Development of an effective single-electron model of the electronic structure of hydronium and hydronium-water clusters

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 Schrödinger 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.