A self-consistent ground-state formulation of the first-principles Hubbard U parameter validated on one-electron self-interaction error

In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard $U$ parameters may be used to quantify and amend the self-interaction errors ascribed to selected subspaces. Here, in order to enable the accurate, computationally convenient calculation of $U$ by means of DFT algorithms that locate the ground-state by direct total-energy minimization, we introduce a reformulation of the successful linear-response method for $U$ in terms of the fully-relaxed constrained ground-state density. Defining $U$ as an implicit functional of the ground-state density implies the comparability of DFT + Hubbard $U$ (DFT+$U$) total-energies, and related properties, as external parameters such as ionic positions are varied together with their corresponding first-principles $U$ values. Our approach provides a framework in which to address the partially unresolved question of self-consistency over $U$, for which plausible schemes have been proposed, and to precisely define the energy associated with subspace many-body self-interaction error. We demonstrate that DFT+$U$ precisely corrects the total energy for self-interaction error under ideal conditions, but only if a simple self-consistency condition is applied. Such parameters also promote to first-principles a recently proposed DFT+$U$ based method for enforcing Koopmans' theorem

Inapplicability of exact constraints and a minimal two-parameter generalization to the DFT plus U based correction of self-interaction error

In approximate density functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using efficient, constraint-resembling methods such as DFT + Hubbard $U$ (DFT+$U$). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of self-consistently optimized Lagrange multipliers, and while its use to automate error corrections is a compelling possibility, we show that it is limited by a fundamental incompatibility with constraints beyond linear order. We circumvent this problem by utilizing separate linear and quadratic correction terms, which may be interpreted either as distinct constraints, each with its own Hubbard $U$ type Lagrange multiplier, or as the components of a generalized DFT+$U$ functional. The latter approach prevails in our tests on a model one-electron system, $H_2^+$, in that it readily recovers the exact total-energy while symmetry-preserving pure constraints fail to do so. The generalized DFT+$U$ functional moreover enables the simultaneous correction of the total-energy and ionization potential or the correction of either together with the enforcement of Koopmans condition. For the latter case, we outline a practical, approximate scheme by which the required pair of Hubbard parameters, denoted as U1 and U2, may be calculated from first-principles.Comment: 7 pages, 5 figures. Accepted for Physical Review B Rapid Communications on 30th November 201

Oral health and elite sport performance

While the research base is limited, studies have consistently reported poor oral health in elite athletes since the first report from the 1968 Olympic Games. The finding is consistent both across selected samples attending dental clinics at major competitions and more representative sampling of teams and has led to calls from the International Olympic Committee for more accurate data on oral health. Poor oral health is an important issue directly as it can cause pain, negative effects on appearance and psychosocial effects on confidence and quality of life and may have long-term consequences for treatment burden. Self-reported evidence also suggests an impact on training and performance of athletes. There are many potential challenges to the oral health of athletes including nutritional, oral dehydration, exercise-induced immune suppression, lack of awareness, negative health behaviours and lack of prioritisation. However, in theory, oral diseases are preventable by simple interventions with good evidence of efficacy. The consensus statement aims to raise awareness of the issues of oral health in elite sport and recommends strategies for prevention and health promotion in addition to future research strategies

A self-contained ground-state approach for the correction of self-interaction error in approximate density-functional theory

Density functional theory (DFT), in its approximate Kohn-Sham formalism, is a highly-acclaimed computational tool that affords the practical and expeditious calculation of ground-state properties of molecules and solids, often with a very reasonable accuracy. It finds routine application in the fields of chemistry, physics, materials science, and biochemistry, where it now contributes in both a descriptive and predictive capacity. It is not, in practice, without systematic errors such as those defined by self-interaction and static correlation. These errors undermine the accurate description of particular systems that are beyond the scope of the approximate exchange-correlation functionals, particularly for those comprising so-called strongly-correlated electrons. The effective treatment of these errors is laid down in a number of formative works now adopted within the canon of Kohn-Sham DFT. Many of the most popular and affordable correction schemes entail the calculation of external parameters to diagnose and treat these pervasive errors on a per-electron basis, such as the DFT+Hubbard U method. A possibility that has not yet been explored, however, is the automation of these correction schemes for the provision of greater efficiency, versatility and comparability between DFT calculations. An automated procedure would enable the correction process to be self-contained, thereby circumventing the need for human input, and establish a standardised approach between the various softwares and electronic systems. Of particular interest is the application in high-throughput materials design, and the comparability of DFT+U total-energies for the calculation of thermodynamical quantities. In this dissertation, we present a comprehensive account of our work in pursuit of this goal. We motivate and describe an efficient self-contained approach for correcting the many-body self-interaction error in strongly-correlated systems from ground-statequantities within the DFT+U framework. Moreover, we implement this procedure in a linear-scaling code, which extends its applicability to large-scale systems. Specifically, we develop a highly accurate variational linear-response approach for calculating the Hubbard U and Hund\u27s J parameters, for which a unique criterion for their self-consistency is identified. Our results demonstrate that this scheme is accurate and versatile, and facilitates the correction of many-body self-interaction error for various systems. Moreover, we propose the novel construction of a generalised DFT+U functional that resolves Koopmans\u27 condition exactly in a one-electron system when supplied with the appropriate self-consistent U value. Our research provides insight into important questions about the practice and consequences of calculating corrective parameters for approximate DFT self-consistently, and opens up several new avenues for future developments