The isotropic and anisotropic coefficients Cn l,m of the long-range spherical expansion ∼1/Rn (R-the intermolecular distance) of the dispersion and induction intermolecular energies are calculated using the first principles for the complexes containing an aromatic molecule (benzene, pyridine, furan, and pyrrole) and alkali-metal (Li, Na, K, Rb, and Cs) or alkaline-earth-metal (Be, Mg, Ca, Sr, and Ba) atoms in their electronic ground states. The values of the first- and second-order properties of the aromatic molecules are calculated using the response theory with the asymptotically corrected LPBE0 functional. The second-order properties of the closed-shell alkaline-earth-metal atoms are obtained using the expectation-value coupled cluster theory and of the open-shell alkali-metal atoms using analytical wavefunctions. These properties are used for the calculation of the dispersion Cn,disp l,m and induction Cn,ind l,m coefficients (Cn l,m=Cn,disp l,m+Cn,ind l,m) with n up to 12 using the available implemented analytical formulas. It is shown that the inclusion of the coefficients with n > 6 is important for reproducing the interaction energy in the van der Waals region at R ≈ 6 Å. The reported long-range potentials should be useful for constructing the analytical potentials valid for the whole intermolecular interaction range, which are needed for spectroscopic and scattering studies.