This paper reports DFT-computed electronic ground states, Mossbauer isomer shifts, O-O and Fe-O vibration frequencies, and thermodynamics of O-2 binding of heme models representing different distal (position E7) interactions, strictly validated against experimental data. Based on the results, the impact of specific types of distal interactions on oxyheme electronic structure can be systematized. Hydrogen bonding increases back-donation, O-O bond activation, and oxygen binding affinity. The heme side chains reduce isomer shifts by -0.06 mm/s due to electron withdrawal from iron, and distal hydrogen bonds can further reduce isomer shifts up to 0.07 mm/s. The O-O stretch vibration, the O-O distance, and the isomer shift possess substantial heuristic value in interpreting electronic structure, whereas other properties are less effective, based on computed correlation coefficients. Shorter Fe-O bond length does not correlate with O-2 affinity, as hydrogen bonding elongates both Fe-O and O-O bonds by similar to 0.01-0.02 angstrom, contrary to the situation absent from distal hydrogen bonds and of potential relevance to ligand activation where distal interactions are involved. An ionic (Weiss-type) model of Fe-O bonding combined with electron withdrawal by hydrogen bonds is shown to robustly explain the structural, spectroscopic, and thermodynamic properties of the hemes. The identified correlations may be useful, e.g., for designing O-2-activating catalysts or for diagnosing heme protein variants.