This work combines for the first time ab initio molecular dynamics (AIMD) within the Born–Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(⁴S) + H₂(¹Σ) → NH(³Σ) + H(²S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H₂ and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.