The topology of the molecular electrostatic potential of 18 molecules, calculated in the framework of Kohn–Sham density functional theory, is studied. For the location of the different kinds of critical points a newly developed search algorithm is applied. A chemical interpretation of the critical points in terms of lone pairs, π bonds, hybrid orbitals and other electronic structure elements is suggested. A Poincaré–Hopf relationship for the molecular electrostatic potential is derived, connecting electronic structure elements and electrostatic reactivity via the topology of the molecular electrostatic potential.