The gaseous ligands, CO, NO and O2 interact with the Fe ion in heme proteins largely via backbonding of Fe electrons to the π* orbitals of the XO (X = C, N, O) ligands. In these FeXO adducts, the Fe–X stretching frequency varies inversely with the X–O stretching frequency, since increased backbonding strengthens the Fe–X bond while weakening the X–O bond. Inverse frequency correlations have been observed for all three ligands, despite differing electronic and geometric structures, and despite variable composition of the `FeX' vibrational mode, in which Fe–X stretching and Fe–X–O coordinates are mixed for bent FeXO adducts. We report experimental data for 5-coordinate CoII(NO) porphyrin adducts (isoelectronic with FeII(OO) adducts), and the results of DFT modeling for 5-coordinate FeII(NO), CoII(NO) and FeII(OO) adducts. Inverse ν(MX)/ν(XO) correlations are obtained computationally, using model porphyrins with graded electron-donating and -withdrawing substituents to modulate the backbonding. Computed slopes agree satisfactorily with experiment, provided non-hybrid functionals are used, which avoid overemphasizing high-spin states. The BP86 functional gives correct ground states, a closed-shell singlet for CoII(NO) and an open-shell singlet for the isoelectronic FeII(OO), as corroborated by structural data for CoII(NO), and the ν(MX)/ν(XO) slope agreement with experiment for both adducts. However, for FeII(OO) adducts, the computed inverse ν(MX)/ν(XO) correlation applies only to porphyrins with electron-donating and withdrawing substituents of moderate strength. For substituents more donating than –CH3, a direct correlation is obtained, the Fe–O and O–O bonds weakening in concert. This effect is ascribed to the dominance of σ bonding via the in-plane dxz(+dz2)-π* orbital, when electron-donating substituents raise the d orbital energies sufficiently to render backbonding (dyz-π*) unimportant.