How Do We Breathe? A Quantum-Mechanical Account of the Forbidden Spin Transition (Triplet → Quintet → Singlet) by Which Blood C

• Published in the American Chemical Society journal ACS Omega, the study represents hemoglobin with the FePIm (iron–porphyrin–imidazole) model and uses spin-polarized density functional theory (DFT) to track, at the atomic level, how the spin state changes over the course of oxygen binding.
• It shows that O2 binding proceeds as a multi-step spin crossing running from the triplet, through the quintet, to the singlet. This spin crossing dramatically lowers the binding activation barrier from 0.82 eV to 0.02 eV, accelerating the reaction.
• It identifies the position of the iron (Fe) atom relative to the porphyrin plane as the key indicator governing oxygen affinity, and it raises the possibility of applying the system as an oxygen-reduction catalyst in fuel cells.

[Quantum Biology Society]

The oxygen molecule (O2) in the air we inhale is, in its ground state, a triplet carrying two unpaired electrons. The oxygen bound to hemoglobin—oxyhemoglobin—is, by contrast, a singlet with no unpaired electrons, a fact already established in 1936 when Linus Pauling observed the diamagnetism of oxyhemoglobin. Yet a fundamental principle of quantum mechanics poses a puzzle here. In a chemical reaction, a transition in which the total spin of the reactants and products differs is forbidden by the spin selection rule (spin-forbidden) and should therefore proceed only very slowly. The direct conversion of triplet oxygen into a singlet complex is exactly such a case. How, then, does our body carry out this forbidden reaction so quickly and reversibly with every breath?

A 2018 study published in the ACS journal ACS Omega, "Spin-Dependent O2 Binding to Hemoglobin," answers this question through quantum-mechanical calculations. Daiichi Kurokawa, Jessiel Siaron Gueriba, and Wilson Agerico Diño of Osaka University in Japan simplified hemoglobin's active site to the FePIm model (iron Fe, porphyrin P, imidazole Im) and used spin-polarized DFT to trace, step by step, how the system's spin state changes along the oxygen-binding pathway. They showed that O2 binding is a spin-crossing process in which the system switches successively between several spin states—and that this very process is the key that unlocks the forbidden reaction.

■ As Oxygen Approaches, the Spin Shifts Step by Step

The researchers narrowed the distance (R) between the iron atom and the oxygen molecule from 7.21 angstroms (Å) in the deoxy state down to 1.84 Å in the oxy state, calculating the system's total magnetization (spin multiplicity) at each point. In the deoxyhemoglobin state, with O2 not yet bound, the entire system (FePIm plus the separated O2 molecule) was a triplet (multiplicity 3), and the iron atom protruded 0.18 Å out of the porphyrin plane.

As oxygen drew closer, the spin state did not change all at once but shifted in stages. At a point about 4 Å from the iron, the electrons in oxygen's antibonding (π*) orbital flipped their spin, raising the system to a septet (multiplicity 7)—a state nearly degenerate in energy with the triplet. Then, around R = 2.4 Å, it changed to a quintet (multiplicity 5), a shift accompanied by a lengthening of the bond between the two oxygen atoms within the O2 molecule. Finally, in the oxyhemoglobin state at R = 1.84 Å, oxygen formed a sigma (σ) bond between the iron's dz² orbital and its own π* orbital and stabilized as a singlet (multiplicity 1). In short, the system's total spin multiplicity traced a path from the triplet (degenerate with the septet), through the quintet, to the singlet.

■ The Key That Unlocks the Forbidden Reaction: Spin Crossing

Why this multi-step spin transition matters becomes clear from the activation-barrier analysis. When the researchers fixed the system's spin state as a septet, the activation barrier for oxygen binding was a substantial 0.82 eV. But when the system was allowed to cross from the septet to the singlet—spin crossing—the binding barrier fell sharply to 0.02 eV. A single spin crossing lowered the barrier roughly fortyfold.

The spin transition, in other words, is not an obstacle blocking oxygen binding but rather the passage that makes the forbidden reaction possible. Instead of directly connecting two states of different total spin (triplet oxygen and the singlet complex), the system detours through intermediate high-spin states, bypassing the spin selection rule and finding a low-energy path. For reference, a minimum-energy-path calculation with the atomic positions fully optimized (CINEB) yielded a binding barrier of 0.38 eV and an oxygen-release barrier of 0.92 eV. The researchers concluded that this spin crossing is the key factor governing the activation barrier.

■ The Switch for Oxygen Affinity: Iron Out of the Plane

The researchers identified one more important indicator: how far the iron atom sits out of the porphyrin plane (d). In the oxygen-free deoxy state the iron protruded 0.18 Å out of the plane, but in the oxygen-bound oxy state it settled almost within the plane, at 0.01 Å. This agrees well with the crystal structure determined by experiment.

Behind this movement lies an interaction between orbitals. In the deoxy state, the iron's dxy orbital interacts antibondingly with the nitrogen atoms of the porphyrin, pushing the iron out of the plane. But as oxygen binds and the electron in the dxy orbital flips its spin and moves to the dyz orbital, the dxy orbital empties and this antibonding interaction vanishes. As a result, the iron is drawn back into the porphyrin plane. The researchers concluded that, together with the iron–oxygen distance (R), this iron out-of-plane distance (d) is one of the two key reaction coordinates controlling oxygen affinity.

■ Significance and Outlook

The greatest significance of this study lies in its concrete explanation, in the language of quantum mechanics, of breathing—the most basic activity of life. Life performs the oxygen-binding reaction, forbidden under the spin selection rule, quickly and reversibly by way of a spin crossing that switches successively through several spin states. In a sense, we harness a quantum-mechanical spin transition with every breath.

The work also points to potential applications. The lengthening of the bond between the two oxygen atoms during an intermediate stage of binding suggests that the FePIm system could function as a catalyst that splits the oxygen molecule. The researchers noted the possibility of using the system as a cathode-electrode catalyst in polymer electrolyte fuel cells (PEFCs), where the oxygen reduction reaction takes place, while also pointing out that the challenge of overcoming the high activation barrier accompanying the reaction remains. By confronting head-on how life resolves the forbidden reaction of triplet oxygen binding to the heme iron, this study offers a solid starting point for further discussion from the standpoint of the quantum mechanics of respiration.

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https://pubs.acs.org/doi/10.1021/acsomega.8b00879