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Organic trisradicals featuring three-fold symmetry have attracted significant interest because of their unique magnetic properties associated with spin frustration. Herein, we describe the synthesis and characterization of a triangular prism-shaped organic cage for which we have coined the name PrismCage6+ and its trisradical trication—TR3(•+). PrismCage6+ is composed of three 4,4'-bipyridinium dications and two 1,3,5-phenylene units bridged by six methylene groups. In the solid state, PrismCage6+ adopts a highly twisted conformation with close to C3 symmetry as a result of encapsulating one PF6− anion as a guest. PrismCage6+ undergoes stepwise reduction to its mono-, di- and trisradical cations in MeCN on account of strong electronic communication between its 4,4'-bipyridinium units. TR3(•+), which is obtained by reduction of PrismCage6+ employing CoCp2, adopts a triangular prism-shaped conformation with close to C2v symmetry in the solid state. Temperature-dependent continuous-wave and nutation frequency-selective EPR spectra of TR3(•+) in frozen N,N-dimethylformamide indicate its doublet ground state. The doublet-quartet energy gap of TR3(•+) is estimated to be −0.06 kcal mol−1 and the critical temperature of spin-state conversion is found to be ca. 50 K, suggesting that it displays pronounced spin-frustration at the molecular level. To the best of our knowledge, this example is the first organic radicalmore »cage to exhibit spin frustration. The trisradical trication of PrismCage6+ opens up new possibilities for fundamental investigations and potential applications in the fields of both organic cages and spin chemistry.« less

Many scientific applications rely on sparse direct solvers for their numerical robustness. However, performance optimization for these solvers remains a challenging task, especially on GPUs. This is due to workloads of small dense matrices that are different in size. Matrix decompositions on such irregular workloads are rarely addressed on GPUs. This paper addresses irregular workloads of matrix computations on GPUs, and their application to accelerate sparse direct solvers. We design an interface for the basic matrix operations supporting problems of different sizes. The interface enables us to develop irrLU-GPU, an LU decomposition on matrices of different sizes. We demonstrate the impact of irrLU-GPU on sparse direct LU solvers using NVIDIA and AMD GPUs. Experimental results are shown for a sparse direct solver based on a multifrontal sparse LU decomposition applied to linear systems arising from the simulation, using finite element discretization on unstructured meshes, of a high-frequency indefinite Maxwell problem.