Free energies of oxygen-linked subunit assembly and cooperative interaction have been determined for 34 molecular species of human hemoglobin, which differ by amino acid alterations as a result of mutation or chemical modification at specific sites. These studies required the development of extensions to our earlier methodology. In combination with previous results they comprise a data base of 60 hemoglobin species, characterized under the same conditions. The data base was analyzed in terms of the five following issues. (1) Range and sensitivity to site modifications. Deoxy tetramers showed greater average energetic response to structural modifications than the oxy species, but the ranges are similar for the two ligation forms. (2) Structural localization of cooperative free energy. Difference free energies of dimer-tetramer assembly (oxy minus deoxy) yielded delta Gc for each hemoglobin, i.e., the free energy used for modulation of oxygen affinity over all four binding steps. A structure-energy map constructed from these results shows that the alpha 1 beta 2 interface is a unique structural location of the noncovalent bonding interactions that are energetically coupled to cooperativity. (3) Relationship of cooperativity to intrinsic binding. Oxygen binding energetics for dissociated dimers of mutants strongly indicates that cooperativity and intrinsic binding are completely decoupled by tetramer to dimer dissociation. (4) Additivity, site-site coupling and adventitious perturbations. All these are exhibited by individual-site modifications of this study. Large nonadditivity may be correlated with global (quaternary) structure change. (5) Residue position vs. chemical nature. Functional response is solely dictated by structural location for a subset of the sites, but varies with side-chain type at other sites. The current data base provides a unique framework for further analyses and modeling of fundamental issues in the structural chemistry of proteins and allosteric mechanisms.