Importance of many-body effects in the Kernel of hemoglobin for ligand binding

Quantum embedding for molecules using auxiliary particles - the ghost Gutzwiller Ansatz

Strong/static electronic correlation mediates the emergence of remarkable phases of matter, and underlies the exceptional reactivity properties in transition metal-based catalysts. Modeling strongly correlated molecules and solids calls for multi-reference Ansätze, which explicitly capture the competition of energy scales characteristic of such systems. With the efficient computational screening of correlated solids in mind, the ghost Gutzwiller (gGut) Ansatz has been recently developed. This is a variational Ansatz which can be formulated as a self-consistent embedding approach, describing the system within a non-interacting, quasiparticle model, yet providing accurate spectra in both low and high energy regimes. Crucially, small fragments of the system are identified as responsible for the strong correlation, and are therefore enhanced by adding a set of auxiliary orbitals, the ghosts. These capture many-body correlations through one-body fluctuations and subsequent out-projection when computing physical observables. gGut has been shown to accurately describe multi-orbital lattice models at modest computational cost. In this work, we extend the gGut framework to strongly correlated molecules, for which it holds special promise. Indeed, despite the asymmetric embedding treatment, the quasiparticle Hamiltonian effectively describes all major sources of correlation in the molecule: strong correlation through the ghosts in the fragment, and dynamical correlation through the quasiparticle description of its environment. To adapt the gGut Ansatz for molecules, we address the fact that, unlike in the lattice model previously considered, electronic interactions in molecules are not local. Hence, we explore a hierarchy of approximations of increasing accuracy capturing interactions between fragments and environment, and within the environment, and discuss how these affect the embedding description of correlations in the whole molecule. We will compare the accuracy of the gGut model with established methods to capture strong correlation within active space formulations, and assess the realistic use of this novel approximation to the theoretical description of correlated molecular clusters.

Dioxygen and glucose force motion of the electron-transfer switch in the iron(III) flavohemoglobin-type nitric oxide dioxygenase

Kinetic and structural investigations of the flavohemoglobin-type NO dioxygenase have suggested critical roles for transient Fe(III)O2 complex formation and O2-forced movements affecting hydride transfer to the FAD cofactor and electron-transfer to the Fe(III)O2 complex. Stark-effect theory together with structural models and dipole and internal electrostatic field determinations provided a semi-quantitative spectroscopic method for investigating the proposed Fe(III)O2 complex and O2-forced movements. Deoxygenation of the enzyme causes Stark effects on the ferric heme Soret and charge-transfer bands revealing the Fe(III)O2 complex. Deoxygenation also elicits Stark effects on the FAD that expose forces and motions that create a more restricted NADH access to FAD for hydride transfer and switch electron-transfer off. Glucose also forces the enzyme toward an off state. Amino acid substitutions at the B10, E7, E11, G8, D5, and F7 positions influence the Stark effects of O2 on resting heme spin states and FAD consistent with the proposed roles of the side chains in the enzyme mechanism. Deoxygenation of ferric myoglobin and hemoglobin A also induces Stark effects on the hemes suggesting a common 'oxy-met' state. The ferric myoglobin and hemoglobin heme spectra are also glucose-responsive. A conserved glucose or glucose-6-phosphate binding site is found bridging the BC-corner and G-helix in flavohemoglobin and myoglobin suggesting novel allosteric effector roles for glucose or glucose-6-phosphate in the NO dioxygenase and O2 storage functions. The results support the proposed roles of a ferric O2 intermediate and protein motions in regulating electron-transfer during NO dioxygenase turnover.

Many-Body Study of Iron(III)-Bound Human Serum Transferrin

We present the very first density functional theory and dynamical mean field theory calculations of iron-bound human serum transferrin. Peaks in the optical conductivity at 250, 300, and 450 nm were observed, in line with experimental measurements. Spin multiplet analysis suggests that the ground state is a mixed state with high entropy, indicating the importance of strong electronic correlation in this system's chemistry.

First principles investigation of electron correlation and Lifshitz transition within iron polynitrides

Metal poly-nitrogen compounds are gaining great interests as potential high energy density materials. Several iron polynitrides have been recently synthesized and investigated under high pressure (2018Nature Communications92756). In this work the electron correlations within these iron poly-nitrogen compounds were self-consistently determined, benchmarked with those obtained from linear response approach. Along with the increase of the concentration of nitrogen, the Coulomb interaction strengths show a monotonic decrease, where FeN and FeN₂are antiferromagnetic and the others are ferromagnetic. Then the electron correlation is studied along with the pressure, where the electrons are more delocalized as pressure becomes higher. One electronic topological transition was found for FeN₂, owing to a breaking of symmetry of spin and a transition of magnetism induced by a structural change. The band structure, densities of states, Fermi surface and absorption spectra were calculated and discussed.

ONETEP + TOSCAM: Uniting Dynamical Mean Field Theory and Linear-Scaling Density Functional Theory

We introduce the unification of dynamical mean field theory (DMFT) and linear-scaling density functional theory (DFT), as recently implemented in ONETEP, a linear-scaling DFT package, and TOSCAM, a DMFT toolbox. This code can account for strongly correlated electronic behavior while simultaneously including the effects of the environment, making it ideally suited for studying complex and heterogeneous systems that contain transition metals and lanthanides, such as metalloproteins. We systematically introduce the necessary formalism, which must account for the nonorthogonal basis set used by ONETEP. In order to demonstrate the capabilities of this code, we apply it to carbon monoxide ligated iron porphyrin and explore the distinctly quantum-mechanical character of the iron 3d electrons during the process of photodissociation.

Magnetic mechanism for the biological functioning of hemoglobin

The role of magnetism in the biological functioning of hemoglobin has been debated since its discovery by Pauling and Coryell in 1936. The hemoglobin molecule contains four heme groups each having a porphyrin layer with a Fe ion at the center. Here, we present combined density-functional theory and quantum Monte Carlo calculations for an effective model of Fe in a heme cluster. In comparison with these calculations, we analyze the experimental data on human adult hemoglobin (HbA) from the magnetic susceptibility, Mössbauer and magnetic circular dichroism (MCD) measurements. In both the deoxygenated (deoxy) and the oxygenated (oxy) cases, we show that local magnetic moments develop in the porphyrin layer with antiferromagnetic coupling to the Fe moment. Our calculations reproduce the magnetic susceptibility measurements on deoxy and oxy-HbA. For deoxy-HbA, we show that the anomalous MCD signal in the UV region is an experimental evidence for the presence of antiferromagnetic Fe-porphyrin correlations. The functional properties of hemoglobin such as the binding of O2, the Bohr effect and the cooperativity are explained based on the magnetic correlations. This analysis suggests that magnetism could be involved in the functioning of hemoglobin.

The ONETEP linear-scaling density functional theory program

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Many-Body Effects in FeN4 Center Embedded in Graphene

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

Adiabatic Ligand Binding in Heme Proteins: Ultrafast Kinetics of Methionine Rebinding in Ferrous Cytochrome c

The dynamics of methionine geminate recombination following photodissociation in ferrous cytochrome c is investigated over a broad temperature range. The kinetic response, above the solvent glass transition ( T_g), is nearly monoexponential and displays a weak temperature dependence. Below T_g, the rebinding kinetics are nonexponential and can be explained using a quenched distribution of enthalpic rebinding barriers, arising from a relatively narrow distribution of heme out-of-plane displacements. The Arrhenius prefactor of this (Δ S = 2) reaction is ∼10¹¹ s^-1, which is similar to what has been found for the (Δ S = 1) NO binding reaction in heme proteins. This observation, along with other examples of ultrafast CO binding, provides strong evidence that ligand binding to heme is an adiabatic reaction with a spin-independent prefactor. In order to simultaneously account for the adiabatic nature of the reaction as well as the temperature dependence of both ultrafast CO and methionine geminate rebinding, it is proposed that a spin triplet state intersects and strongly couples to the reactant ( S = 2) and product ( S = 0) state surfaces in the transition state region along the reaction coordinate. It is also suggested that the nature of the intersecting triplet state and the reaction path may depend upon the proximity of the photolyzed ligand relative to the iron atom. At temperatures below ∼60 K, the kinetic data suggest that there is either an unexpected retardation of the heme photoproduct relaxation or that heavy atom quantum mechanical tunneling becomes significant.

Toward a predictive theory of correlated materials

Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green's functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

Applications of large-scale density functional theory in biology

Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

Dynamical mean field theory-based electronic structure calculations for correlated materials

We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.

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

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.

The superior catalytic CO oxidation capacity of a Cr-phthalocyanine porous sheet

Two-dimensional organometallic sheets containing regularly and separately distributed transition atoms (TMs) have received tremendous attentions due to their flexibility in synthesis, well-defined geometry and the promising applications in hydrogen storage, electronic circuits, quantum Hall effect, and spintronics. Here for the first time we present a study on the superior catalytic CO oxidation capacity of a Cr-phthalocyanine porous sheet proceeding first via Langmuir-Hinshelwood (LH) mechanism and then via Eley-Rideal (ER) mechanism. Compared to the noble metal based catalysts or graphene supported catalysts, our studied system has following unique features: without poisoning effect and clustering problem, having comparable reaction energy barrier for low-temperature oxidation, and low cost for large-scale catalytic CO oxidation in industry.

Polarized Protein-Specific Charges from Atoms-in-Molecule Electron Density Partitioning

Atomic partial charges for use in traditional force fields for biomolecular simulation are often fit to the electrostatic potentials of small molecules and, hence, neglect large-scale electronic polarization. On the other hand, recent advances in atoms-in-molecule charge derivation schemes show promise for use in flexible force fields but are limited in size by the underlying quantum mechanical calculation of the electron density. Here, we implement the density derived electrostatic and chemical charges method in the linear-scaling density functional theory code ONETEP. Our implementation allows the straightforward derivation of partial atomic charges for systems comprising thousands of atoms, including entire proteins. We demonstrate that the derived charges are chemically intuitive, reproduce ab initio electrostatic potentials of proteins and are transferable between closely related systems. Simulated NMR data derived from molecular dynamics of three proteins using force fields based on the ONETEP charges are in good agreement with experiment.

Electrostatic considerations affecting the calculated HOMO-LUMO gap in protein molecules

A detailed study of energy differences between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps) in protein systems and water clusters is presented. Recent work questioning the applicability of Kohn-Sham density-functional theory to proteins and large water clusters (Rudberg 2012 J. Phys.: Condens. Matter 24 072202) has demonstrated vanishing HOMO-LUMO gaps for these systems, which is generally attributed to the treatment of exchange in the functional used. The present work shows that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Practical solutions for ensuring the gap is maintained when the system size is increased are demonstrated. This work has important implications for the use of large-scale density-functional theory in biomolecular systems, particularly in the simulation of photoemission, optical absorption and electronic transport, all of which depend critically on differences between energies of molecular orbitals.