Palladium, platinum, and their alloys are promising catalysts for electrochemical CO 2 reduction reactions (CO 2 RR), leading to the design of durable and efficient catalysts for the production of useful chemicals in a more sustainable way. However, a deep understanding of the CO 2 RR mechanisms is still challenging because of the complexity and the factors influencing the system. The purpose of this study is to investigate at the atomic scale the first steps of the CO 2 RR, CO 2 activation and dissociation mechanisms on Pd x Pt 4−x clusters in the gas phase.To do it, we use Density Functional Theory (DFT)-based reaction path and ab initio molecular dynamics (AIMD) computations. Our research focuses on the description of CO 2 activation and dissociation processes via the computation of multistep reaction paths, providing insights into the site and binding mode dependent reactivity. Detailed understanding of the CO 2 −cluster interaction mechanisms and estimating of the reaction energy barriers facilitate comprehension of why and how catalysts are poisoned and identification of the most stable activated adducts configurations. We show that increasing the platinum content induces fluxional behavior of the cluster structure and biases CO 2 dissociation; in fact, our computations unveiled several dissociated CO 2 isomers that are very stable and that there are various isomerization processes leading to a dissociated structure (possibly a CO poisoned state) from an intactly bound CO 2 one (activated state). On the basis of the comparison of the Pd x Pt 4−x reaction paths, we can observe the promising catalytic activity of Pd 3 Pt in the studied context. Not only does this cluster composition favor CO 2 activation against dissociation (thereby expected to facilitate the hydrogenation reactions of CO 2 ), the potential energy surface (PES) is very flat among activated CO 2 isomers.
This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.
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