Accounting for Strong Electronic Correlation in Metalloproteins

Metalloproteins play a crucial role in many key biological processes, from oxygen transport to photosynthesis. In the case of photosynthesis, the oxygen evolving complex (OEC) --- a CaMn\textsubscript{4}O\textsubscript{5} cluster --- catalyses water-to-oxygen-gas conversion. From a computational standpoint, accurately modelling the electronic structure of the OEC and other metalloproteins \emph{ab initio} is difficult, due to two challenges. Firstly, there is that of the strong electronic correlation present due to the partially-filled $3d$-subshells of the transition metal atoms, a classic example of where semi-local density functional theory (DFT) --- a go-to method for computational physicists --- fails. The second challenge is that of size: as this thesis will demonstrate, we must consider large cluster models that are thousands of atoms in size, which takes us beyond the reach of both plane-wave DFT and quantum chemistry methods. This thesis explores the capacity of density functional theory-plus-$U$ (DFT+$U$) and dynamical mean field theory (DMFT) to meet both of these challenges. It will demonstrate how both DFT+$U$ and DMFT can be readily married with linear-scaling DFT, meaning that these theories can be applied to protein systems containing thousands of atoms. In particular, this thesis presents the unification of ONETEP (a linear-scaling DFT code) and TOSCAM (a DMFT solver). It also presents a novel approach for determining Hubbard and Hund's parameters via linear response that is compatible with linear-scaling DFT and resolves inconsistencies between the linear response method and the DFT+$U$ corrective functional. These techniques are then applied to haem, haemocyanin, and the OEC, providing insight into the role of strong correlation in their electronic structure and function. In so doing, this thesis demonstrates how one can perform large-scale simulations of metalloproteins that account for strong electronic correlation. The results of this thesis are of significant interest due to both the importance of metalloproteins in nature, and the wealth of potential applications that would spring from a thorough understanding of their catalytic and binding properties.Cambridge Rutherford Memorial Scholarshi

Testing Koopmans spectral functionals on the analytically-solvable Hooke's atom

Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn-Sham density-functional theory counterparts, as demonstrated in earlier works on benchmarks of molecules and bulk systems. This work is a complementary study where -- instead of comparing against real, many-electron systems -- we test Koopmans spectral functionals on Hooke's atom, a toy two-electron system that has an analytical solution. As these calculations clearly illustrate, Koopmans spectral functionals do an excellent job of describing Hooke's atom. This work also provides broader insight into the features and capabilities of Koopmans spectral functionals more generally.Comment: 8 pages, 4 figures, 1 tabl

Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of any orbital. In crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy to a ground state provides a set of minimizing variational orbitals that are localized and thus break the periodicity of the underlying lattice. Despite this, we show that Bloch symmetry can be preserved and it is possible to describe the electronic states with a band-structure picture, thanks to the Wannier-like character of the variational orbitals. We also present a method to unfold and interpolate the electronic bands from supercell ($\Gamma$-point) calculations, which enables us to calculate full band structures with Koopmans-compliant functionals. The results obtained for a set of benchmark semiconductors and insulators show very good agreement with state-of-the-art many-body perturbation theory and experiments, underscoring the reliability of these spectral functionals in predicting band structures.Comment: 34 pages, 4 figure

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 containing transition metals and lanthanides, such as metalloproteins. We systematically introduce the necessary formalism, which must account for the non-orthogonal 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.Comment: Contains 46 pages and 12 figures, including 5 pages of supplementary materia

koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional formulation. These functionals address two fundamental issues with density functional theory (DFT). First, while Kohn-Sham eigenvalues can loosely mirror experimental quasiparticle energies, they are not meant to reproduce excitation energies and there is formally no connection between the two (except for the HOMO for the exact functional). Second, (semi-)local DFT deviates from the expected piecewise linear behavior of the energy as a function of the total number of electrons. This can make eigenvalues an even poorer proxy for quasiparticle energies and, together with the absence of the exchange-correlation derivative discontinuity, contributes to DFT's underestimation of band gaps. By enforcing a generalized piecewise linearity condition to the entire electronic manifold, Koopmans functionals yield molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost and preserving a functional formulation. This paper introduces "koopmans", an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations without requiring expert knowledge. The theory and algorithms behind Koopmans functionals are summarized, and it is shown how one can easily use the koopmans package to obtain reliable spectral properties of molecules and materials.Comment: 60 pages, 5 figures, 2 tables. Document includes supporting informatio

High-throughput determination of Hubbard U and Hund J values for transition metal oxides via linear response formalism

DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund's J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 2000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an atomate workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. To demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-p U value results in a significantly improved agreement between the computed lattice parameters and experiment.Comment: 18 pages, 6 figure

Abnormal reward prediction-error signalling in antipsychotic naive individuals with first-episode psychosis or clinical risk for psychosis.

Ongoing research suggests preliminary, though not entirely consistent, evidence of neural abnormalities in signalling prediction errors in schizophrenia. Supporting theories suggest mechanistic links between the disruption of these processes and the generation of psychotic symptoms. However, it is unknown at what stage in the pathogenesis of psychosis these impairments in prediction-error signalling develop. One major confound in prior studies is the use of medicated patients with strongly varying disease durations. Our study aims to investigate the involvement of the meso-cortico-striatal circuitry during reward prediction-error signalling in earliest stages of psychosis. We studied patients with first-episode psychosis (FEP) and help-seeking individuals at-risk for psychosis due to sub-threshold prodromal psychotic symptoms. Patients with either FEP (n = 14), or at-risk for developing psychosis (n = 30), and healthy volunteers (n = 39) performed a reinforcement learning task during fMRI scanning. ANOVA revealed significant (p < 0.05 family-wise error corrected) prediction-error signalling differences between groups in the dopaminergic midbrain and right middle frontal gyrus (dorsolateral prefrontal cortex, DLPFC). FEP patients showed disrupted reward prediction-error signalling compared to controls in both regions. At-risk patients showed intermediate activation in the midbrain that significantly differed from controls and from FEP patients, but DLPFC activation that did not differ from controls. Our study confirms that FEP patients have abnormal meso-cortical signalling of reward-prediction errors, whereas reward-prediction-error dysfunction in the at-risk patients appears to show a more nuanced pattern of activation with a degree of midbrain impairment but preserved cortical function

Koopmans spectral functionals in periodic-boundary conditions

Koopmans spectral functionals aim to describe simultaneously ground state properties and charged excitations of atoms, molecules, nanostructures and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically motivated orbital-density-dependent corrections. These corrections act on a set of localized orbitals that, in periodic systems, resemble maximally localized Wannier functions. At variance with the original, direct supercell implementation [Phys. Rev. X 8, 021051 (2018)], we discuss here i) the complex but efficient formalism required for a periodic-boundary code using explicit Brillouin zone sampling, and ii) the calculation of the screened Koopmans corrections with density-functional perturbation theory. In addition to delivering improved scaling with system size, the present development makes the calculation of band structures with Koopmans functionals straightforward. The implementation in the open-source Quantum ESPRESSO distribution and the application to prototypical insulating and semiconducting systems are presented and discussed

Edward L. Linscott Correspondence

Entries include a biography and a typed letter from Linscott