The low lying isomers of the copper nonamer cluster, Cu9

Hierarchical structures and magnetism of Co clusters: a perspective from integration of deep learning and a hybrid differential evolution algorithm

Theoretically determining the lowest-energy structure of a cluster has been a persistent challenge due to the inherent difficulty in accurate description of its potential energy surface (PES) and the exponentially increasing number of local minima on the PES with the cluster size. In this work, density-functional theory (DFT) calculations of Co clusters were performed to construct a dataset for training deep neural networks to deduce a deep potential (DP) model with near-DFT accuracy while significantly reducing computational consumption comparable to classic empirical potentials. Leveraging the DP model, a high-efficiency hybrid differential evolution (HDE) algorithm was employed to search for the lowest-energy structures of CoN (N = 11-50) clusters. Our results revealed 38 of these clusters superior to those recorded in the Cambridge Cluster Database and identified diverse architectures of the clusters, evolving from layered structures for N = 11-27 to Marks decahedron-like structures for N = 28-42 and to icosahedron-like structures for N = 43-50. Subsequent analyses of the atomic arrangement, structural similarity, and growth pattern further verified their hierarchical structures. Meanwhile, several highly stable clusters, i.e., Co13, Co19, Co22, Co39, and Co43, were discovered by the energetic analyses. Furthermore, the magnetic stability of the clusters was verified, and a competition between the coordination number and bond length in affecting the magnetic moment was observed. Our study provides high-accuracy and high-efficiency prediction of the optimal structures of clusters and sheds light on the growth trend of Co clusters containing tens of atoms, contributing to advancing the global optimization algorithms for effective determination of cluster structures.

Stability limits of elemental 2D metals in graphene pores

Two-dimensional (2D) materials can be used as stabilizing templates for exotic nanostructures, including pore-stabilized, free-standing patches of elemental metal monolayers. Although these patches represent metal clusters under extreme conditions and are thus bound for investigations, they are poorly understood as their energetic stability trends and the most promising elements remain unknown. Here, using density-functional theory simulations and the liquid drop model to explore the properties of 45 elemental metal candidates, we identify metals that enable the largest and most stable patches. Simulations show that pores can stabilize patches up to ∼8 nm² areas and that the most prominent candidate in a graphene template is Cu. The results, which are generalizable to templates also beyond graphene, provide encouragement for further, even more resolute experimental pursuit of 2D metals.

Stern-Gerlach experiments on Mn@Sn12: identification of a paramagnetic superatom and vibrationally induced spin orientation

Beam deflection experiments in inhomogeneous magnetic fields reveal a new limiting case of the magnetization distribution of isolated clusters. Endohedrally doped clusters are produced in a temperature controlled, cryogenically cooled laser ablation source. Temperature dependent experiments indicate a crucial contribution of molecular vibrations to the spin dynamics of Mn@Sn12. In its vibrational ground state the cluster behaves magnetically like a paramagnetic atom, with quantized spin states. However, excited molecular vibrations induce spin orientation in the magnetic field.

Binary compounds of boron and beryllium: a rich structural arena with space for predictions

We explore ground-state structures and stoichiometries of the Be-B system in the static limit, with Be atom concentrations of 20 % or greater, and from P = 1 atm up to 320 GPa. At P = 1 atm, predictions are offered for several known compounds, the structures of which have not yet been determined experimentally. Specifically, at 1 atm, we predict a structure of R3m symmetry for the compound Be2B3, seen experimentally at high temperatures, which contains interesting BeBBBBe rods; and for the compound BeB4 we calculate metastability with respect to the elements with a structure similar to MgB4, which is quickly replaced as the pressure is elevated by a Cmcm structure that features 6- and 4-membered rings in B cages, with Be interstitials. For another high-temperature compound, Be2B, we confirm the CaF2 structure, but find a competitive and actually slightly more stable ground-state structure of C2/m symmetry that features B2 pairs. In the case of BeB2, a material for which the stoichiometry has been the subject of debate, we have a clear prediction of a stable F43m structure at P=1 atm. It has a diamondoid structure that is based on cubic (lower P) or hexagonal (higher P) diamond networks of B, but with Be in the interstices. This Zintl structure is a semiconductor at low and intermediate pressures. At higher pressures, BeB2 dominates the phase diagram. In general, the Zintl-Klemm concept of effective electron transfer from the more electropositive ion and bond formation among the resulting anions has proven useful in analyzing the structural preferences of many compositions in the Be-B system at P=1 atm and at elevated pressures. An unusual feature of this binary system is that the 1:1 BeB stoichiometry never appears to reach stability in the static limit, although it comes close, as does Be17B12. Also stable at high pressures are stoichiometries BeB3, BeB4, and Be5B2.

Icosahedral to double-icosahedral shape transition of copper clusters

The lowest-energy isomers of Cu(N) clusters for N = 20-30 are identified using an unbiased search algorithm and density functional theory calculations. The low-energy structures over this size range are dominated by those based on a 13-atom icosahedral (I(h)) core and a 19-atom double icosahedron (DI(h)) core. A transition in the ground-state isomers from I(h)-based to DI(h)-based structures is predicted overt N = 21-23. We discuss this transition in the broader context of the growth pattern for Cu(N) over N = 2-30 that features regions of gradual evolution in which atoms successively add to the cluster surface, separated by sudden changes to a different structural organization and more compact shape. These transitions result from a competition between interatomic bonding energy and surface energy. The implications of this growth pattern for the further evolution of copper from microstructure to bulk are discussed.

High pressure ices

H(2)O will be more resistant to metallization than previously thought. From computational evolutionary structure searches, we find a sequence of new stable and meta-stable structures for the ground state of ice in the 1-5 TPa (10 to 50 Mbar) regime, in the static approximation. The previously proposed Pbcm structure is superseded by a Pmc2(1) phase at p = 930 GPa, followed by a predicted transition to a P2(1) crystal structure at p = 1.3 TPa. This phase, featuring higher coordination at O and H, is stable over a wide pressure range, reaching 4.8 TPa. We analyze carefully the geometrical changes in the calculated structures, especially the buckling at the H in O-H-O motifs. All structures are insulating--chemistry burns a deep and (with pressure increase) lasting hole in the density of states near the highest occupied electronic levels of what might be component metallic lattices. Metallization of ice in our calculations occurs only near 4.8 TPa, where the metallic C2/m phase becomes most stable. In this regime, zero-point energies much larger than typical enthalpy differences suggest possible melting of the H sublattice, or even the entire crystal.

Icosahedral crown gold nanocluster au(43)cu(12) with high catalytic activity

Structural and catalytic properties of the gold alloy nanocluster Au(43)Cu(12) are investigated using a density-functional method. In contrast to the pure Au(55) nanocluster, which exhibits a low-symmetry C(1) structure, the 55-atom "crown gold" nanocluster exhibits a multishell structure, denoted by Au@Cu(12)@Au(42), with the highest icosahedral group-symmetry. In addition, density functional calculations suggest that this geometric magic-number nanocluster possesses comparable catalytic capability as a small-sized Au(10) cluster for the CO oxidation, due in part to their low-coordinated Au atoms on vertexes. The gold alloy nanocluster also shows higher selectivity for styrene oxidation than the bare Au(111) surface.