  We carry out a first-principles atomistic study of the electronic mechanisms
of ligand binding and discrimination in the myoglobin protein. Electronic
correlation effects are taken into account using one of the most advanced
methods currently available, namely a linear-scaling density functional theory
(DFT) approach wherein the treatment of localized iron 3d electrons is further
refined using dynamical mean-field theory (DMFT). This combination of methods
explicitly accounts for dynamical and multi-reference quantum physics, such as
valence and spin fluctuations, of the 3d electrons, whilst treating a
significant proportion of the protein (more than 1000 atoms) with density
functional theory. The computed electronic structure of the myoglobin complexes
and the nature of the Fe-O2 bonding are validated against experimental
spectroscopic observables. We elucidate and solve a long standing problem
related to the quantum-mechanical description of the respiration process,
namely that DFT calculations predict a strong imbalance between O2 and CO
binding, favoring the latter to an unphysically large extent. We show that the
explicit inclusion of many body-effects induced by the Hund's coupling
mechanism results in the correct prediction of similar binding energies for
oxy- and carbonmonoxymyoglobin.
