- The complex dielectric function ϵ(E)= ϵ R (E)+i ϵ I (E) ϵ of a semiconductor is a key parameter that dictates the material's optical and electrical properties. Surprisingly, the ϵ(E) ϵ of Lead Sulfide (PbS) quantum dots (QDs) has not been widely studied. In the present work, we develop a new model that aims to simulate the ϵ(E) ϵ of QDs. Our model is based on the fact that the quantum confinement in the nano regime affects all the electronic transitions throughout the entire Brillouin zone. Hence, as a first approximation, we attribute an equal contribution of energy, equivalent to the bandgap broadening, to each critical point (CP) in the E-k diagram. This is mathematically realized by adding these energy contributions to the central energy parameters of the Lorentz oscillator model. In order to validate our model, we used the CP parameters of bulk PbS to simulate the ϵ(E) ϵ of PbS QDs. Next, we use Maxwell Relations to calculate the refractive index and the extinction coefficient of PbS QDs from ϵ(E). ϵ Our results were compared with those published in the previous literature and showed good agreement. Our findings open a new avenue that may enable the calculation of the ϵ(E) ϵ for nanoparticle systems.