The exploration of chemical reactions preceding ignition is essential for the development of ideal hypergolic propellants. Unexpected reaction pathways of a hypergolic mixture composed of monomethylhydrazine and nitrogen dioxide are predicted through a cooperative combination of (i) spin-unrestricted ab initio molecular dynamics (AIMD) and (ii) wave packet dynamics of protons. Ensembles of AIMD trajectories reveal a sequence of reaction steps for proton transfer and rupture of the C-N bond. The details of proton transfer are explored by wave packet dynamics on the basis of ab initio potential energy surfaces from AIMD trajectories. The possibility of spontaneous ignition of this hypergolic mixture at room temperature is predicted as a quantized feature of proton-transfer dynamics.