Iron nitrosyl complexes with {FeNO}(7) (S = 3/2) configuration have a complex electronic structure and display remarkable but not fully understood spectroscopic properties. In particular, {FeNO}(7) (S = 3/2) complexes have very large zero-field splittings (ZFSs), which arise from strong spin-orbit coupling, a relativistic effect. The accurate prediction and microscopic interpretation of ZFSs in transition metal complexes can aid in the interpretation of a vast amount of spectroscopic (e.g., Mossbauer and electron paramagnetic resonance) and other experimental (e.g,, magnetic susceptibility) data. We report the accurate calculation of the sign and magnitude of ZFSs for a set of representative diatomic molecules based on a combined spin density functional theory and perturbation theory (SDFT-PT) methodology. In addition, we apply the SDFT-PT methodology to accurately calculate the magnitude and sign of the ZFS parameters of an {FeNO}(7) (S = 3/2) complex and to interpret its spectrocopic data. We find that the principal component D-zz of the ZFS tensor is very closely oriented along the Fe-N(O) bond, indicating that nitric oxide dominates the very intricate electronic structure of the {FeNO}(7) (S = 3/2) compound. We find a direct correlation between electronic delocalization along the Fe-N(O) bond, which is due to pi-bonding, and the large ZFS.