The interplay between FeC and CO bonding in carboxymyoglobin (MbCO) and the role of potential hydrogen bonding between the CO moiety and the side chains of the surrounding protein amino acids have been the subject of numerous experimental and theoretical studies. In this work, we present a quantitative measure for the intrinsic FeC and CO bond strength in MbCO, as well as for CO⋯H bonding, based on the local vibrational mode analysis, originally developed by Konkoli and Cremer. We investigated a gas phase model, two models of the wild-type protein, and 17 protein mutations that change the distal polarity of the heme pocket, as well as two protein mutations of the heme porphyrin ring. Based on local mode force constants, we could quantify for the first time the suggested inverse relationship between the CO and FeC bond strength, the strength of CO⋯H bonding, and how it weakens the CO bond. Combined with the natural orbital analysis, we could also confirm the key role of π back donation between Fe and the CO moiety in determining the FeC bond strength. We further clarified that CO and FeC normal modes couple with other protein motions in the protein environment. Therefore, normal mode frequencies/force constants are not suited as bond strength descriptors and instead their local mode counterparts should be used. Our comprehensive results provide new guidelines for the fine-tuning of existing and the design of MbCO models with specific FeC, CO, and CO⋯H bond strengths.Graphical abstract.
Keywords: DFT; Local mode force constants; Local vibrational theory; Myoglobin; QM/MM; Vibrational spectroscopy.