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1. DFT Analysis of Methane C−H Activation and Over‐Oxidation by [Cu ₂ O] ²⁺ and [Cu ₂ O ₂ ] ²⁺ Sites in Zeolite Mordenite: Intra‐ versus Inter‐site Over‐Oxidation

   https://doi.org/10.1002/cphc.202100580  

   Panthi, Dipak; Adeyiga, Olajumoke; Odoh, Samuel_O (October 2021, ChemPhysChem)

   Abstract Methane over‐oxidation by copper‐exchanged zeolites prevents realization of high‐yield catalytic conversion. However, there has been little description of the mechanism for methane over‐oxidation at the copper active sites of these zeolites. Using density functional theory (DFT) computations, we reported that tricopper [Cu₃O₃]²⁺active sites can over‐oxidize methane. However, the role of [Cu₃O₃]²⁺sites in methane‐to‐methanol conversion remains under debate. Here, we examine methane over‐oxidation by dicopper [Cu₂O]²⁺and [Cu₂O₂]²⁺sites using DFT in zeolite mordenite (MOR). For [Cu₂O₂]²⁺, we considered the μ‐(η²:η²) peroxo‐, and bis(μ‐oxo) motifs. These sites were considered in the eight‐membered (8MR) ring of MOR. μ‐(η²:η²) peroxo sites are unstable relative to the bis(μ‐oxo) motif with a small interconversion barrier. Unlike [Cu₂O]²⁺which is active for methane C−H activation, [Cu₂O₂]²⁺has a very large methane C−H activation barrier in the 8MR. Stabilization of methanol and methyl at unreacted dicopper sites however leads to over‐oxidation via sequential hydrogen atom abstraction steps. For methanol, these are initiated by abstraction of the CH₃group, followed by OH and can proceed near 200 °C. Thus, for [Cu₂O]²⁺and [Cu₂O₂]²⁺species, over‐oxidation is an inter‐site process. We discuss the implications of these findings for methanol selectivity, especially in comparison to the intra‐site process for [Cu₃O₃]²⁺sites and the role of Brønsted acid sites. 

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2. Quantum-vibrational-state-selected Integral Cross Sections and Product Branching Ratios for the Ion-molecule Reactions of N ₂ ⁺ ( X ² Σ _g ⁺ ; v ⁺ = 0–2) + H ₂ O and H ₂ O ⁺ ( X ² B ₁ : v ₁ ⁺ v ₂ ⁺ v ₃ ⁺ = 000 and 100) + N ₂ in the Collision Energy Range of 0.04–10.00 eV

   https://doi.org/10.3847/1538-4357/aac9bf  

   Xu, Yuntao; Xiong, Bo; Chang, Yih Chung; Ng, Cheuk-Yiu (July 2018, The Astrophysical Journal)
3. Conversion of He(2 ³ S ) to He ₂ ( a ³ Σ _u ⁺ ) in Liquid Helium

   https://doi.org/10.1021/acs.jpclett.8b02454  

   Nijjar, P.; Krylov, A. I.; Prezhdo, O. V.; Vilesov, A. F.; Wittig, C. (September 2018, The Journal of Physical Chemistry Letters)
4. The factorisation property of l ^∞ ( X_k )

   https://doi.org/10.1017/s0305004120000304  

   LECHNER, RICHARD; MOTAKIS, PAVLOS; MÜLLER, PAUL F.X.; SCHLUMPRECHT, THOMAS (September 2021, Mathematical Proceedings of the Cambridge Philosophical Society)

   Abstract In this paper we consider the following problem: let X k , be a Banach space with a normalised basis ( e (k, j) ) j , whose biorthogonals are denoted by $${(e_{(k,j)}^*)_j}$$ , for $$k\in\N$$ , let $$Z=\ell^\infty(X_k:k\kin\N)$$ be their l ∞ -sum, and let $$T:Z\to Z$$ be a bounded linear operator with a large diagonal, i.e. , $$\begin{align*}\inf_{k,j} \big|e^*_{(k,j)}(T(e_{(k,j)})\big|>0.\end{align*}$$ Under which condition does the identity on Z factor through T ? The purpose of this paper is to formulate general conditions for which the answer is positive. 

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5. Investigation of Pb–B Bonding in PbB ₂ (BO) _n ⁻ ( n = 0–2): Transformation from Aromatic PbB ₂ ⁻ to Pb[B ₂ (BO) ₂ ] ^−/0 Complexes with BB Triple Bonds

   https://doi.org/10.1039/D3CP02800C  

   Chen, Qiang; Chen, Wei-Jia; Wu, Xin-Yao; Chen, Teng-Teng; Yuan, Rui-Nan; Lu, Hai-Gang; Yuan, Dao-Fu; Li, Si-Dian; Wang, Lai-Sheng (February 2024, Physical Chemistry Chemical Physics)

   Joint photoelectron spectroscopy and first-principles theory investigations indicate that the Pb-doped PbB₂(BO)_n⁻clusters (n= 0−2) undergo a transformation from σ + π doubly aromatic triangle PbB₂⁻to PbB₄(BO)₂^−/0complexes with a B≡B triple bond. 

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