In this work, we investigate the mechanism of the ammonia-dinitrogen exchange reaction, which is the decisive step to close the catalytic cycle of Schrock's dinitrogen reduction sequence under ambient conditions. We identify several viable pathways for the approach of dinitrogen to the five-coordinate molybdenum center of the ammonia complex by means of first-principles molecular-dynamics simulations. These exploratory simulations are then complemented by rigorous quantum-chemical structure optimizations. Our calculations have been performed for the full Schrock catalyst without simplifying the large chelate ligand, and are hence not affected by model assumptions. We show that the reaction obeys an addition-elimination mechanism via a stable six-coordinate intermediate. This intermediate has been fully characterized by stationary quantum-chemical methods. The predicted infrared spectrum of this species features an N[triple bond]N stretching vibration, which is well separated in frequency from all other N[triple bond]N stretching vibrations of N(2)-binding complexes involved in the Schrock cycle. Depending on the life time of this intermediate in the reaction liquor, the production of this intermediate might even be monitored by the absorption of the N[triple bond]N stretching vibration.