We have carried out a density functional theory study of the S = 1/2 [FeNO]7 tropocoronand complex, Fe(5,5-TC)NO, as well as of some simplified models of this compound. The calculations accurately reproduce the experimentally observed trigonal-bipyramidal geometry of this complex, featuring a linear NO in an equatorial position and a very short Fe-N(NO) distance. Despite these unique structural features, the qualitative features of the bonding turn out to be rather similar for Fe(5,5-TC)NO and [FeNO]7 porphyrins. Thus, there is a close correspondence between the molecular orbitals (MOs) in the two cases. However, there is a critical, if somewhat subtle, difference in the nature of the singly occupied MOs (SOMOs) between the two. For square-pyramidal heme-NO complexes, the SOMO is primarily Fe d(z)2-based, which favors sigma-bonding interactions with an NO pi orbital, and hence a bent FeNO unit. However, for trigonal-bipyramidal Fe(5,5-TC)(NO), the SOMO is best described as primarily Fe d(x2-z2) in character, with the Fe-N(NO) vector being identified as the z direction. Apparently, such a d orbital is less adept at sigma bonding with NO and, as such, pi bonding dominates the Fe-NO interaction, leading to an essentially linear FeNO unit and a short Fe-N(NO) distance.