  The discrete and charge-separated nature of matter - electrons and nuclei -
results in local electrostatic fields that are ubiquitous in nanoscale
structures and are determined by their shape, material, and environment. Such
fields are relevant in catalysis, nanoelectronics and quantum nanoscience, and
their control will become even more important as the devices in question reach
few-nanometres dimensions. Surface-averaging techniques provide only limited
experimental access to these potentials at and around individual
nanostructures. Here, we use scanning quantum dot microscopy to investigate how
electric potentials evolve as nanostructures are built up atom by atom. We
image the potential over adatoms, chains, and clusters of Ag and Au atoms on
Ag(111) and quantify their surface dipole moments. By focusing on the total
charge density, these data establish a new benchmark for ab initio
calculations. Indeed, our density functional theory calculations not only show
an impressive agreement with experiment, but also allow a deeper analysis of
the mechanisms behind the dipole formation, their dependence on fundamental
atomic properties and on the atomic configuration of the nanostructures. This
allows us to formulate an intuitive picture of the basic mechanisms behind
dipole formation, which enables better design choices for future nanoscale
systems such as single atom catalysts.
