  Many-body electron interactions are at the heart of chemistry and solid-state
physics. Understanding these interactions is crucial for the development of
molecular-scale quantum and nanoelectronic devices. Here, we investigate
single-electron tunneling through an edge-fused porphyrin oligomer and
demonstrate that its transport behavior is well described by the Hubbard dimer
model. This allows us to study the role of electron-electron interactions in
the transport setting. In particular, we empirically determine the molecule's
on-site and inter-site electron-electron repulsion energies, which are in good
agreement with density functional calculations, and establish the molecular
electronic structure within various charge states. The gate-dependent
rectification behavior is used to further confirm the selection rules and state
degeneracies resulting from the Hubbard model. We therefore demonstrate that
current flow through the molecule is governed by a non-trivial set of
vibrationally coupled electronic transitions between various many-body states,
and experimentally confirm the importance of electron-electron interactions in
single-molecule devices.
