Collisional dynamics of symmetric two-dimensional quantum droplets

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross−Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle numberN_c ≃ 48 for the quasi-Gaussian and flat-top shapes of the droplets.     

Classifying the ground-state phases of spin–orbit coupled spin-2 Bose–Einstein condensate in momentum space

The ground-state phases of two-dimensional spin-2 Bose–Einstein condensate with Rashba spin–orbit coupling are studied. For the equal strengths of the density-density interaction and the spin-exchange interaction, we classify the ground-state phases into four types of stable phases with spin–orbit coupling and spin singlet-pairing interaction in momentum space, i.e., the ring phase, the stripe phase, the triangular phase and the square phase. With increasing the spin–orbit coupling strength, the system undergoes a sequence phase transitions from the ring phase to the stripe phase, and to the square phase for the attractive spin singlet-pairing interaction ($c_2<0$), and the system undergoes a sequence phase transitions from the ring phase to the stripe phase, to the triangular phase, and to the square phase for the repulsive spin singlet-pairing interaction ($c_2>0$).     

Na原子链表面等离激元特性的含时密度泛函研究

本文用含时密度泛函理论研究了线性Na原子链的表面等离激元机理.主要在原子尺度下模拟计算了体系随着原子数增加及原子间距变化的集体激发过程.研究发现线性原子链有一个普遍的特性——存在一个纵模和两个横模.两个横模一般在实验上很难被观测到.纵模随着原子链长度增加,能量红移的同时,该纵模主峰的强度呈线性增长.随着原子个数的增加,端点模式(TE)开始蓝移,能量和偶极强度都逐渐趋向饱和.横模能量被劈裂的原因概括如下:(一)每个位置的电子受到的势不同,在两端的电子受到的势要比在中间的电子受到的势要高,因此两端的电荷积累也比中间多;(二)端点存在悬挂键,所以中间的电子-电子间相互作用与端点的不一样,这两方面又都与原子间距d有关.     

Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.     

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer

The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born–Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H₂O)₂. It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.     

Crystal structures of two isostructural compounds: a second polymorph of dipotassium hydrogen citrate,K2HC6H5O7, and potassium rubidium hydrogen citrate,KRbHC6H5O7

The crystal structures of a new polymorph of dipotassium hydrogen citrate, 2K⁺·HC₆H₅O₇^2?, and potassium rubidium hydrogen citrate, K⁺·Rb⁺·HC₆H₅O₇^2?, have been solved and refined using laboratory powder X‐ray diffraction and optimized using density functional techniques. In the new polymorph of the dipotassium salt, KO₇ and KO₈ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis and [111]. The hydrophobic methylene groups face each other in the channels. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to the central ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to a different central carboxylate group. In the potassium rubidium salt, the K⁺ and Rb⁺ cations are disordered over two sites, in approximately 0.72:0.28 and 0.28:0.72 ratios. KO₈ and RbO₉ coordination polyhedra share corners and edges to form a three‐dimensional framework with channels parallel to the a axis. The un‐ionized carboxylic acid group forms a strong charge‐assisted hydrogen bond to an ionized carboxylate group. The hydroxy group forms an intermolecular hydrogen bond to the central carboxylate group. Density functional theory (DFT) calculations on the ordered cation structures suggest that interchange of K⁺ and Rb⁺ at the two cation sites changes the energy insignificantly.     

Molecular Bridging Enables Isolated Iron Atoms on Stereoassembled Carbon Framework To Boost Oxygen Reduction for Zinc-Air Batteries

Realizing the synergy between active site regulation and rational structural engineering is essential in the electrocatalysis community but still challenging. Here, a matrix-confined co-pyrolysis strategy based on molecular bridging is demonstrated to realize highly dispersed Fe atoms on stereoassembled carbon framework. Both polyacrylonitrile matrix and organic linker from metal–organic frameworks (MOFs) provide sufficient N-anchoring sites for the generation of Fe−N₄ moieties. A high Fe loading of 2.9 wt.% is readily achieved based on the scalable approach without post-treatment. Owing to the presence of highly exposed Fe−N−C sites and well-tuned pore structures, isolated Fe atoms on porous carbon nanofiber framework (Fe−SA/NCF) exhibits decent oxygen reduction activity and stability in alkaline conditions via a near four-electron path, demonstrating superior performance as air cathode for zinc-air batteries (ZABs) to commercial Pt/C catalyst.     

Computational, 1H NMR,and X‐ray structural studies on 1‐arylurazole tetrazane dimers

Nitrogen‐centered urazole radicals exist in equilibrium with tetrazane dimers in solution. The equilibrium established typically favors the free‐radical form. However, 1‐arylurazole radicals bearing substituents at the ortho position favor the dimeric form. We were able to determine the structure of one of the dimers (substituted at both ortho positions with methyl groups), namely 1,2‐(2,4‐dimethylphenyl)‐2‐[2‐(2,4‐dimethylphenyl)‐4‐methyl‐3,5‐dioxo‐1,2,4‐triazolidin‐1‐yl]‐4‐methyl‐1,2,4‐triazolidine‐3,5‐dione, C₂₄H₂₈N₆O₄, via X‐ray crystallography. The experimentally determined structure agreed well with the computationally obtained geometry at the B3LYP/6‐311G(d,p) level of theory. The preferred syn conformation of these 1‐arylurazole dimers results in the two aromatic rings being proximate and nearly parallel, which leads to some interesting shielding effects of certain signals in the ¹H NMR spectrum. Armed with this information, we were able to decipher the more complicated ¹H NMR spectrum obtained from a dimer that was monosubstituted at the ortho position with a methyl group.