The gaseous ligands, CO, NO, and O-2 interact with the Fe ion in heme proteins largely via backbonding of Fe electrons to the pi* 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 Co-II(NO) porphyrin adducts (isoelectronic with Fe-II(OO) adducts), and the results of density functional theory (DFT) modeling for 5-coordinate Fe-II(NO), Co-II(NO), and Fe-II(OO) adducts. Inverse nu(MX)/nu(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 nonhybrid functionals are used, which avoid overemphasizing high-spin states. The BP86 functional gives correct ground states, a closed-shell singlet for Co-II(NO) and an open-shell singlet for the isoelectronic Fe-II(OO), as corroborated by structural data for Co-II(NO), and the nu(MX)/nu(XO) slope agreement with experiment for both adducts. However, for Fe-II(OO) adducts, the computed inverse nu(MX)/nu(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 sigma bonding via the in-plane d(xz)(+d(z)(2))-pi* orbital, when electron-donating substituents raise the d orbital energies sufficiently to render backbonding (d(yz)-pi*) unimportant.