The differences in electronic structures of two (1)Sigma(g)(+) states of the hydrogen molecule are vividly reflected in their intracule densities I(r). The ground-state wave function of H-2 is associated with two distinct topologies of I(r) (one of which pertains to the united atom limit), whereas no fewer than 11 unequivalent sets of critical entities are found for I(r) of the EF state that involves multiple electronic configurations. These sets and the catastrophes that interrelate them, which arise from conflicts between topological features of I(r) pertinent to different configurations, are characterized in detail. The usefulness of topological analysis of I(r) in the detection and characterization of various types of electron correlation is demonstrated.