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We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and a locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the quimb library. Using hyperoptimized approximate contraction strategies, we present benchmark fermionic projected entangled pair state simulations of finite Hubbard models defined on the three-dimensional diamond lattice and random regular graphs. Published by the American Physical Society2025 

Abstract Cyclobutanes are prominent structural components in natural products and drug molecules. With the advent of strain‐release‐driven synthesis, ring‐opening reactions of bicyclo[1.1.0]butanes (BCBs) provide an attractive pathway to construct these three‐dimensional structures. However, the stereoselective difunctionalization of the central C−C σ‐bonds remains challenging. Reported herein is a covalent‐based organocatalytic strategy that exploits radical NHC catalysis to achieve diastereoselective acylfluoroalkylation of BCBs under mild conditions. The Breslow enolate acts as a single electron donor and provides an NHC‐bound ketyl radical with appropriate steric hindrance, which effectively distinguishes between the two faces of transient cyclobutyl radicals. This operationally simple method tolerates various fluoroalkyl reagents and common functional groups, providing a straightforward access to polysubstituted cyclobutanes (75 examples, up to >19 : 1 d.r.). The combined experimental and theoretical investigations of this organocatalytic system confirm the formation of the NHC‐derived radical and provide an understanding of how stereoselective radical‐radical coupling occurs. 

“Concentrate-and-degrade” is an effective strategy to promote mass transfer and degradation of pollutants in photocatalytic systems, yet suitable and cost-effective photocatalysts are required to practice the new concept. In this study, we doped a post-transition metal of Indium (In) on a novel composite adsorptive photocatalyst, activated carbon-supported titanate nanotubes (TNTs@AC), to effectively degrade perfluorooctanoic acid (PFOA). In/TNTs@AC exhibited both excellent PFOA adsorption (>99% in 30 min) and photodegradation (>99% in 4 h) under optimal conditions (25 °C, pH 7, 1 atm, 1 g/L catalyst, 0.1 mg/L PFOA, 254 nm). The heterojunction structure of the composite facilitated a cooperative adsorption mode of PFOA, i.e., binding of the carboxylic head group of PFOA to the metal oxide and attachment of the hydrophobic tail to AC. The resulting side-on adsorption mode facilitates the electron (e‒) transfer from the carboxylic head to the photogenerated hole (h+), which was the major oxidant verified by scavenger tests. Furthermore, the presence of In enables direct electron transfer and facilitates the subsequent stepwise defluorination. Finally, In/TNTs@AC was amenable to repeated uses in four consecutive adsorption-photodegradation runs. The findings showed that adsorptive photocatalysts can be prepared by hybridization of carbon and photoactive semiconductors and the enabled “concentrate-and-degrade” strategy is promising for the removal and degradation of trace levels of PFOA from polluted waters.