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We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equiv- ariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant net- work, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the inno- vative design of QHNet architecture, which not only obeys the underlying symmetries, but also en- ables the reduction of number of tensor products by 92%. In addition, QHNet prevents the expo- nential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular sys- tems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less mem- ory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). 

Lithium–sulfur (Li–S) batteries are regarded as one of the most promising next-generation electrochemical cells. However, shuttling of lithium polysulfide intermediates and sluggish kinetics in random deposition of lithium sulfide (Li 2 S) have significantly degraded their capacity, rate and cycling performance. Herein, few-layered MoS 2 nanosheets enriched with sulfur vacancies are anchored inside hollow mesoporous carbon (MoS 2−x /HMC) via S–C bonding and proposed as a novel functional mediator for Li–S batteries. Ultrathin MoS 2 sheets with abundant sulfur vacancies have strong chemical affinity to polysulfides and in the meantime catalyze their fast redox conversion with enhanced reaction kinetics as proved by experimental observations and first-principles density functional theory (DFT) calculations. At a current density of 1C, the MoS 2−x /HMC-S composite cathode exhibits a high initial capacity of 945 mA h g −1 with a high retained capacity of 526 mA h g −1 and a coulombic efficiency of nearly 100% after 500 cycles. The present work sheds light on the design of novel functional electrodes for next-generation electrochemical cells based on a simple yet effective vacancy engineering strategy. 

The shuttling of polysulfides with sluggish redox kinetics has severely retarded the advancement of lithium–sulfur (Li–S) batteries. In this work oxygen-deficient titanium dioxide (TiO 2 ) has been investigated as a novel functional host for Li–S batteries. Experimental and first-principles density functional theory (DFT) studies reveal that oxygen vacancies help to reduce polysulfide shuttling and catalyze the redox kinetics of sulfur/polysulfides during cycling. Consequently, the resulting TiO 2 /S composite cathode manifests superior electrochemical properties in terms of high capacity (1472 mA h g −1 at 0.2C), outstanding rate capability (571 mA h g −1 at 2C), and excellent cycling properties (900 mA h g −1 over 100 cycles at 0.2C). The present strategy offers a viable way through vacancy engineering for the design and optimization of high-performance electrodes for advanced Li–S batteries and other electrochemical devices.