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. This combination of methods explicitly accounts for dynamical and multireference quantum physics, such as valence and spin fluctuations, of the 3d electrons, while treating a significant proportion of the protein (more than 1,000 atoms) with DFT. 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 the many-body effects induced by the Hund’s coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin.

https://www.pnas.org/content/pnas/111/16/5790.full.pdf

Renormalization of myoglobin–ligand binding energetics by quantum many-body effects

The transfer matrix approach for the calculation of layer Green functions with a tight-binding Hamiltonian is extended to the case of a nonorthogonal basis. The problem can be rewritten in terms of an energy- and overlap-dependent pseudopotential. An application is made to the calculation of the spectral and total densities of states for the (100) and (100) faces of tungsten. Comparisons with calculations without overlap indicates that overlap effects do not play an important role except at the point Gamma of the (100) surface, where changes in the energy positions and the intensities of the peaks are found.

https://iopscience.iop.org/article/10.1088/0022-3719/18/9/014/pdf

A nonorthogonal-basis calculation of the spectral density of surface states for the (100) and (110) faces of tungsten

The hemocyanin protein binds and transports molecular oxygen via two copper atoms at its core. The singlet state of the $${{\rm{Cu}}}_{2}{{\rm{O}}}_{2}$$
 core is thought to be stabilised by a superexchange pathway, but detailed in situ computational analysis is complicated by the multi-reference character of the electronic ground state. Here, electronic correlation effects in the functional site of hemocyanin are investigated using a novel approach, treating the localised copper 3d electrons with cluster dynamical mean field theory. This enables us to account for dynamical and multi-reference quantum mechanics, capturing valence and spin fluctuations of the 3d electrons. Our approach explains the stabilisation of the experimentally observed di-Cu singlet for the butterflied $${{\rm{Cu}}}_{2}{{\rm{O}}}_{2}$$
 core, with localised charge and incoherent scattering processes across the oxo-bridge that prevent long-lived charge excitations. This suggests that the magnetic structure of hemocyanin is largely influenced by the many-body corrections. The electronic structure of copper-based metalloproteins is important for their function in biological processes, but studying this from a computational standpoint can be challenging. Here, the authors report a dynamical mean field theory approach which reveals the role of strong electronic correlation effects in oxygen binding in the hemocyanin protein.

/pdf/superexchange-mechanism-and-quantum-many-body-excitations-in-2706vuh939.pdf

Superexchange mechanism and quantum many body excitations in the archetypal di-Cu oxo-bridge

For a generalized tight binding model of amorphous one-component systems, where the energy levels and the surrounding overlap and hopping integrals are linearly coupled, the localization theory of Economou and Cohen is applied. In terms of several approximations the localization function L(E) is discussed. Thereby it is confirmed that the off-diagonal randomness has a delocalization effect. An Anderson transition can only take place if diagonal disorder is strong enough. As an example, the influence of diagonal spin disorder due to electron correlation, treated in the alloy analogy for the Hubbard model, is studied.



Fur ein verallgemeinertes “tight-binding”-Modell von amorphen Ein-Komponenten-Systemen, wobei die Energieniveaus und die umgebenden Uberlappungs- und Hopping-Integrale linear gekoppelt sind, wird die Lokalisierungstheorie von Economou und Cohen angewendet. Die Lokalisierungsfunktion L(E) wird an Hand einiger Naherungen diskutiert. Dabei bestatigt sich, das die nichtdiagonale Unordnung einen Delokalisierungseffekt besitzt. Ein Andersonubergang findet nur statt, wenn die diagonale Unordnung gros genug ist. Als Beispiel wird der Einflus der diagonalen Spinunordnung untersucht, die durch Elektronenkorrelation, behandelt in der Legierungsanalogie fur das Hubbard-Modell, verursacht ist.

On the theory of electron localization in amorphous systems

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}.

Super-exchange mechanism and quantum many body excitations in the archetypal hemocyanin/tyrosinase di-Cu oxo-bridge

Formulae are derived for the electronic Green function of a system, and in particular of a crystal, when this is expressed as a linear combination of basis functions which are not mutually orthogonal. Expressions are derived for the electronic density of states and the electrical conductivity of a system in this representation, and the differences in these properties between perfect and imperfect crystals, and between different types of crystal, are examined. Application of the method to a simple cubic crystal with the Mathieu potential shows that, as for a one dimensional system, the use of optimized in place of fixed atomic orbitals as basis functions leads to a great increase in accuracy.

http://iopscience.iop.org/article/10.1088/0022-3719/5/15/010/pdf

A Bergmann

Papers

Calculation of electronic Green functions using nonorthogonal basis functions: application to crystals