A one-electron model potential for calculating the binding energy of an excess electron interacting with polar molecules and their clusters is described. The unique feature of this potential is the treatment of polarization and dispersion effects by means of a Drude model. The approach is tested by calculating the energies for binding an excess electron to HCN, (HCN)(2), HNC, and (HNC)(2). The model potential results are found to be in good agreement with the predictions of high-level all-electron calculations.