Eigen, M. Proton transfer, acid–base catalysis, and enzymatic hydrolysis. Part I: elementary processes. Angew. Chem. Int. Ed. Engl. 3, 1–19 (1964).

Article  Google Scholar 

Zundel, G. & Metzger, H. Energiebänder der tunnelnden Überschuß-Protonen in flüssigen Säuren. Eine IR-spektroskopische Untersuchung der Natur der Gruppierungen H5O2+. Z. Phys. Chem. 58, 225–245 (1968).

Article  CAS  Google Scholar 

Zundel, G. Hydrogen bonds with large proton polarizability and proton transfer processes in electrochemistry and biology. Adv. Chem. Phys. 111, 1–217 (1999).

Google Scholar 

Tuckerman, M., Laasonen, K., Sprik, M. & Parrinello, M. Ab initio molecular dynamics simulation of the solvation and transport of H3O+ and OH− ions in water. J. Phys. Chem. 99, 5749–5752 (1995).

Article  CAS  Google Scholar 

Vuilleumier, R. & Borgis, D. An extended empirical valence bond model for describing proton mobility in water. Isr. J. Chem. 39, 457–467 (1999).

Article  CAS  Google Scholar 

Marx, D., Tuckerman, M. E., Hutter, J. & Parrinello, M. The nature of the hydrated excess proton in water. Nature 397, 601–604 (1999).

Article  CAS  Google Scholar 

Marx, D. Proton transfer 200 years after von Grotthuss: insights from ab initio simulations. ChemPhysChem 7, 1848–1870 (2006).

Article  CAS  PubMed  Google Scholar 

Markovitch, O. et al. Special pair dance and partner selection: elementary steps in proton transport in liquid water. J. Phys. Chem. B 112, 9456–9466 (2008).

Article  CAS  PubMed  Google Scholar 

Berkelbach, T. C. & Tuckerman, M. E. Concerted hydrogen-bond dynamics in the transport mechanism of the hydrated proton: a first-principles molecular dynamics study. Phys. Rev. Lett. 103, 238302 (2009).

Article  PubMed  Google Scholar 

Hassanali, A., Giberti, F., Cuny, J., Kühne, T. D. & Parrinello, M. Proton transfer through the water gossamer. Proc. Natl Acad. Sci. USA 110, 13723–13728 (2013).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Napoli, J. A., Marsalek, O. & Markland, T. E. Decoding the spectroscopic features and time scales of aqueous proton defects. J. Chem. Phys. 148, 222833 (2018).

Article  PubMed  Google Scholar 

Roy, S. et al. Resolving heterogeneous dynamics of excess protons in aqueous solution with rate theory. J. Phys. Chem. B 124, 5665–5675 (2020).

Article  CAS  PubMed  Google Scholar 

Lapid, H., Agmon, N., Petersen, M. K. & Voth, G. A. A bond-order analysis of the mechanism for hydrated proton mobility in liquid water. J. Chem. Phys. 122, 14506 (2005).

Article  PubMed  Google Scholar 

Thämer, M., De Marco, L., Ramasesha, K., Mandal, A. & Tokmakoff, A. Ultrafast 2D IR spectroscopy of the excess proton in liquid water. Science 350, 78–82 (2015).

Article  PubMed  Google Scholar 

Dahms, F., Fingerhut, B. P., Nibbering, E. T. J., Pines, E. & Elsaesser, T. Large-amplitude transfer motion of hydrated excess protons mapped by ultrafast 2D IR spectroscopy. Science 357, 491–495 (2017).

Article  CAS  PubMed  Google Scholar 

Fournier, J. A., Carpenter, W. B., Lewis, N. H. C. & Tokmakoff, A. Broadband 2D IR spectroscopy reveals dominant asymmetric H5O2+ proton hydration structures in acid solutions. Nat. Chem. 10, 932–937 (2018).

Article  CAS  PubMed  Google Scholar 

Kundu, A. et al. Hydrated excess protons in acetonitrile/water mixtures: solvation species and ultrafast proton motions. J. Phys. Chem. Lett. 10, 2287–2294 (2019).

Article  CAS  PubMed  Google Scholar 

Luz, Z. & Meiboom, S. The activation energies of proton transfer reactions in water. J. Am. Chem. Soc. 86, 4768–4769 (1964).

Article  CAS  Google Scholar 

Ando, K. & Hynes, J. T. HCl acid ionization in water: a theoretical molecular modeling. J. Mol. Liq. 64, 25–37 (1995).

Article  CAS  Google Scholar 

Tuckerman, M. E., Marx, D., Klein, M. L. & Parrinello, M. On the quantum nature of the shared proton in hydrogen bonds. Science 275, 817–820 (1997).

Article  CAS  PubMed  Google Scholar 

Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).

Article  PubMed  Google Scholar 

Rossi, M., Ceriotti, M. & Manolopoulos, D. E. How to remove the spurious resonances from ring polymer molecular dynamics. J. Chem. Phys. 140, 234116 (2014).

Article  PubMed  Google Scholar 

Sluyters, J. H. & Sluyters-Rehbach, M. Rotation of water molecules and its relation with the chemistry and physics of liquid water. J. Phys. Chem. B 114, 863–869 (2010).

Article  CAS  PubMed  Google Scholar 

Fournier, J. A. et al. Vibrational spectral signature of the proton defect in the three-dimensional H+(H2O)21 cluster. Science 344, 1009–1012 (2014).

Article  CAS  PubMed  Google Scholar 

Calio, P. B., Li, C. & Voth, G. A. Resolving the structural debate for the hydrated excess proton in water. J. Am. Chem. Soc. 143, 18672–18683 (2021).

Article  CAS  PubMed  Google Scholar 

Woutersen, S. & Bakker, H. J. Ultrafast vibrational and structural dynamics of the proton in liquid water. Phys. Rev. Lett. 96, 138305 (2006).

Article  PubMed  Google Scholar 

Meiboom, S. Nuclear magnetic resonance study of the proton transfer in water. J. Chem. Phys. 34, 375 (1961).

Article  CAS  Google Scholar 

Yuan, R. et al. Tracking aqueous proton transfer by two-dimensional infrared spectroscopy and ab initio molecular dynamics simulations. ACS Cent. Sci. 5, 1269–1277 (2019).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Calio, P. B., Li, C. & Voth, G. A. Molecular origins of the barriers to proton transport in acidic aqueous solutions. J. Phys. Chem. B 124, 8868–8876 (2020).

Article  CAS  PubMed  Google Scholar 

Tse, Y.-L. S., Knight, C. & Voth, G. A. An analysis of hydrated proton diffusion in ab initio molecular dynamics. J. Chem. Phys. 142, 014104 (2015).

Article  PubMed  Google Scholar 

Chen, M. et al. Hydroxide diffuses slower than hydronium in water because its solvated structure inhibits correlated proton transfer. Nat. Chem. 10, 413–419 (2018).

Article  PubMed  Google Scholar 

Hammes-Schiffer, S. & Billeter, S. R. Hybrid approach for the dynamical simulation of proton and hydride transfer in solution and proteins. Int. Rev. Phys. Chem. 20, 591–616 (2001).

Article  CAS  Google Scholar 

Daly, C. A. et al. Decomposition of the experimental Raman and infrared spectra of acidic water into proton, special pair, and counterion contributions. J. Phys. Chem. Lett. 8, 5246–5252 (2017).

Article  CAS  PubMed  Google Scholar 

Decornez, H., Drukker, K. & Hammes-Schiffer, S. Solvation and hydrogen-bonding effects on proton wires. J. Phys. Chem. A 103, 2891–2898 (1999).

Article  CAS  Google Scholar 

Eaves, J. D. et al. Hydrogen bonds in liquid water are broken only fleetingly. Proc. Natl Acad. Sci. USA 102, 13019–13022 (2005).

Article  CAS