With the ongoing efforts on synthesizing mononuclear single-ion magnets (SIMs) with promising applications in high-density data storage and spintronics devices, the linear or quasi-linear Fe(I) complexes emerge as the enticing candidates possessing large unquenched angular momentum. Herein, we have studied five experimentally synthesized linear Fe(I) complexes to uncover the origin of single-molecule magnetic behavior of these complexes. To begin with, we benchmarked the methodology on the experimentally and theoretically well-studied complex [Fe(C(SiMe3)3)2]-1 (1) (SiMe3 = trimethylsilyl), which is characterized with a large spin-reversal barrier of 226 cm-1. Subsequently, the spin-phonon coupling coefficients are calculated for the low-frequency vibrational modes to understand the relaxation mechanism of the complex. Furthermore, the two Fe(I) complexes, that is, [Fe(cyIDep)2]+1 (2) (cyIDep = 1,3-bis(2',6'-diethylphenyl)-4,5-(CH2)4-imidazole-2-ylidene) and [Fe(sIDep)2]+1 (3) (sIDep = 1,3-bis(2',6'-diethylphenyl)-imidazolin-2-ylidene), are studied that are experimentally reported with no SIM behavior under ac or dc magnetic fields; however, they exhibit large opposite axial zero field splitting (-62.4 and +34.0 cm-1, respectively) from ab initio calculations. We have unwrapped the origin of this contrasting observation between experiment and theory by probing their magnetic relaxation pathways and the pattern of d orbital splitting. Additionally, the two experimentally synthesized Fe(I) complexes, that is, [(η6-C6H6)FeAr*-3,5-Pr2i] (4) (Ar*-3,5-Pr2i = C6H-2,6-(C6H2-2,4,6-Pr3i)2-3,5-Pr2i) and [(CAAC)2Fe]+1 (5) (CAAC = cyclic (alkyl) (amino)carbene), are investigated for SIM behavior, since there is no report on their magnetic anisotropy. To this end, complex 4 presents itself as the possible candidate for SIM.