The topology of the electrostatic potential phi(r) has been studied for single molecules using geometries and electron distributions p(r) determined from high-resolution single-crystal X-ray diffraction data. The electrostatic potential gradient del phi(r), which is the negative of the electric field E = -del phi, has been represented, revealing the position of zero-flux surfaces and critical points. Local maxima and minima of the electrostatic potential are interpreted in terms of electrophilic and nucleophilic sites, which present influence zones delimited by zero-flux surfaces containing saddle points. The influence zones of the nucleophilic and electrophilic sites define two alternative partitions of the space in disjoint volumes, the completeness of these partitions depending on either the neutral or ionic character of the molecule. The results obtained by using this methodology are useful for the interpretation of the saddle points of the electrostatic potential, which are related to the limits of the influence zones and reveal the path for preferred attack on reactive sites with finite influence zones.