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At least 199 records · Page 11

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗

Local thermodynamic mapping for effective liquid density-functional theory

The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.

Kyrlidis, Agathagelos↗

Zero-Field NMR and Millitesla-SLIC Spectra for >200 Molecules from Density Functional Theory and Spin Dynamics

NMR is usually performed at magnetic fields of 1 T and above to obtain sufficient sensitivity and spectral dispersion to identify chemicals based on chemical shifts and J couplings. At lower fields, the advent of hyperpolarization technologies and sensitive detectors can address sensitivity concerns. However, it remains disputed whether spectral signatures at zero and ultra-low fields are sufficient for chemical identification. Here, we report an all–electron DFT-based batch calculation of J-coupling constants, which are used to generate J coupling NMR spectra at zero field and 6.5 mT for over 200 small molecules. In the developed computational tool chain, we first used the all-electron FHI-aims code to calculate the molecular J couplings and chemical shifts. We then fed the calculated NMR parameters into the NMR simulation package SPINACH to simulate both heteronuclear J coupling spectra at zero-field, and homonuclear J coupling spectra as spin-lock induced crossing (SLIC) spectra at ultra-low field (6.5 mT). The resulting spectra demonstrate that zero and ultra-low field NMR spectra can represent unique identifiers of chemical structure for small molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploring Anomalous Photoelectron Angular Distributions in the Photoelectron Spectra of Gd 3 O 3 – : Study of Gd 3 O 2 – and Gd 3 O 3 – Using Photoelectron Spectroscopy and Density Functional Theory Calculations

Anion photoelectron (PE) spectra of lanthanide oxide clusters obtained previously have exhibited anomalous photoelectron angular distributions which were attributed to strong PE–valence electron (PEVE) interactions. Here, to further explore this effect, we have obtained the PE spectra of Gd 3 O 2 – and Gd 3 O 3 – , two clusters that have similarly complex electronic structures but contrasting symmetries. The spectra exhibit manifolds of detachment transitions at similar binding energies in a 0.5 eV window of energy. The electron affinity of Gd 3 O 2 is measured to be 1.29 ± 0.05 eV, and that of Gd 3 O 3 is 1.31 ± 0.05 eV. As seen in previous studies on lanthanide oxide cluster anions in lower than conventional oxidation states, transitions in spectra obtained lower photon energies are more congested than those obtained with higher photon energy, a signature of strong PEVE interactions. While the detachment transitions have predominantly parallel photoelectron angular distributions (PAD), the PAD varies across the manifold of transitions in the PE spectrum of Gd 3 O 3 – in a way that suggests four different subgroups of transitions. Results of calculations on Gd 3 O 2 – suggest kite or V-shape structures with antiferromagnetic coupling between one of the 4f 7 subshells with the two others. Calculations on Gd 3 O 3 – more definitively point to ring structures with a nearly isoenergetic ferromagnetically coupled high spin (24-tet) state and a dectet state in which one of the 4f 7 subshells is antiferromagnetically coupled with the other two. Taking these results as qualitative, we propose that strong mixing between the unperturbed states predicted computationally leads to overlapping transitions with different PADs.

anions↗

Correction to “Toward Chemical Accuracy for Chemi- and Physisorption with an Efficient Density Functional”

In the original manuscript, the value of parameter c was not explicitly provided. We wish to clarify that c was refitted to the hydrogen atom exchange energy, using the updated value of κ. With the updated κ = 0.2501, the optimized value of the parameter is c = 0.391596228. These values supersede any implicit assumptions about c in the original manuscript, and readers are encouraged to use these parameters for reproducing the results presented therein.

Adsorption↗

Systematic correction of the density functional theory spectra via a quantum Monte Carlo approach

Numerical outputs and driver scripts supporting auxiliary-boson corrected diffusion Monte Carlo (ABCDMC) benchmarks on second-row neutral atoms, cations, and dications, plus a C2 molecule active-space study. Includes NIST reference energies, ABCDMC timestep extrapolation summaries, orbital generation inputs, singles-only CASCI driver scripts, an O-atom basis-set convergence study, and the PyQMC boson code snapshot used for the calculations.

36 MATERIALS SCIENCE↗