  We perform first-principles quantum mechanical studies of dioxygen ligand
binding to the hemocyanin protein. Electronic correlation effects in the
functional site of hemocyanin are investigated using a state-of-the-art
approach, treating the localised copper 3\emph{d} electrons with cluster
dynamical mean field theory (DMFT) for the first time. This approach has
enabled us to account for dynamical and multi-reference quantum mechanics,
capturing valence and spin fluctuations of the 3\emph{d} electrons. Our
approach explains the stabilisation of the experimentally observed di-Cu
singlet for the butterflied Cu$_2$O$_2$ core, with localised charge and
incoherent scattering processes across the oxo-bridge that prevent long-lived
charge excitations, suggesting that the magnetic structure of hemocyanin is
largely influenced by the many-body corrections. Our computational model is
supported by agreement with experimental optical absorption data, and provides
a revised understanding of the bonding of the peroxide to the di-Cu system
\emph{in vivo}.
