We employ ab initio calculations of van der Waals complexes to study the potential energy parameters (C-6 coefficients) of van der Waals interactions for modeling of the adsorption of silver clusters on the graphite surface. Electronic structure calculations of the (Ag-2)(2), Ag-2-H-2, and Ag-2-C6H6 complexes are performed using a coupled cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)), Moller-Plesset second-order perturbation theory (MP2), and spin-component-scaled MP2 (SCS-MP2) methods. Using the atom pair approximation, the C-6 coefficients for silver silver, silver hydrogen, and silver carbon atom systems are obtained after subtracting the energies of quadrupole-quadrupole interactions from the total electronic energy.