Structural and functional details of heme protein complexes with HNO and the isoelectronic RNO (R = alkyl and aryl) molecules (metabolic intermediates) are largely unknown. We report a quantum chemical investigation of three characteristic spectroscopic properties, H-1 and N-15 NMR chemical shifts and NO vibrational frequencies in synthetic HNO and RNO heme complexes, with theory-versus-experiment correlation coefficients R-2 = 0.990-0.998. A new density functional theory (DFT) method was found to yield excellent predictions of experimental structures of HNO, RNO, and NO heme systems. Interestingly, this method also helps the identification of an excellent linear quantitative structure observable relationship between NO vibrational frequencies and bond lengths in all of these NO-containing systems. This suggests that NO vibrations are largely local effects of the NO bonds in these complexes and may help deduce the NO bond lengths from using experimental vibrational data in these systems. The NO vibrational frequencies in HNO, RNO, and NO metalloporphyrins were found to follow a general trend of NO > RNO > HNO complexes, as a result of the electron populations in the antibonding NO orbitals of NO < RNO < HNO complexes. Investigations of the NMR and IR/Raman spectroscopic data in HNO metal complexes show that HNO is a strong pi-acid. In addition, we performed the first quantum chemical investigation of the hydrogen-bond effect on HNO in MbHNO (Mb = myoglobin) models. On the basis of comparisons with experimental H-1 and N-15 NMR results and NO vibrational frequency in MbHNO, a dual hydrogen-bond mode for HNO in MbHNO was proposed. The enhanced stability from this dual hydrogen bonding may provide a basis for the unusual stability of MbHNO observed experimentally. These results should facilitate spectroscopic characterizations and structural investigations of HNO and RNO heme proteins and models.