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, pi bonds, hybrid orbitals and other electronic structure elements is suggested. A Poincare-Hopf relationship for the molecular electrostatic potential is derived, connecting electronic structure elements and electrostatic reactivity via the topology of the molecular electrostatic potential.