Letters to Nature

Nature 397, 601-604 (18 February 1999) | doi:10.1038/17579; Received 12 August 1998; Accepted 9 November 1998

The nature of the hydrated excess proton in water

Dominik Marx1, Mark E. Tuckerman2, Jürg Hutter1 & Michele Parrinello1

  1. Max-Planck-Institut für Festkrperforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany
  2. Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 4 Washington Place, New York, New York 10003, USA

Correspondence to: Dominik Marx1 Correspondence and requests for materials should be addressed to D.M. (e-mail: Email: marx@prr.mpi-stuttgart.mpg.de).

Explanations for the anomalously high mobility of protons in liquid water began with Grotthuss's idea1, 2 of 'structural diffusion' nearly two centuries ago. Subsequent explanations have refined this concept by invoking thermal hopping3, 4, proton tunnelling5, 6 or solvation effects7. More recently, two main structural models have emerged for the hydrated proton. Eigen8, 9 proposed the formation of an H9O4 + complex in which an H3O+ core is strongly hydrogen-bonded to three H2O molecules. Zundel10, 11, meanwhile, supported the notion of an H5O2 + complex in which the proton isshared between two H2O molecules. Here we use ab initio path integral12, 13, 14 simulations to address this question. These simulations include time-independent equilibrium thermal and quantum fluctuations of all nuclei, and determine interatomic interactions from the electronic structure. We find that the hydrated proton forms a fluxional defect in the hydrogen-bonded network, with both H9O4 + and H5O2 + occurring only in thesense of 'limiting' or 'ideal' structures. The defect can become delocalized over several hydrogen bonds owing to quantum fluctuations. Solvent polarization induces a small barrier to proton transfer, which is washed out by zero-point motion. The proton can consequently be considered part of a 'low-barrier hydrogen bond'15, 16, in which tunnelling is negligible and the simplest concepts of transition-state theory do not apply. The rate of proton diffusion is determined by thermally induced hydrogen-bond breaking in the second solvation shell.