  We use scanning tunneling microscopy to visualize and thermal desorption
spectroscopy to quantitatively measure that the binding of naphthalene
molecules to graphene (Gr), a case of pure van der Waals (vdW) interaction,
strengthens with $n$- and weakens with $p$-doping of Gr. Density functional
theory calculations that include the vdW interaction in a seamless, ab initio
way accurately reproduce the observed trend in binding energies. Based on a
model calculation, we propose that the vdW interaction is modified by changing
the spatial extent of Gr's $\pi$ orbitals via doping.
