Thermodynamics of the Flexible Metal-Organic Framework Material MIL-53(Cr) From First Principles

We use first-principles density functional theory total energy and linear response phonon calculations to compute the Helmholtz and Gibbs free energy as a function of temperature, pressure, and cell volume in the flexible metal-organic framework material MIL-53(Cr) within the quasiharmonic approximation. GGA and metaGGA calculations were performed, each including empirical van der Waals (vdW) forces under the D2, D3, or D3(BJ) parameterizations. At all temperatures up to 500 K and pressures from -30 MPa to 30 MPa, two minima in the free energy versus volume are found, corresponding to the narrow pore ($np$) and large pore ($lp$) structures. Critical positive and negative pressures are identified, beyond which there is only one free energy minimum. While all results overestimated the stability of the $np$ phase relative to the $lp$ phase, the best overall agreement with experiment is found for the metaGGA PBEsol+RTPSS+U+J approach with D3 or D3(BJ) vdW forces. For these parameterizations, the calculated free energy barrier for the $np$-$lp$ transition is only 3 to 6 kJ per mole of Cr$_4$(OH)$_4$(C$_8$H$_4$O$_4$)$_4$

A review of R-packages for random-intercept probit regression in small clusters

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision

Hydrogen adsorption in metal-organic frameworks: the role of nuclear quantum effects

The role of nuclear quantum effects on the adsorption of molecular hydrogen in metal-organic frameworks (MOFs) has been investigated on grounds of Grand-Canonical Quantized Liquid Density-Functional Theory (GC-QLDFT) calculations. For this purpose, we have carefully validated classical H2 -host interaction potentials that are obtained by fitting Born-Oppenheimer ab initio reference data. The hydrogen adsorption has first been assessed classically using Liquid Density-Functional Theory (LDFT) and the Grand-Canonical Monte Carlo (GCMC) methods. The results have been compared against the semi-classical treatment of quantum effects by applying the Feynman-Hibbs correction to the Born-Oppenheimer-derived potentials, and by explicit treatment within the Grand-Canonical Quantized Liquid Density-Functional Theory (GC-QLDFT). The results are compared with experimental data and indicate pronounced quantum and possibly many-particle effects. After validation calculations have been carried out for IRMOF-1 (MOF-5), GC-QLDFT is applied to study the adsorption of H2 in a series of MOFs, including IRMOF-4, -6, -8, -9, -10, -12, -14, -16, -18 and MOF-177. Finally, we discuss the evolution of the H2 quantum fluid with increasing pressure and lowering temperature

The Bregman Variational Dual-Tree Framework

Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them quickly infeasible for moderate to large scale datasets. A significant effort to find more efficient solutions to the problem has been made in the literature. One of the state-of-the-art methods that has been recently introduced is the Variational Dual-Tree (VDT) framework. Despite some of its unique features, VDT is currently restricted only to Euclidean spaces where the Euclidean distance quantifies the similarity. In this paper, we extend the VDT framework beyond the Euclidean distance to more general Bregman divergences that include the Euclidean distance as a special case. By exploiting the properties of the general Bregman divergence, we show how the new framework can maintain all the pivotal features of the VDT framework and yet significantly improve its performance in non-Euclidean domains. We apply the proposed framework to different text categorization problems and demonstrate its benefits over the original VDT.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013

Efficient construction of free energy profiles of breathing metal–organic frameworks using advanced molecular dynamics simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials

Nuclear transparencies in relativistic A(e,e'p) models

Relativistic and unfactorized calculations for the nuclear transparency extracted from exclusive A(e,e'p) reactions for 0.3 \leq Q^2 \leq 10 (GeV/c)^2 are presented for the target nuclei C, Si, Fe and Pb. For Q^2 \geq 0.6 (GeV/c)^2, the transparency results are computed within the framework of the recently developed relativistic multiple-scattering Glauber approximation (RMSGA). The target-mass and Q^2 dependence of the RMSGA predictions are compared with relativistic distorted-wave impulse approximation (RDWIA) calculations. Despite the very different model assumptions underlying the treatment of the final-state interactions in the RMSGA and RDWIA frameworks, they predict comparable nuclear transparencies for kinematic regimes where both models are applicable.Comment: 15 pages, 4 figure

Forecasting of commercial sales with large scale Gaussian Processes

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.Comment: 1o pages, 5 figure