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For simultaneous testing of multivariate normal means with known correlation matrix against two-sided alternatives, this paper introduces new methods with proven finite-sample control of false discovery rate. The methods are obtained by shifting each p-value to the left and considering a Benjamini–Hochberg-type linear step-up procedure based on these shifted p-values. The amount of shift for each -value is appropriately determined from the correlation matrix to achieve the desired false discovery rate control. Simulation studies and real-data application show favorable performances of the proposed methods when compared with relevant competitors. 

Abstract We report copper(II) and copper(III) trifluoromethyl complexes supported by a pyridinedicarboxamide ligand (L) as a platform for investigating the role of electron transfer in C(sp²)−H trifluoromethylation. While the copper(II) trifluoromethyl complex is unreactive towards (hetero)arenes, the formal copper(III) trifluoromethyl complex performs C(sp²)−H trifluoromethylation of a wide range of (hetero)arenes. Mechanistic studies using the copper(III) trifluoromethyl complex suggest that the mechanism of arene trifluoromethylation is substrate‐dependent. When the thermodynamic driving force for electron transfer is high, the reaction proceeds through a previously unidentified single electron transfer (SET) mechanism, where an initial electron transfer occurs between the substrate and oxidant prior to CF₃group transfer. Otherwise, a CF₃radical release/electrophilic aromatic substitution (S_EAr) mechanism is followed. These studies provide valuable insights into the role of strong oxidants and potential mechanistic dichotomy in Cu‐mediated C(sp²)−H trifluoromethylation. 

Abstract Due to their diverse potential in advanced electronics and energy technologies, electrically conducting metal‐organic frameworks (MOFs) are drawing significant attention. Although hexagonal 2D MOFs generally display impressive electrical conductivity because of their dual in‐plane (through bonds) and out‐of‐plane (through π‐stacked ligands) charge transport pathways, notable differences between these two orthogonal conduction routes cause anisotropic conductivity and lower bulk conductivity. To address this issue, we have developed the first redox‐complementary dual‐ligand 2D MOF Cu₃(HHTP)(HHTQ), featuring a π‐donor hexahydroxytriphenylene (HHTP) ligand and a π‐acceptor hexahydroxytricycloquinazoline (HHTQ) ligand located at alternate corners of the hexagons, which form either parallel HHTP and HHTQ stacks (AA stacking) or alternating HHTP/HHTQ stacks (AB stacking) along the c‐axis. Regardless of the stacking pattern, Cu₃(HHTP)(HHTQ) supports more effective out‐of‐plane conduction through either separate π‐donor and π‐acceptor stacks or alternating π‐donor/acceptor stacks, while promoting in‐plane conduction through the pushpull‐like heteroleptic coordination network. As a result, Cu₃(HHTP)(HHTQ) exhibits higher bulk conductivity (0.12 S/m at 295 K) than single‐ligand MOFs Cu₃(HHTP)₂(7.3 × 10⁻²S/m) and Cu₃(HHTQ)₂(5.9 × 10⁻⁴S/m). This work introduces a new design approach to improve the bulk electrical conductivity of 2D MOFs by supporting charge transport in both in‐ and out‐of‐plane direcations.