The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.
Postcombustion CO 2 capture technologies need to undergo several costly scale-up stages before their deployment to the industry. Rigorous process models with uncertainty quantification generate more informative simulations that can offer increased design confidence, and a measure of the technical risk the modeled system carries, enabling the effective development of fewer prototypes during scale-up. To assist the development and scale-up of fixed bed CO 2 adsorption technologies, we propose a framework for the quantification of uncertainty applied to the process of CO 2 adsorption using zeolite 13X. Two major sources of uncertainty are considered at the small, laboratory scale in the Langmuir adsorption model: parameter uncertainty and model-form discrepancy. First, the parameter uncertainty is quantified and analyzed, followed by the quantification and analysis of the parameter uncertainty and model-form discrepancy together. The uncertainty is quantified via Bayesian statistical calibration of the Langmuir isotherm model to experimental adsorption isotherm data. Orthogonal discrepancy terms are added to the Langmuir model, leading to a discrepancy-augmented sorbent model that adjusts for physical and chemical deficiencies of the pure Langmuir model (e.g., accounting for adsorption of multiple species on multiple sites instead of the assumed monolayer homogeneous adsorption). Modelform discrepancy is also caused by the deviation of the sorbent model from reality across scales; therefore, its inclusion in the adsorption model developed using data from the small-scale system improves inference and process model predictions at the large, fixed bed process scale. To study the propagation of the small-scale uncertainty to process scale, a rigorous one-dimensional dynamic, nonisothermal mathematical model of a fixed bed adsorber is developed. Both the parameter and model-form uncertainties are propagated through the adsorber model to evaluate the resulting uncertainty in key performance measures such as the breakthrough time. Results show that, if only parameter uncertainty is considered, it can lead to a highly conservative design of the adsorber resulting in higher capital investment. A third source of uncertainty, boundary data variability, is also studied at the process scale by means of sensitivity analysis: the effect of changes in the reactor inlet gas composition, flow rate, and temperature are examined.
Density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard corrections to treat strongly correlated electronic states. Unfortunately, the exact values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchangecorrelation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.
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