  A dispersion-corrected density functional theory study of the photosensitizer
[Ir(ppy)$_2$(bpy)]$^+$ and its derivatives bound to silver clusters Ag$_n$
($n$=2-20, 92) is performed. The goal is to provide a new system-specific set
of $C_{\rm 6}^{}$ interaction parameters for Ag and Ir atoms. To this end a
QM:QM scheme is employed using the PBE functional and RPA as well as MP2
calculation as a reference. The obtained $C_{\rm 6}^{}$ coefficients were
applied to calculate dissociation curves of selected IrPS-Ag$_n$ complexes and
binding energies of derivatives containing oxygen and sulphur as heteroatoms in
the ligands. Comparing different $C_{\rm 6}^{}$ parameters it is concluded that
RPA-based dispersion correction produces binding energies close to standard D2
and D3 models, whereas MP2-derived parameters overestimate these energies.
