  Crystalline nanoporous molecular networks are assembled on the Ag(111)
surface, where the pores confine electrons originating from the surface state
of the metal. Depending on the pore sizes and their coupling, an antibonding
level is shifted upwards by 0.1 to 0.3 eV as measured by scanning tunneling
microscopy. On molecular sites, a down-shifted bonding state is observed, which
is occupied under equilibrium conditions. Low-temperature force spectroscopy
reveals energy dissipation peaks and jumps of frequency shifts at bias
voltages, which are related to the confined states. The dissipation maps show
delocalization on the supra-molecular assembly and a weak distance-dependence
of the dissipation peaks. These observations indicate that two-dimensional
arrays of coupled quantum dots are formed, which are quantitatively
characterized by their quantum capacitances and resonant tunneling rates. Our
work provides a method for studying the capacitive and dissipative response of
quantum materials with nanomechanical oscillators.
