Flower pollination is an intriguing process in the natural world. Its evolutionary characteristics can be used to design new optimization algorithms. In this paper, we propose a new algorithm, ...namely, flower pollination algorithm, inspired by the pollination process of flowers. We first use ten test functions to validate the new algorithm, and compare its performance with genetic algorithms and particle swarm optimization. Our simulation results show the flower algorithm is more efficient than both GA and PSO. We also use the flower algorithm to solve a nonlinear design benchmark, which shows the convergence rate is almost exponential.
This paper presents a new algorithm, termed truncated amplitude flow (TAF), to recover an unknown vector <inline-formula> <tex-math notation="LaTeX"> {x} </tex-math></inline-formula> from a system of ...quadratic equations of the form <inline-formula> <tex-math notation="LaTeX">y_{i}=|\langle {a}_{i}, {x}\rangle |^{2} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX"> {a}_{i} </tex-math></inline-formula>'s are given random measurement vectors. This problem is known to be NP-hard in general. We prove that as soon as the number of equations is on the order of the number of unknowns, TAF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with both the number of unknowns and the number of equations. Our TAF approach adapts the amplitude-based empirical loss function and proceeds in two stages. In the first stage, we introduce an orthogonality-promoting initialization that can be obtained with a few power iterations. Stage two refines the initial estimate by successive updates of scalable truncated generalized gradient iterations , which are able to handle the rather challenging nonconvex and nonsmooth amplitude-based objective function. In particular, when vectors <inline-formula> <tex-math notation="LaTeX"> {x} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">{a}_{i} </tex-math></inline-formula>'s are real valued, our gradient truncation rule provably eliminates erroneously estimated signs with high probability to markedly improve upon its untruncated version. Numerical tests using synthetic data and real images demonstrate that our initialization returns more accurate and robust estimates relative to spectral initializations. Furthermore, even under the same initialization, the proposed amplitude-based refinement outperforms existing Wirtinger flow variants, corroborating the superior performance of TAF over state-of-the-art algorithms.
The rare earth element doped germanium cluster represents a fundamental nanomaterial and exhibits potential in next‐generation industrial electronic nanodevices and applied semiconductors. Herein, ...the cerium‐doped germanium anionic nanocluster CeGen− (n = 5–17) has been comprehensively investigated by the double hybrid density functional theory of mPW2PLYP associated with the unbiased global searching technique of artificial bee colony algorithm. The cluster's growth pattern undergoes three stages: n = 5–9 with the replaced structure, n = 10–15 with the linked structure, and n ≥ 16 forming a Ce‐encapsulated in Ge inner cage motif. The clusters' PES, IR, and Raman spectra were simulated, and their HOMO‐LUMO gap, magnetism, charge transfer, and relative stability were predicted. These theoretical values can serve as a reference for future experiments to some extent. Moreover, the special D2d symmetry cage geometry of CeGe16− leads to a higher stability and preferred energy gap, making it an ideal candidate for further studies on its aromaticity, UV–vis spectra, and chemical bonding characteristics. In summary, CeGe16− has excellent optical activity that can be potentially employed as a building block in the development of optoelectronic functional materials.
Nanocluster CeGen− (n = 5–17) was investigated by mPW2PLYP quantum calculation associated with the ABCluster unbiased global searching technique. The structure growth pattern and various physicochemical properties of the clusters were predicted. The result shows CeGe16− has good stability, aromaticity, and broad sunlight absorption range.
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The design of new materials is an important subject in order to attain new properties and applications, and it is of particular interest when some peculiar topological properties such as reduced ...dimensionality and rule‐breaking chemical bonding are involved. In this work, we designed a novel two‐dimensional (2D) inorganic material, namely Be2C monolayer, by comprehensive density functional theory (DFT) computations. In Be2C monolayer, each carbon atom binds to six Be atoms in an almost planar fashion, forming a quasi‐planar hexacoordinate carbon (phC) moiety. Be2C monolayer has good stability and is the lowest‐energy structure in 2D space confirmed by a global minima search based on the particle‐swarm optimization (PSO) method. As a semiconductor with a direct medium band gap, Be2C monolayer is promising for applications in electronics and optoelectronics.
Promising material: In the two‐dimensional Be2C monolayer, each carbon atom binds to six Be atoms forming a quasi‐planar hexacoordinate carbon moiety (see structure; C black, Be green). Be2C monolayer has good stability and is the global minimum structure in 2D space. Further, it is semiconducting with a moderate direct band gap.
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Among the list of planar tetracoordinate atoms, the smallest element hydrogen is missing. No experimental and theoretical evidence have ever been put forwarded. Herein, we introduce the first planar ...tetracoordinate hydrogen atom (ptH) in the global minimum geometry of In4H+ cluster. Bonding analysis indicates that the central hydrogen atom is acting like a proton and significant charge transfer from the surrounding In4 framework results in a negative charge of the central hydrogen atom. The proposed global minimum geometry possesses σ‐aromaticity and the central hydrogen atom forms unusual multicentre bond with more than three centres.
Planar tetracoordinate hydrogen atom has been predicted for the first time in the global minimum D4h geometry of In4H+ cluster.
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Experimental and computational simulations revealed that boron clusters, which favor planar (2D) structures up to 18 atoms, prefer 3D structures beginning at 20 atoms. Using global optimization ...methods, we found that the B 20 neutral cluster has a double-ring tubular structure with a diameter of 5.2 Å. For the anion, the tubular structure is shown to be isoenergetic to 2D structures, which were observed and confirmed by photoelectron spectroscopy. The 2D-to-3D structural transition observed at B 20 , reminiscent of the ring-to-fullerene transition at C 20 in carbon clusters, suggests it may be considered as the embryo of the thinnest single-walled boron nanotubes. photoelectron spectroscopy density functional calculation global minimum search
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•A new complex platinum compound is investigated.•Up to two DESO molecules may exist as neutral ligands in the platinum (IV) complex ion.•Strong cation-anion coordination explains an ...experimentally derived high melting point.
Diethyl sulfoxide (DESO) is far less known than its shorter-alkyl-chain homolog, dimethyl sulfoxide. New fundamental and applied research works routinely appear from a few research groups in the world. Recently, the tetraethylammonium diethylsulfoxidopentachloroplatinate complex compound was synthesized containing the DESO molecule as a neutral ligand. In the present paper, we use a systematic computational method to rationalize the mentioned synthetic achievement in coordination chemistry. We show that only up to two DESO molecules may exist in the platinum (IV) complex ion, whereas all higher contents of DESO are thermodynamically unstable and the sterical factor plays an important role in their instabilities. Structural analysis of the tetraethylammonium diethylsulfoxidopentachloroplatinate ion pair reveals its rather strong cation–anion coordination and for the first time explains an experimentally derived high melting point. The reported results are expected to inspire experimental efforts to extend the universe of senior sulfoxides as neutral organic ligands in d-metal complexes.
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Chirality plays an important role in chemistry, biology, and materials science. The recent discovery of the B40 –/0 borospherenes marks the onset of a class of boron-based nanostructures. Here we ...report the observation of axially chiral borospherene in the B39 – nanocluster on the bases of photoelectron spectroscopy, global minimum searches, and electronic structure calculations. Extensive structural searches in combination with density functional and CCSD(T) calculations show that B39 – has a C 3 cage global minimum with a close-lying C 2 cage isomer. Both the C 3 and C 2 B39 – cages are chiral with degenerate enantiomers. The C 3 global minimum consists of three hexagons and three heptagons around the vertical C 3 axis. The C 2 isomer is built on two hexagons on the top and at the bottom of the cage with four heptagons around the waist. Both the C 3 and C 2 axially chiral isomers of B39 – are present in the experiment and contribute to the observed photoelectron spectrum. The chiral borospherenes also exhibit three-dimensional aromaticity, featuring σ and π double delocalization for all valence electrons. Molecular dynamics simulations reveal that these chiral B39 – cages are structurally fluxional above room temperature, compared to the highly robust D 2d B40 borospherene. The current findings add chiral members to the borospherene family and indicate the structural diversity of boron-based nanomaterials.
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9.
B7Be6B7: A Boron‐Beryllium Sandwich Complex Dong, Xue; Tiznado, William; Liu, Yu‐qian ...
Angewandte Chemie International Edition,
August 1, 2023, 20230801, Volume:
62, Issue:
31
Journal Article
Peer reviewed
Open access
Planar boron clusters have often been regarded as “π‐analogous” to aromatic arenes because of their similar delocalized π‐bonding. However, unlike arenes such as C5H5− and C6H6, boron clusters have ...not previously shown the ability to form sandwich complexes. In this study, we present the first sandwich complex involving beryllium and boron, B7Be6B7. The global minimum of this combination adopts a unique architecture having a D6h geometry, featuring an unprecedented monocyclic Be6 ring sandwiched between two quasi‐planar B7 motifs. The thermochemical and kinetic stability of B7Be6B7 can be attributed to strong electrostatic and covalent interactions between the fragments. Chemical bonding analysis shows that B7Be6B7 can be considered as a B73−Be66+B73− complex. Moreover, there is a significant electron delocalization within this cluster, supported by the local diatropic contributions of the B7 and Be6 fragments.
We report the discovery of a previously unknown sandwich‐type complex consisting of beryllium and boron, which exhibits remarkable thermochemical and kinetical stability and displays aromatic characteristics. Through chemical bonding analysis, we show that B7Be6B7 can be conceptualized as a B73−Be66+B73− complex.
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•We developed a global minimum search program named TGMin.•TGMin program is based on the basin hopping algorithm with several improvements.•TGMin program is highly effecient in ...finding the global minima of nanoclusters.•An overview of recent improvements and applications of TGMin are presented.
Finding the global minima of nanoclusters is of great importance in cluster science and nanoscience. We have developed an efficient global minimum search program, named Tsinghua Global Minimum (TGMin, first released in 2012), based on the Basin-Hopping algorithm to find the global minima of nanoclusters, as well as periodic systems. We have recently made several improvements to the original Basin-Hopping algorithm, including a constrained perturbation function, a covalent-radius-based relaxation algorithm, an improved ultrafast shape recognition algorithm, and a planeness-check mechanism. The TGMin program has been successfully applied to search the global minima of a number of nanoclusters and periodic structures, including B30, B35, B36, B39, B40, CoB18−, RhB18−, MnB16−, and Au7 on the α-Al2O3(0001) surface. An overview of the TGMin code and several of its recent applications are presented here.
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