The electron-centric approach to the exchange-correlation energy.

The Kohn-Sham theory addresses the challenge of representing the kinetic energy by re-quantizing density functional theory at a level of non-interacting electrons. It transforms the many-electron problem into a fictitious non-interacting electron problem, with the many-electron effects concealed within the exchange-correlation (XC) energy, which is expressed in terms of the electron density ρ(r). Unlike the wave function, ρ(r) can be viewed as a classical quantity, and expressing the XC energy in terms of it circumvents the need for correlated wave functions. In this work, we once again employ the re-quantization strategy and determine the XC energy using a local one-particle Schrödinger equation. The ground-state eigenfunction of the corresponding Hamiltonian is a reference point (r) dependent orbital φr,σ(u, σ') which is subsequently used to generate the XC hole and the XC energy. The spin coordinate is denoted by σ and u is the electron-electron separation. The one-particle equation for φr,σ(u, σ') includes a local potential vr,σ(u, σ') that we approximate using two simple physical constraints. We assess the approximation by applying it to the helium iso-electronic series, the homogeneous electron gas, and the dissociation of the hydrogen molecule.

Generating Exchange-Correlation Functionals with a Simplified, Self-Consistent Correlation Factor Model.

We focus on the spherically averaged exchange-correlation hole ρXC(r, u) of density functional theory, which describes the reduction in the electron density at a distance u due to the reference electron localized at position r. The correlation factor (CF) approach, where the model exchange hole ρXmodel(r, u) is multiplied by a CF (fC(r, u)) to yield an approximation to the exchange-correlation hole ρXC(r, u) = fC(r, u) ρXmodel(r, u), has proven to be a powerful tool for the development of new approximations. One of the remaining challenges within the CF approach is the self-consistent implementation of the resulting functionals. To address this issue, here we propose a simplification of the previously developed CFs such that self-consistent implementations become feasible. As an illustration of the simplified CF model, we develop a new meta-GGA functional, and using only a minimum of empiricism, we provide an easy derivation of an approximation that is of an accuracy similar to more involved meta-GGA functionals.

The fourth-order expansion of the exchange hole and neural networks to construct exchange-correlation functionals.

The curvature Qσ of spherically averaged exchange (X) holes ρX,σ(r, u) is one of the crucial variables for the construction of approximations to the exchange-correlation energy of Kohn-Sham theory, the most prominent example being the Becke-Roussel model [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)]. Here, we consider the next higher nonzero derivative of the spherically averaged X hole, the fourth-order term Tσ. This variable contains information about the nonlocality of the X hole and we employ it to approximate hybrid functionals, eliminating the sometimes demanding calculation of the exact X energy. The new functional is constructed using machine learning; having identified a physical correlation between Tσ and the nonlocality of the X hole, we employ a neural network to express this relation. While we only modify the X functional of the Perdew-Burke-Ernzerhof functional [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], a significant improvement over this method is achieved.

The factorization ansatz for non-local approximations to the exchange-correlation hole.

Among the various types of approximations to the exchange-correlation energy (EXC), the completely non-local approach is one of the lesser explored approximation schemes. It has not yet reached the predictive power of the widely used generalized gradient approximations, meta-generalized gradient approximations, hybrids, etc. In non-local functionals pursued here, the electron density at every point in space is employed to express the exchange-correlation energy per particle ϵXC(r) at a given position r. Here, we use the non-local, spherical-averaged density ρ(r,u)=∫dΩu4πρ(r+u) as a starting point to construct approximate exchange-correlation holes through the factorization ansatz ρXC(r, u) = f(r, u)ρ(r, u). We present upper and lower bounds to the exchange energy per particle ϵX(r) in terms of ρ(r, u). The factor f(r, u) is then designed to satisfy various conditions that represent important exchange and correlation effects. We assess the resulting approximations and find that the complex, oscillatory structure of ρ(r, u) makes the construction of a corresponding f(r, u) very challenging. This conclusion, identifying the main issue of the non-local approximation, is supported by a detailed analysis of the resulting exchange-correlation holes.

Constructing and representing exchange-correlation holes through artificial neural networks.

One strategy to construct approximations to the exchange-correlation (XC) energy EXC of Kohn-Sham density functional theory relies on physical constraints satisfied by the XC hole ρXC(r, u). In the XC hole, the reference charge is located at r and u is the electron-electron separation. With mathematical intuition, a given set of physical constraints can be expressed in a formula, yielding an approximation to ρXC(r, u) and the corresponding EXC. Here, we adapt machine learning algorithms to partially automate the construction of X and XC holes. While machine learning usually relies on finding patterns in datasets and does not require physical insight, we focus entirely on the latter and develop a tool (ExMachina), consisting of the basic equations and their implementation, for the machine generation of approximations. To illustrate ExMachina, we apply it to calculate various model holes and show how to go beyond existing approximations.

The correlation factor approach: Combining density functional and wave function theory.

Several of the limitations of approximate exchange-correlation functionals within Kohn-Sham density functional theory can be eliminated by extending the single-determinant reference system to a multi-determinant one. Here, we employ the correlation factor ansatz to combine multi-configurational, self-consistent field (MCSCF) with approximate density functionals. In the proposed correlation factor approach, the exchange-correlation hole ρXC(r, u), a function of the reference point r and the electron-electron separation u, is written as a product of the correlation factor fC(r, u) and an exchange plus static-correlation hole ρXS(r, u), i.e., ρXC CFXS(r, u) = fC(r, u)ρXS(r, u). ρXS(r, u) is constructed to reproduce the exchange-correlation energy of an MCSCF reference wave function. The correlation factor fC(r, u) is designed to account for dynamic correlation effects that are absent in ρXS(r, u). The resulting approximation to the exchange-correlation energy, which we refer to as CFXStatic, is free of empirical parameters, and it combines the qualitatively correct description of the electronic structure obtainable with MCSCF with the advantages of approximate density functionals in accounting for dynamic correlation.

Characterization factors for terrestrial acidification at the global scale: a systematic analysis of spatial variability and uncertainty.

Characterization factors (CFs) are used in life cycle assessment (LCA) to quantify the potential impact per unit of emission. CFs are obtained from a characterization model which assess the environmental mechanisms along the cause-effect chain linking an emission to its potential damage on a given area of protection, such as loss in ecosystem quality. Up to now, CFs for acidifying emissions did not cover the global scale and were only representative of their characterization model geographical scope. Consequently, current LCA practices implicitly assume that all emissions from a global supply chain occur within the continent referring to the characterization method geographical scope. This paper provides worldwide 2°×2.5° spatially-explicit CFs, representing the change in relative loss of terrestrial vascular plant species due to an emission change of nitrogen oxides (NOx), ammonia (NH3) and sulfur dioxide (SO2). We found that spatial variability in the CFs is much larger compared to statistical uncertainty (six orders of magnitude vs. two orders of magnitude). Spatial variability is mainly caused by the atmospheric fate factor and soil sensitivity factor, while the ecological effect factor is the dominant contributor to the statistical uncertainty. The CFs provided in our study allow the worldwide spatially explicit evaluation of life cycle impacts related to acidifying emissions. This opens the door to evaluate regional life cycle emissions of different products in a global economy.

Life cycle impact assessment of terrestrial acidification: modeling spatially explicit soil sensitivity at the global scale.

This paper presents a novel life cycle impact assessment (LCIA) approach to derive spatially explicit soil sensitivity indicators for terrestrial acidification. This global approach is compatible with a subsequent damage assessment, making it possible to consistently link the developed midpoint indicators with a later endpoint assessment along the cause-effect chain-a prerequisite in LCIA. Four different soil chemical indicators were preselected to evaluate sensitivity factors (SFs) for regional receiving environments at the global scale, namely the base cations to aluminum ratio, aluminum to calcium ratio, pH, and aluminum concentration. These chemical indicators were assessed using the PROFILE geochemical steady-state soil model and a global data set of regional soil parameters developed specifically for this study. Results showed that the most sensitive regions (i.e., where SF is maximized) are in Canada, northern Europe, the Amazon, central Africa, and East and Southeast Asia. However, the approach is not bereft of uncertainty. Indeed, a Monte Carlo analysis showed that input parameter variability may induce SF variations of up to over 6 orders of magnitude for certain chemical indicators. These findings improve current practices and enable the development of regional characterization models to assess regional life cycle inventories in a global economy.

Development of normalization factors for Canada and the United States and comparison with European factors.

In Life Cycle Assessment (LCA), normalization calculates the magnitude of an impact (midpoint or endpoint) relative to the total effect of a given reference. The goal of this work is to calculate normalization factors for Canada and the US and to compare them with existing European normalization factors. The differences between geographical areas were highlighted by identifying and comparing the main contributors to a given impact category in Canada, the US and Europe. This comparison verified that the main contributors in Europe and in the US are also present in the Canadian inventory. It also showed that normalized profiles are highly dependent on the selected reference due to differences in the industrial and economic activities. To meet practitioners' needs, Canadian normalization factors have been calculated using the characterization factors from LUCAS (Canadian), IMPACT 2002+ (European), and TRACI (US) respectively. The main sources of uncertainty related to Canadian NFs are data gaps (pesticides, metals) and aggregated data (metals, VOC), but the uncertainty related to CFs generally remains unknown. A final discussion is proposed based on the comparison of resource extraction and resource consumption and raises the question of the legitimacy of defining a country by its geographical borders.

Epidemiology of Crohn's disease in Québec, Canada.

BACKGROUND: Crohn's disease (CD) is an idiopathic inflammatory bowel disease (IBD). We aimed to determine the prevalence and incidence of CD in Québec and characterize the demographic and health-related factors associated with this disease. METHODS: We identified CD cases in the provincial administrative databases for the years 1993-2002. The CD prevalence and incidence rates were estimated respectively for the periods 1993-2002 and 1998-2000. We validated the identified cases using clinically confirmed IBD cases. Predictor variables of CD were analyzed using the Poisson regression model to explain the variation in CD incidence rates across Québec. RESULTS: In all, 21,172 patients fulfilled the CD case definition for the period. The age and sex standardized average prevalence rate for 1993-2002 was 189.7 cases / 100,000 population and the age and sex standardized incidence rate of CD for the 1998-2000 period was 20.2 cases / 100,000 person-years. The female/male cases ratio among incident cases was 0.74 for the 0-14-year-old group, 1.30 for the 15-64-year-old group, and 1.77 for the cases older than 65 years old. After adjustment, independent predictors of CD incidence were: incidence of 5 reportable enteric diseases, proportion of individuals of Jewish ethnicity, and proportion of immigrant people. CONCLUSIONS: The identified predictors of CD explained 20% of the regional variance in the incidence rate of CD in the Québec population. Other factors such as genetic susceptibility to CD or the effect of an environmental cause should be taken into consideration in the models to explain the residual variance.

Artificial exomuscle investigations for applications--metal hydride.

In pursuing the development of bionic devices, Victhom identified a need for technologies that could replace current motorized systems and be better integrated into the human body motion. The actuators used to obtain large displacements are noisy, heavy, and do not adequately reproduce human muscle behavior. Subsequently, a project at Victhom was devoted to the development of active materials to obtain an artificial exomuscle actuator. An exhaustive literature review was done at Victhom to identify promising active materials for the development of artificial muscles. According to this review, metal hydrides were identified as a promising technology for artificial muscle development. Victhom's investigations focused on determining metal hydride actuator potential in the context of bionics technology. Based on metal hydride properties and artificial muscle requirements such as force, displacement and rise time, an exomuscle was built. In addition, a finite element model, including heat and mass transfer in the metal hydride, was developed and implemented in FEMLAB software.