Within a molecule, the potential acting on an electron (PAEM) is defined as the interaction energy of a local electron with the rest of the particles, i.e., all nuclei and remaining electrons. The formalism of the PAEM is first derived, and the calculated PAEMs are then obtained by using the ab initio program based on the MELD program package for a series of diatomic halides, namely, HX, LiX, NaX, and X-2 molecules (X= F, Cl, Br, and I), as well as H2O and NH3, and some organic molecules. By comparing the 3D topological graphs of the PAEMs. we found that there is a saddle point along every chemical bond axis. Further, the good linear correlations of the force constant and bond length with the PAEMs are explored through a definition of D-pb, which is the absolute value (i.e., the negative) of the PAEM at the saddle point along the chemical bond axis. In addition, the difference between the PAEM and molecular electrostatic potential (MEP) is pointed out by analyzing both their definitions and numerical results.