Hemoglobin (Hgb) forms tetramers (dimerized alpha-beta dimers), which enhance its globular stability and may also facilitate small gas molecule transport, as shown by recent all-atom Newtonian solvated simulations. Hydropathic bioinformatic thermodynamic scaling enables close comparisons of hemoglobin dimers with myoglobin and neuroglobin, and reveals many nonlocal wave-like features of strained Hgb structures at the coarse-grained amino acid level. The thermodynamic analysis employs two hydropathic scales, one describing abrupt first-order unfolding transitions, the other continuous second-order transitions. Small molecule exchange at hemes is a first-order process. Wave-like collective tetrameric features appropriate to ligand absorption and release, seen in optical experiments (short times), are identified thermodynamically at long times. Strain fields localized near hemes interfere with extended strain fields associated with dimer interfacial misfit, resulting in novel wavelength dependent dimer correlation function Fano antiresonances.