  In this work we show that the molecular chemical bond formation and
dissociation in presence of the d-band of a metal catalyst can be described as
a Quantum Dynamical Phase Transition (QDPT). This agree with DFT calculations
that predict sudden jumps in some observables as the molecule breaks. According
to our model this phenomenon emerges because the catalyst provides for a non-
Hermitian Hamiltonian. We show that when the molecule approaches the surface,
as occurs in the Heyrovsky reaction of H 2, the bonding H 2 orbital has a
smooth crossover into a bonding molecular orbital built with the closest H
orbital and the surface metal d-states. The same occurs for the antibonding
state. Meanwhile, two resonances appear within the continuous spectrum of the
d- band which are associated with bonding and antibonding orbitals between the
furthest H atom and the d-states at the second metallic layer. These move
towards the band center where they collapse into a pure metallic resonance and
an almost isolated H orbital. This phenomenon constitutes a striking example of
the non-trivial physics enabled when one deals with non-Hermitian Hamiltonian
beyond the usual wide band approximation.
