The Electric Dipole Moment of the electron (eEDM) is typically investigated in experiments using paramagnetic molecules. However, the physical observable in these searches consists of a linear combination of CP-violating interactions, rather than the eEDM alone, which is commonly referred to as the \emph{equivalent} EDM of the system. Assuming the presence of new CP-odd physics from heavy degrees of freedom, I parametrize its effects within the Standard Model Effective Field Theory (SMEFT) framework. In this talk, I will present the contributions to the full low-energy direction probed by EDM searches, focusing on leading-order effects at dimension six and one-loop level, while also discussing selected two-loop contributions. I will highlight that eEDM experiments are sensitive to a broader class of SMEFT operators than previously recognized.