New medium-size basis sets are constructed for rare-gas (Rg) atoms and tested on their dimers Rg2. The main part of the these bases contains the standard aug-cc-pVTZ basis set modified and extended by the g- and h-polarization functions. Their optimization allows accurate calculations of the dispersion interaction without the involvement of the bond functions. A new convenient analytical potential function is invented to fit accurately the interaction energy. The potentials derived for Rg dimers predict the vibrational transition energies and rotational constants to accuracy of 1%. Graphical abstract: New medium-size basis sets without the involvement of bond functions are constructed for raregas atoms and tested on their dimers.