM/MM Sampling. J. Phys. Chem. B. 2012;116:10342–10356. doi: 10.1021/jp304678d. PubMed DOI

Curtolo F., Arantes G. M.. Molecular properties and tautomeric equilibria of isolated flavins. J. Comput. Chem. 2022;43:1561–1572. doi: 10.1002/jcc.26957. PubMed DOI

Arantes, G. M. Dataset: Redox-Activated Proton Transfer through a Redundant Network in the Q PubMed DOI PMC

Baydin A. G., Pearlmutter B. A., Radul A. A., Siskind J. M.. Automatic differentiation in machine learning: a survey. J. Mach. Learn. Res. 2018;18:1–43.

Friede M., Hölzer C., Ehlert S., Grimme S.. dxtb - An efficient and fully differentiable framework for extended tight-binding. J. Chem. Phys. 2024;161(6):062501. doi: 10.1063/5.0216715. PubMed DOI

The pDynamo 3 molecular modeling and simulation program. https://github.com/pdynamo/pDynamo3, Accessed: 2024–November–20.

Benchmark of Approximate Quantum Chemical and Machine Learning Potentials for Biochemical Proton Transfer Reactions