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Low-temperature scanning tunneling microscopy has been employed to analyze the formation of quantum well states (QWS) in 2D gold islands, containing between 50-200 at-oms, on MgO thin films. The energy position and symmetry of the eigenstates are revealed from conductance spectroscopy and imaging. The majority of the QWS originates from over-lapping Au 6p orbitals in the individual atoms and is unoccupied. Their characteristic is re-produced already with simple particle-in-a-box models that account for the symmetry of the islands (rectangular, triangular or linear). Better agreement is achieved when considering the true atomic structure of the aggregates via a density-functional-tight-binding approach. Based on a statistically relevant number of single-island data, we have established a correlation be-tween the island geometry and the HOMO-LUMO gap that opens up due to the finite island size. The linear eccentricity is identified as a suitable descriptor for this relationship, as it combines information on both the island size and shape. Finally, the depth of the confinement potential is determined from the spatial extension of QWS beyond the physical boundaries of the Au islands. Our work demonstrates how electron quantization effects can be analyzed in detail in metal nanostructures. The results may help elucidating the interplay between elec-tronic and chemical properties of oxide-supported clusters as used in heterogeneous catalysis

Electron quantization in arbitrarily shaped gold islands on MgO thin films