Sunday, June 10, 2012

Living and breathing quantum entanglement


Take a deep breath. You just created an entangled quantum state!

There is a really interesting paper on the arXiv

Quantum entanglement and Hund's rule are determinants to respiration
Cedric Weber, David D. O'Regan, Nicholas D. M. Hine, Peter B. Littlewood, Gabriel Kotliar, Mike C. Payne

They use DFT-DMFT (Density Functional Theory + Dynamical Mean-Field Theory) to study the binding of oxygen and carbon monoxide to iron-porphyrin (heme).

This is the process by which respiration occurs. Oxygen binds reversibly to the heme group in myoglobin. Unfortunately, CO does not bind reversibly and you die!

[Aside: Haemoglobin consists of four myoglobin molecules and they exhibit some interesting and important collective behaviour (allostery) first elucidated by Linus Pauling (who else!) from simple thermodynamic considerations.
This is nicely described in Thermal Physics by Kittel and Kroemer].

This new work shows that as the iron atom Hund's rule coupling J varies from 0 to 1 eV significant qualitative changes occur in the ground state. Specifically, it becomes a superposition of different iron spin (and valence) states.
Such behaviour cannot be captured by purely DFT-(Kohn-Sham) based calculations which are by assumption of single determinant character and so involve only one spin and charge state for the Fe atom.

As far as I am aware this is the first concrete application of DMFT to quantum chemistry. A few recent developments (e.g. this PRL from Columbia) were concerned with benchmark studies.

Earlier DFT studies show fine different states within 15 kJ/mole [~0.15 eV] of one another. Hence, it is reasonable that small J value variations could change the character of the ground state.

The TOTAL spin of the ground state must be definite. If I recally correctly, experimentally it is found to be a singlet with oxygen bound.

The authors don't mention that back in 1979 Case, Huynh, and Karplus studied a Pariser-Parr-Pople (like an extended Hubbard) model for heme-O2 and heme-CO. They found that the ground state of the former was an equal mixture of Fe2+(S=0)O2(S=0) and Fe2+(S=1)O2(S=1).

In a Barley Peroxidase there is experimental evidence for a Quantum Mixed-Spin Heme State consisting of a superposition of S=5/2 and S=3/2.

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