A one-electron model is developed which is able to describe the electronic structure and potential-energy (PE) surface of the Rydberg molecule H3O, in particular the Rydberg-to-valence transition of the singly occupied orbital along the H3O --> H2O + H reaction path. An analytic PE function for the unpaired electron is obtained by numerical inversion of the one-particle Schrodinger equation and a least-squares fitting using a Thomas-Fermi-type model. Application of this procedure to H5O2 indicates the transferability of the model parameters from H3O to H3O-water clusters in a good approximation. The long-term goal of this work is the development of an accurate pseudopotential which can be employed in computer simulations of excess electrons and excess protons in liquid water. (C) 2002 Published by Elsevier Science B.V.