We have observed the branching rearrangement of a straight-chain secondary carbocation (C9H19+) in an ab initio molecular dynamics (AIMD) reverse-annealing (rising-temperature) simulation. The mechanism observed is one involving closed (protonated-cyclopropane) structures, previously observed in traditional geometry optimization calculations. However, the simulations give us a better understanding of the dynamics involved, leading to two advances: a simpler description of carbenium ion structures in general and the discovery of important entropy effects.