Hydrogen bonded complexes formed between the square pyramidal Fe(CO)5 with HX (X = F, Cl, Br), showing X-H···Fe interactions, have been investigated theoretically using density functional theory (DFT) including dispersion correction. Geometry, interaction energy, and large red shift of about 400 cm(-1) in the HX stretching frequency confirm X-H···Fe hydrogen bond formation. In the (CO)5Fe···HBr complex, following the significant red-shift, the HBr stretching mode is coupled with the carbonyl stretching modes. This clearly affects the correlation between frequency shift and binding energy, which is a hallmark of hydrogen bonds. Atoms in Molecule (AIM) theoretical analyses show the presence of a bond critical point between the iron and the hydrogen of HX and significant mutual penetration. These X-H···Fe hydrogen bonds follow most but not all of the eight criteria proposed by Koch and Popelier (J. Phys. Chem. 1995, 99, 9747) based on their investigations on C-H···O hydrogen bonds. Natural bond orbital (NBO) analysis indicates charge transfer from the organometallic system to the hydrogen bond donor. However, there is no correlation between the extent of charge transfer and interaction energy, contrary to what is proposed in the recent IUPAC recommendation (Pure Appl. Chem. 2011, 83, 1637). The "hydrogen bond radius" for iron has been determined to be 1.60 ± 0.02 Å, and not surprisingly it is between the covalent (1.27 Å) and van der Waals (2.0) radii of Fe. DFT and AIM theoretical studies reveal that Fe in square pyramidal Fe(CO)5 can also form halogen bond with ClF and ClH as "halogen bond donor". Both these complexes show mutual penetration as well, though the Fe---Cl distance is closer to the sum of van der Waals radii of Fe and Cl in (CO)5Fe···ClH, and it is about 1 Å less in (CO)5Fe···ClF.