We investigate isovector pygmy dipole resonance (IVPDR) for the case of neutron-rich soft nuclei Ni-68, and heavy nuclei such as Sn-112 and Pb-208 using effective nucleon-nucleon Skyrme interaction. We use the mean-field theory and employ the random phase approximation (RPA) . We observe that our results for the pygmy dipole resonance (PDR) for neutron-rich nuclei are in reasonable agreement with their experimental results. We also predict PDR for very neutron-rich heavy nuclei. We then study two-neutron separation Skyrme energies (S-2n) using the Hartree-Fock + BCS with and without tensor interaction in the same nucleus and compare our results with their experimental values. We see that the total binding energies of nuclei Pb-208 are not extremely sensitive to the tensor interaction.