  We present a novel approach to determine the onset of contact between a tip
and a surface. The real contact area depending on the distance is calculated
using Bader's quantum theory of atoms in molecules. The jump to contact, which
is often observed in atomic force microscopy experiments, is used as an
indicator for the initial point of contact, which in turn is defined by atomic
relaxations and thus without the need of external parameters. Within our
approach the contact area is estimated by evaluating the zero flux surfaces
between the touching Bader-atoms, where the necessary electronic density cutoff
for the Bader-partitioning is calculated to depend on the initial point of
contact. Our proposed approach is therefore completely ab-initio and we are
able to define and calculate the real area of contact without imposing
restrictions or free parameters. As a prototype system we choose a tip made of
a ten atom tungsten pyramid above a moir\'{e} layer of graphene on an fcc
iridium (111) substrate. We find that the contact area depends exponentially on
the effective distance between the tip apex and the surface atom directly below
within the atomically relaxed nanosystem.
