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To gain insight into the protonation state of enzymatic ferryl species we have examined the applicability of Badger's rule to heme and non-heme iron-oxygen bonds. Using density functional theory we have calculated r(e) and nu(e) for the Fe-O bonds of complexes with different axial ligands, iron-oxidation, oxygen-protonation, and spin states. Our results indicate that Badger's rule holds for heme and non-heme oxo and hydroxo complexes. We find that the long Fe-O bonds that have been reported in the crystal structures of the ferryl forms of myoglobin, horseradish peroxidase, cytochrome c peroxidase, and catalase deviate substantially from the values predicted by Badger's rule, while the short Fe-O bonds obtained from X-ray absorption measurements are in good agreement with Badger's rule. In light of our analysis we conclude that the ferryl forms of myoglobin, horseradish peroxidase, and cytochrome c peroxidase are authentic iron(IV)oxos with Fe-O bonds on the order of 1.66 A and pKa's < 4.
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