Importance of Many-Body Effects in the Kernel of Hemoglobin for Ligand Binding

We propose a mechanism for binding of diatomic ligands to heme based on a dynamical orbital selection process. This scenario may be described as bonding determined by local valence fluctuations. We support this model using linear-scaling first-principles calculations, in combination with dynamical mean-field theory, applied to heme, the kernel of the hemoglobin metalloprotein central to human respiration. We find that variations in Hund’s exchange coupling induce a reduction of the iron $3d$ density, with a concomitant increase of valence fluctuations. We discuss the comparison between our computed optical absorption spectra and experimental data, our picture accounting for the observation of optical transitions in the infrared regime, and how the Hund’s coupling reduces, by a factor of 5, the strong imbalance in the binding energies of heme with CO and ${\mathrm{O}}_2$ ligands.

Figure 1

Orbital selection process. Dependence of (a) the iron $3d$ subspace occupancy $n_d$ and (b) the effective spin quantum number $s$ on the Hund’s coupling $J$, for both unligated and ligated heme models. The physically relevant region $0.5<J<1\mathrm{eV}$ is highlighted in light gray (yellow). Isosurfaces of the real-space representation of the electronic spectral density of the HOMO of FeP-$d$ for (c) $J=0\mathrm{eV}$ and (d) $J=0.8\mathrm{eV}$. The large central sphere shows the location of the iron atom, and the four dark gray (blue) spheres indicate nitrogen atoms.

Figure 2

Valence fluctuations. (a) von Neumann entropy $\Lambda$ obtained by $\mathrm{DFT}+\mathrm{DMFT}$ for FeP-$p$ (circles) and FeP-$d$ (squares). The dominant electronic configurations for FeP-$d$ for (b) $J=0\mathrm{eV}$ and (c) $J=0.8\mathrm{eV}$. The pie wedge labeled other contains configurations with a weight smaller than 3%. The iron $3d$ spin $S^z$ and iron $3d$ occupancy $n_d$ of the dominant configurations are indicated.

Figure 3

Energetics. (a) Difference in CO and ${\mathrm{O}}_2$ binding energies $\Delta \Delta E$. The binding to CO is always favored; however, the imbalance is strongly reduced for $J>0.5\mathrm{eV}$. (b) Total energy of FeP as a function of $J$. The minimum of the total energy is obtained for $J=0.9\mathrm{eV}$.

Figure 4

Optical response. Optical conductivity of FeP-$d$ (bold line), FeP(CO) (solid), and $\mathrm{FeP}({\mathrm{O}}_2)$ (dashed line). The vertical arrow indicates the energy of the experimental peak associated with the Fe-N charge transfer. Inset: Experimental measurements [28] for unligated heme (bold line), oxyheme (dashed line) and carboxyheme (solid) are shown for comparison. $J=0.8\mathrm{eV}$ was used for these calculations.