Ab-initio molecular dynamics (AIMD) simulations based on density functional theory show that N adatoms are chemisorbed in threefold sites close to a N surface atom and between the two diagonally-opposed neighboring Ti surface atoms on TiN(001). The most probable N adatom reaction pathway, even in the presence of nearby N adatoms, is for the N adatom and N surface atom pair to first undergo several exchange reactions and then desorb as a N2 molecule, resulting in a surface anion vacancy, with an activation barrier Edes of 1.37 eV and an attempt frequency Ades = 3.4x10 13 s -1 . Edes is essentially equal to the N adatom surface diffusion barrier, Es = 1.39 eV, whileAs is only three to four times larger than Ades, indicating that isolated N adatoms migrate for only short distances prior to N2 desorption. The probability of N2 desorption via recombination of N adatoms on TiN(001) is much lower due to repulsive adatom/adatom interactions at separations less than ~3 Å which rapidly increase to ~2 eV at a separation of 1.5 Å. We obtain good qualitative and quantitative agreement with the above results using the modified embedded atom method (MEAM) potential to perform classical molecular dynamics (CMD) simulations.