Fig. 1. Schematic representation of the construction of atomic-field representations. Top: 1-D atomic chain; bottom: hypothetical “doped graphene” 2-D system. Left: atoms are represented by their position in Cartesian coordinates. Middle: the structure is represented as an atom-density field, built as a superimposition of localized functions centred on each atom; each element is associated with a separate channel, represented by color coding. Right: the atom-density potential is formally equivalent to the electrostatic field generated by the decorated atom density; similarly to the density, each element is treated separately.