Pt-195, N-14, and N-15 NMR data for five azido (N-3(-)) complexes are studied using relativistic density functional theory (DFT). Good agreement with experiment is obtained for Pt and N chemical shifts as well as Pt-N J-coupling constants. Calculated N-14 electric field gradients (EFGs) reflect experimentally observed trends for the line broadening of azido NMR signals. A localized molecular orbital analysis of the nitrogen EFGs and chemical shifts is performed to explain some interesting trends seen experimentally and in the first-principles calculations: (i) N-14 NMR signals for the Pt-coordinating (N-alpha) nuclei in the azido ligands are much broader than for the central (N-beta) or terminal (N-gamma) atoms. The N-beta signals are particularly narrow; (ii) compared to N-gamma, the N-alpha nuclei are particularly strongly shielded; (iii) N-beta nuclei have much larger chemical shifts than N-alpha and N-gamma ; and (iv) The Pt-N-alpha J-coupling constants are small in magnitude when considering the formal sp hybridization of Na It is found that for N-alpha a significant shielding reduction due to formation of the dative N-alpha Pt bond is counterbalanced by an increased shielding from spin-orbit (SO) coupling originating at Pt. Upon coordination, the strongly delocalized pi system of free azide localizes somewhat on N-beta and N-gamma . This effect, along with rehybridization at N-alpha upon bond formation with Pt, is shown to cause a deshielding of N-gamma relative to N-alpha and a strong increase of the EFG at N-alpha The large 2p character of the azide sigma bonds is responsible for the particularly high N-beta chemical shifts. The nitrogen s-character of the Pt-N-alpha bond is low, which is the reason for the small J-coupling. Similar bonding situations are likely to be found in azide complexes with other transition metals.