DFT simulations of selected strongly correlated functional materials: electronic and redox properties of vanadium and manganese oxides

A theoretical investigation is presented on three correlated transition metal oxide systems - one oxide of vanadium, a manganate and a manganite. Beyond theoretical interest in the strongly interacting electronic structures, each system is relevant to materials design and developing new technologies. For each material in the thesis, vanadium dioxide (VO2), manganese dioxide (β-MnO2) and lanthanum manganite (LaMnO3), reports are presented on the electronic, structural and thermodynamic properties calculated using density functional theory (DFT). Strongly interacting electrons are a major challenge to modelling techniques, so to begin we examine the capacity of DFT to describe VO2. Analysis is presented on the effect of on-site direct and exchange Coulomb corrections, and the exchange mixing parameter in hybrid functional calculations. VO2 phase transition potential energy surfaces are presented in terms of electronic and structural transition parameters. To access transition thermodynamics, zero temperature imaginary phonon modes are transformed to their transition temperature energies. The phonon and electron contributions to the total transition entropy are calculated, which allows us to discuss the nature of the VO2 phase transition. Surface thermodynamics are presented for VO2. Results predict the energetically favoured surfaces, particle morphologies, and surface terminations as a function of temperature and pressure. The Li and O adsorption thermodynamics of β-MnO2 surfaces are explored from the perspective of reducing cathode over-potentials in the Li-air cell. The surface redox chemistry and electronic structure are studied with and without Li adatoms, leading to predictions on the operation of β-MnO2 as a battery cathode material. For LaMnO3 it is found that intra-orbital exchange corrections to DFT reproduce electronic, magnetic and structural observables simultaneously. The importance of Hund's coupling to the LaMnO3 ground state is explored in detail

Gaussian process nowcasting: application to COVID-19 mortality reporting

Updating observations of a signal due to the delays in the measurement process is a common problem in signal processing, with prominent examples in a wide range of fields. An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty? Without this correction, raw data will often mislead by suggesting an improving situation. We present a flexible approach using a latent Gaussian process that is capable of describing the changing auto-correlation structure present in the reporting time-delay surface. This approach also yields robust estimates of uncertainty for the estimated nowcasted numbers of deaths. We test assumptions in model specification such as the choice of kernel or hyper priors, and evaluate model performance on a challenging real dataset from Brazil. Our experiments show that Gaussian process nowcasting performs favourably against both comparable methods, and against a small sample of expert human predictions. Our approach has substantial practical utility in disease modelling -- by applying our approach to COVID-19 mortality data from Brazil, where reporting delays are large, we can make informative predictions on important epidemiological quantities such as the current effective reproduction number

Lithium and oxygen adsorption at the beta-MnO2 (110) surface

The adsorption and co-adsorption of lithium and oxygen at the surface of rutile-like manganese dioxide (β-MnO2), which are important in the context of Li–air batteries, are investigated using density functional theory. In the absence of lithium, the most stable surface of β-MnO2, the (110), adsorbs oxygen in the form of peroxo groups bridging between two manganese cations. Conversely, in the absence of excess oxygen, lithium atoms adsorb on the (110) surface at two different sites, which are both tri-coordinated to surface oxygen anions, and the adsorption always involves the transfer of one electron from the adatom to one of the five-coordinated manganese cations at the surface, creating (formally) Li+ and Mn3+ species. The co-adsorption of lithium and oxygen leads to the formation of a surface oxide, involving the dissociation of the O2 molecule, where the O adatoms saturate the coordination of surface Mn cations and also bind to the Li adatoms. This process is energetically more favourable than the formation of gas-phase lithium peroxide (Li2O2) monomers, but less favourable than the formation of Li2O2 bulk. These results suggest that the presence of β-MnO2 in the cathode of a non-aqueous Li–O2 battery lowers the energy for the initial reduction of oxygen during cell discharge

Comparing the responses of the UK, Sweden and Denmark to COVID-19 using counterfactual modelling

The UK and Sweden have among the worst per-capita COVID-19 mortality in Europe. Sweden stands out for its greater reliance on voluntary, rather than mandatory, control measures. We explore how the timing and effectiveness of control measures in the UK, Sweden and Denmark shaped COVID-19 mortality in each country, using a counterfactual assessment: what would the impact have been, had each country adopted the others’ policies? Using a Bayesian semi-mechanistic model without prior assumptions on the mechanism or effectiveness of interventions, we estimate the time-varying reproduction number for the UK, Sweden and Denmark from daily mortality data. We use two approaches to evaluate counterfactuals which transpose the transmission profile from one country onto another, in each country’s first wave from 13th March (when stringent interventions began) until 1st July 2020. UK mortality would have approximately doubled had Swedish policy been adopted, while Swedish mortality would have more than halved had Sweden adopted UK or Danish strategies. Danish policies were most effective, although differences between the UK and Denmark were significant for one counterfactual approach only. Our analysis shows that small changes in the timing or effectiveness of interventions have disproportionately large effects on total mortality within a rapidly growing epidemic

Spontaneous Frenkel pair formation in zirconium carbide

With density functional theory we have performed molecular dynamics simulations of ZrC which displayed spontaneous Frenkel pair formation at a temperature of 3200 K, some 500 K below the melting point. To understand this behaviour, rarely seen in equilibrium simulations, we quenched and examined a set of lattices containing a Frenkel pair. Five metastable structures were found, and their formation energies and electronic properties were studied. Their thermal generation was found to be facilitated by a reduction of between 0.7 and 1.5 eV in formation energy due to thermal expansion of the lattice. With input from a quasi-harmonic description of the defect free energy of formation, an ideal solution model was used to estimate lower bounds on their concentration as a function of temperature and stoichiometry. At 3000 K (0.81 of the melting temperature) their concentration was estimated to be 1.2% per mole in a stoichiometric crystal, and 0.3% per mole in a crystal with 10% per mole of constitutional vacancies. Their contribution to heat capacity, thermal expansion and bulk modulus was estimated

Fast anharmonic free energy method with an application to vacancies in ZrC

We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature-dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a × 10 speedup on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make predictions on the thermodynamics of substoichiometric ZrC x , including vacancy concentration and heat capacity

The effectiveness of reference-free modified embedded atom method potentials demonstrated for NiTi and NbMoTaW

One of the effective potentials that has proven to be very versatile and useful for describing metals is the modified embedded atom method (MEAM) potential. The reference-free version of the MEAM (RF-MEAM) potential provides more flexibility for fitting than the 2NN-MEAM because it also describes the pair potential as an explicit function. In this work, we present a methodology to fit RF-MEAM potentials to DFT data. We then evaluate the performance of the fitted potential by comparing MD simulations with experimental and DFT data. As an example, the methodology is applied to a binary and a quaternary alloy, namely NiTi and NbMoTaW. In the case of the equi-atomic NiTi shape memory alloy, our attention focuses on designing a potential that properly captures its mechanical behavior, given that the existing potentials fail to predict elastic constants in agreement with experiments. To reach our aim, we included the stress tensors of different high temperature NiTi configurations in the fitting database. The obtained RF-MEAM potential outperforms existing EAM and MEAM potentials in predicting the lattice and elastic constants of austenitic and martensitic phases as well as the corresponding transformation temperatures. To demonstrate the suitability of this methodology also for more complex systems, a RF-MEAM potential is fitted to model the multi-component NbMoTaW high-entropy alloy. Validation is achieved through comparison between observables obtained through the MD output and ab initio data. The article also reports key improvements to the optimization code MEAMfit v2 and the freely-available LAMMPS implementation of the RF-MEAM formalism. Most notably, resorting to analytic derivatives of the objective function with respect to the potential parameters rather than derivatives through finite differences, the time necessary for fitting has decreased by an order of magnitude

Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil

Cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in Manaus, Brazil, resurged in late 2020 despite previously high levels of infection. Genome sequencing of viruses sampled in Manaus between November 2020 and January 2021 revealed the emergence and circulation of a novel SARS-CoV-2 variant of concern. Lineage P.1 acquired 17 mutations, including a trio in the spike protein (K417T, E484K, and N501Y) associated with increased binding to the human ACE2 (angiotensin-converting enzyme 2) receptor. Molecular clock analysis shows that P.1 emergence occurred around mid-November 2020 and was preceded by a period of faster molecular evolution. Using a two-category dynamical model that integrates genomic and mortality data, we estimate that P.1 may be 1.7- to 2.4-fold more transmissible and that previous (non-P.1) infection provides 54 to 79% of the protection against infection with P.1 that it provides against non-P.1 lineages. Enhanced global genomic surveillance of variants of concern, which may exhibit increased transmissibility and/or immune evasion, is critical to accelerate pandemic responsiveness

Unifying incidence and prevalence under a time-varying general branching process

Renewal equations are a popular approach used in modelling the number of new infections, i.e., incidence, in an outbreak. We develop a stochastic model of an outbreak based on a time-varying variant of the Crump–Mode–Jagers branching process. This model accommodates a time-varying reproduction number and a time-varying distribution for the generation interval. We then derive renewal-like integral equations for incidence, cumulative incidence and prevalence under this model. We show that the equations for incidence and prevalence are consistent with the so-called back-calculation relationship. We analyse two particular cases of these integral equations, one that arises from a Bellman–Harris process and one that arises from an inhomogeneous Poisson process model of transmission. We also show that the incidence integral equations that arise from both of these specific models agree with the renewal equation used ubiquitously in infectious disease modelling. We present a numerical discretisation scheme to solve these equations, and use this scheme to estimate rates of transmission from serological prevalence of SARS-CoV-2 in the UK and historical incidence data on Influenza, Measles, SARS and Smallpox