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  1. 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 radical 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. 
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    Free, publicly-accessible full text available June 1, 2024
  2. In this paper we consider the training stability of recurrent neural networks (RNNs) and propose a family of RNNs, namely SBO-RNN, that can be formulated using stochastic bilevel optimization (SBO). With the help of stochastic gradient descent (SGD), we manage to convert the SBO problem into an RNN where the feedforward and backpropagation solve the lower and upper-level optimization for learning hidden states and their hyperparameters, respectively. We prove that under mild conditions there is no vanishing or exploding gradient in training SBO-RNN. Empirically we demonstrate our approach with superior performance on several benchmark datasets, with fewer parameters, less training data, and much faster convergence. Code is available at 
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