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Through an appropriate election of the molecular orbital basis, we showanalytically that the molecular dissociation occurring in a Heyrovsky reactioncan be interpreted as a Quantum Dynamical Phase Transition, i.e., an analyticaldiscontinuity in the molecular energy spectrum induced by the catalyst. Themetallic substrate plays the role of an environment that produces an energyuncertainty on the adatom. This broadening induces a critical behavior notpossible in a quantum closed system. We use suitable approximations onsymmetry, together with both Lanczos and canonical transformations, to giveanalytical estimates for the critical parameters of molecular dissociation.This occurs when the bonding to the surface is (\sqrt{2}) times the molecularbonding. This value is slightly weakened for less symmetric situations. Howeversimple, this conclusion involves a high order perturbative solution of themolecule-catalyst system. This model is further simplified to discuss how anenvironment-induced critical phenomenon can be evaluated through an idealizedperturbative tunneling microscopy set-up. In this case, the energyuncertainties in one or both atoms are either Lorentzian or Gaussian. Theformer results from the Fermi Golden Rule, i.e., a Markovian approximation. TheGaussian uncertainty, associated with non-Markovian decoherent processes,requires the introduction of a particular model of a spin bath. The partiallycoherent tunneling current is obtained from the Generalized Landauer-B\"uttikerEquations. The resonances observed in these transport parameters reflect, inmany cases, the critical properties of the resonances in the molecularspectrum.

Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment