In Situ Detection of Active Edge Sites in Single-Layer MoS2_2 Catalysts

MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and hydrogen evolution, but unravelling their atomic-scale structure under catalytic working conditions has remained significantly challenging. Ambient pressure X-ray Photoelectron Spectroscopy (AP-XPS) allows us to follow in-situ the formation of the catalytically relevant MoS2 edge sites in their active state. The XPS fingerprint is described by independent contributions to the Mo3d core level spectrum whose relative intensity is sensitive to the thermodynamic conditions. Density Functional Theory (DFT) is used to model the triangular MoS2 particles on Au(111) and identify the particular sulphidation state of the edge sites. A consistent picture emerges in which the core level shifts for the edge Mo atoms evolve counter-intuitively towards higher binding energies when the active edges are reduced. The shift is explained by a surprising alteration in the metallic character of the edge sites, which is a distinct spectroscopic signature of the MoS2 edges under working conditions

Properties of Classical and Quantum Jensen-Shannon Divergence

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (JD_alpha for alpha>0), the Jensen divergences of order alpha, which generalize JD as JD_1=JD. Using a result of Schoenberg, we prove that JD_alpha is the square of a metric for alpha lies in the interval (0,2], and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order alpha (QJD_alpha). We strengthen results by Lamberti et al. by proving that for qubits and pure states, QJD_alpha^1/2 is a metric space which can be isometrically embedded in a real Hilbert space when alpha lies in the interval (0,2]. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.Comment: 13 pages, LaTeX, expanded contents, added references and corrected typo

Continuity of the Maximum-Entropy Inference

We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous map from the convex set of expected values to the convex set of states because the image contains states of reduced support, while this map restricts to a smooth parametrization of a Gibbsian family of fully supported states. Here we prove for arbitrary ranking functions that the inference is continuous up to boundary points. This follows from a continuity condition in terms of the openness of the restricted linear map from states to their expected values. The openness condition shows also that ranking functions with a discontinuous inference are typical. Moreover it shows that the inference is continuous in the restriction to any polytope which implies that a discontinuity belongs to the quantum domain of non-commutative observables and that a geodesic closure of a Gibbsian family equals the set of maximum-entropy states. We discuss eight descriptions of the set of maximum-entropy states with proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur

MÖSSBAUER STUDIES OF THE ACTTVATED STATE OF Co-Mo HYDRODESULFURIZATION CATALYSTS

Des Co-Mo catalyseurs à hydrodésulfuration ont été étudiés par application de spectroscopie Mössbauer. En état calciné les Co ions se trouvent localisés dans le support en alumine. Pendant l'activation, une structure de surface se forme contenant Co, Mo, et S. Les résultats de mesures indiquent que le procédé catalytique est associé avec un changement en valence des Co ions.Co-Mo hydrodesulfurization catalysts have been studied by the use of Mössbauer spectroscopy. In the calcined state the Co ions are found to be located in the alumina carrier. During activation a surface structure containing Co, Mo, and S is formed. The measurements indicate that the catalytic process is associated with a valence change of the Co ions

The Bond Energy Model for Hydrotreating Reactions: Theoretical and Experimental Aspects

Recently, we have shown that the periodic variations in the HDS activities of different transition metal sulfides can be explained by a Bond Energy Model (BEM) based on theoretically calculated metal sulfur bond energies. The model differs from many previous explanations for the observed Balandin-type volcano curves. Specifically, the BEM model suggests that under most conditions, the variations in HDS activities are dominated by differences in the concentration of coordinatively unsaturated sites (CUS). The model has also been used to estimate the metal sulfur-bond strength of Co-Mo-S and NL-Mo-S and the promotion is explained in terms of the estimated bond energies for the different types of surface structures. EXAFS and TPR-S results are seen to provide experimental evidence for the BEM model. Besides coordinatively unsaturated sites, surface SH groups are also present and new evidence is presented based on 1H MAS NMR measurements. SH groups may also play an important catalytic role in the supply of hydrogen and for acid catalyzed reactions. The relative importance of the SH groups and the CUS sites appears to depend critically on the metal-sulfur bond energy. Furthermore, the BEM model is shown to provide a useful starting point for understanding various reactivity trends observed under different reaction conditions