Magnesium Clusters Research Articles

Searching new structures of beryllium‐doped in small‐sized magnesium clusters: Be2MgnQ (Q = 0, −1; n = 1–11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be2 Mgn Q (Q = 0, -1; n = 2-11) clusters is performed. Based on the structural optimization, it is found that the Be2 Mgn Q (Q = 0, -1) clusters are shown by tetrahedral-based geometries at n = 2-6 and tower-like-based geometries at n = 7-11. The calculations of stability indicate that Be2 Mg5 Q=0 , Be2 Mg5 Q=-1 , and Be2 Mg8 Q=-1 clusters are "magic" clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg5 or Mg8 host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be2 Mgn Q (Q = 0, -1; n = 1-11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.

BeMg9: A tower-like type doped magnesium clusters with high stability

Using CALYPSO code to search the global minima followed by density functional theory (DFT) calculations, a theoretical investigation of structures and electronic properties of beryllium-doped magnesium clusters is carried out. It can be found that the BeMgn clusters possess tetrahedron-based structures at n = 3–7 and the tower-like-based structures at n = 8–12. According to the stability calculations, BeMg9 cluster with fascinating tower type geometry is found to have the strongest relative stability and can be consider as the most stable cluster. The chemical bond analysis of BeMg9 cluster including MOs, LOL and AdNDP shows that its relative high stability is originated from the interactions between the beryllium atom and Mg9 host as well as Mg-Mg and Be-Mg σ-bonds. Finally, the IR and Raman spectra of BeMg9 cluster are further analyzed. We believe that this research will definitely enrich the database of geometrical structures of alkaline earth metal-doped magnesium clusters and will stimulate future synthesis of magnesium-based nanomaterials.

Probing the Geometric and Electronic Effects of Aluminum–Magnesium Clusters on Reactivity Toward Oxygen

In this work, we perform detailed density functional theory (DFT) calculations to systematically study the composition-dependent structural, thermodynamic and electronic properties of Mg–Al alloy clusters with 55 atoms. It is found that the Al-rich clusters, such as Mg12Al43 and Mg12Al43− generally possess higher thermodynamic stability and exhibit distinctive electronic properties. Especially for Mg12Al43−, there is relatively large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), suggesting that the Mg12Al43− may possess higher resistance to the reactivity with oxygen. In addition, we also study single O atom and 3O2 adsorption on the Al55, Mg55, Mg12Al43 and Mg12Al43− clusters. Through comparing their adsorption energies, we find that the H1 sites (on the hollow site of one triangular facet among two edge and one vertex atoms) energetically are the most stable O adsorption site for all clusters. Most importantly, for 3O2 adsorbed on Mg12Al43 and Mg12Al43− clusters, replacing the Al atoms of Al55 cluster with Mg atoms can effectively weaken the adsorption of oxygen and enhance the resistance to oxidation.

Heat Treatments and Critical Quenching Rates in Additively Manufactured Al–Si–Mg Alloys

Laser powder-bed fusion (LPBF) has significantly gained in importance and has become one of the major fabrication techniques within metal additive manufacturing. The fast cooling rates achieved in LPBF due to a relatively small melt pool on a much larger component or substrate, acting as heat sink, result in fine-grained microstructures and high oversaturation of alloying elements in the α-aluminum. Al–Si–Mg alloys thus can be effectively precipitation hardened. Moreover, the solidified material undergoes an intrinsic heat treatment, whilst the layers above are irradiated and the elevated temperature in the built chamber starts the clustering process of alloying elements directly after a scan track is fabricated. These silicon–magnesium clusters were observed with atom probe tomography in as-built samples. Similar beneficial clustering behavior at higher temperatures is known from the direct-aging approach in cast samples, whereby the artificial aging is performed immediately after solution annealing and quenching. Transferring this approach to LPBF samples as a possible post-heat treatment revealed that even after direct aging, the outstanding hardness of the as-built condition could, at best, be met, but for most instances it was significantly lower. Our investigations showed that LPBF Al–Si–Mg exhibited a high dependency on the quenching rate, which is significantly more pronounced than in cast reference samples, requiring two to three times higher quenching rate after solution annealing to yield similar hardness results. This suggests that due to the finer microstructure and the shorter diffusion path in Al–Si–Mg fabricated by LPBF, it is more challenging to achieve a metastable oversaturation necessary for precipitation hardening. This may be especially problematic in larger components.

Theoretical Modeling of Stepwise Addition of H2 Molecules to Magnesium Clusters Mg18 and Mg17Ni

The potential energy surface (PES) along minimum energy paths of elementary hydrogenation reactions Mg18 + H2 → Mg18H2 and Mg17Ni + H2 → Mg17NiH2 + H2 → Mg17NiH4 + H2 → Mg17NiH6 has been calculated by the density functional theory method. Local PES minima in the vicinity of low-lying isomers, intermediates, and transition states have been determined, and their energies, geometries, and spectroscopic parameters have been calculated. The effect of the Ni dopant on the energies and activation barriers of these reactions has been examined, depending on the position of the dopant on the surface and inside the internal cavity of the Mg17 cage.

The effect of silicon doping on the geometrical structures, stability, and electronic and spectral properties of magnesium clusters: DFT study of SiMgn (n = 1‐12) clusters

AbstractUsing the density functional theory (DFT) method at the B3LYP /6−311G (D) level, we studied how silicon doping affects the geometrical structure, stability, and electronic and spectral properties of magnesium clusters. The stable isomers of SiMg n (n = 1‐12) clusters were calculated by searching numerous initial configurations using the CALYPSO program. The geometrical structure optimization shows that most stable SiMg n (n = 3‐12) clusters are three‐dimensional. In addition, geometrical structure growth patterns show that some structures of SiMg n clusters can be directly formed by replacing one Mg atom in the corresponding Mg n + 1 cluster with one silicon atom, such as SiMg8 and Mg9 clusters. The stability of SiMg n clusters is analyzed by calculating the average binding energy, fragmentation energy, and second‐order energy difference. The results show that SiMg n clusters with n = 5 and 8 are more stable than others. MO contents analysis show that the Si 3p‐orbitals and Mg 3s‐orbital are mainly responsible for the stability of these two clusters. The results of the natural charge population (NCP) and natural electronic configure (NEC) analysis of the electronic properties reveal that the charges in SiMgn (n = 1‐12) clusters transfer from magnesium atoms to silicon frame, and electronic charge distributions are primarily governed by s‐ and p‐orbital interactions. In addition, the Vertical ionization potential (VIP), vertical electron affinity (VEA), and chemical hardness of ground sates of SiMg n (n = 1‐12) clusters were studied in detail and compared with the experimental results. The conclusions show that the chemical hardness of most SiMg n clusters are lower than that of pure Mg n + 1 (n = 1‐12) clusters, except for n = 1 and 8. This indicates that the doping of silicon atom can always reduce the chemical hardness of pure magnesium clusters. Finally, the infrared and Raman spectral properties of SiMg5 and SiMg8 clusters were calculated and discussed in detail.

Effect of magnesium cluster size on Grignard reagent formation mechanism. A quantum-chemical study

The density functional theory (B3PW91/6-311[Formula: see text]G(2d,2p)) was used to obtain optimized geometry, energy and electronic properties of Mg[Formula: see text]EtBr adsorption complexes, Et[Formula: see text]Mg[Formula: see text]Br intermediates and transition states for ethyl bromide reaction with the magnesium atom and Mgn ([Formula: see text]–20) clusters modeling the distorted surface of the metallic magnesium. We suggest a consecutive multi-stage scheme of EtBr[Formula: see text]Mgn process in vacuum that includes adsorption of reagents on external cluster atoms, chemical interaction with Grignard reagent formation and desorption of products to the volume. Two fundamentally different reaction channels were investigated — the radical and molecular ones. Influence of Mgn cluster size on the preference of each of channels was established. It is shown that the reaction route is primarily determined with the position of the reactive group of atoms participating in formation of the transition state or radical intermediates and the activation energy of EtMgBr formation correlates with the energy of atom detachment from a cluster. For both pathways, reaction activation energies and thermodynamic parameters of the elementary steps were calculated.

Nanomaterials design for super-degenerate electronic state beyond the limit of geometrical symmetry

Spherical atoms have the highest geometrical symmetry. Due to this symmetry, atomic orbitals are highly degenerate, leading to closed-shell stability and magnetism. No substances with greater degrees of degeneracy are known, due to geometrical limitations. We now propose that realistic magnesium, zinc, and cadmium clusters having a specific tetrahedral framework possess anomalous higher-fold degeneracies than spherical symmetry. Combining density functional theory calculations with simple tight-binding models, we demonstrate that these degeneracies can be attributed to dynamical symmetry. The degeneracy condition is fully identified as an elegant mathematical sequence involving interatomic parameters. The introduction of dynamical symmetry will lead to the discovery of a novel category of substances with super-degenerate orbitals.

Photochemistry and spectroscopy of small hydrated magnesium clusters Mg+(H2O)n, n = 1-5.

Hydrated singly charged magnesium ions Mg+(H2O)n, n ≤ 5, in the gas phase are ideal model systems to study photochemical hydrogen evolution since atomic hydrogen is formed over a wide range of wavelengths, with a strong cluster size dependence. Mass selected clusters are stored in the cell of an Fourier transform ion cyclotron resonance mass spectrometer at a temperature of 130 K for several seconds, which allows thermal equilibration via blackbody radiation. Tunable laser light is used for photodissociation. Strong transitions to D1–3 states (correlating with the 3s-3px,y,z transitions of Mg+) are observed for all cluster sizes, as well as a second absorption band at 4–5 eV for n = 3-5. Due to the lifted degeneracy of the 3px,y,z energy levels of Mg+, the absorptions are broad and red shifted with increasing coordination number of the Mg+ center, from 4.5 eV for n = 1 to 1.8 eV for n = 5. In all cases, H atom formation is the dominant photochemical reaction channel. Quantum chemical calculations using the full range of methods for excited state calculations reproduce the experimental spectra and explain all observed features. In particular, they show that H atom formation occurs in excited states, where the potential energy surface becomes repulsive along the O⋅⋅⋅H coordinate at relatively small distances. The loss of H2O, although thermochemically favorable, is a minor channel because, at least for the clusters n = 1-3, the conical intersection through which the system could relax to the electronic ground state is too high in energy. In some absorption bands, sequential absorption of multiple photons is required for photodissociation. For n = 1, these multiphoton spectra can be modeled on the basis of quantum chemical calculations.

Scaling of the self-energy correction to the HOMO-LUMO gap with magnesium cluster size and its potential for extrapolating to larger magnesium clusters

This paper presents a computational method for the estimation of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of metallic nano-clusters using efficient density functional computations with the high accuracy of the GW method. Electronic structures of magnesium nano-clusters Mgn (n = 1–22, 25, 30, 35, and 40) are computed using the density functional theory (DFT) and the quasiparticle GW method. It is found that the energy difference between the DFT and GW results, defined as the scissors operator or correction, is only dependent on the cluster size and independent of the electronic shell filling effect. The scissors operators of HOMOs and LUMOs of metallic clusters can thus be fitted by using simple power functions of the cluster size n. Therefore, the HOMOs and LUMOs of metallic clusters can be efficiently calculated using DFT with a modification of scissors operators. The scissors operators are also demonstrated to be applicable to occupied and unoccupied states near the Fermi level.

Benchmark CCSD(T) and DFT study of binding energies in Be7 − 12: in search of reliable DFT functional for beryllium clusters

ABSTRACTWe present a computational study of the stability of small homonuclear beryllium clusters Be7 − 12 in singlet electronic states. Our predictions are based on highly correlated CCSD(T) coupled cluster calculations. Basis set convergence towards the complete basis set limit as well as the role of the 1s core electron correlation are carefully examined. Our CCSD(T) data for binding energies of Be7 − 12 clusters serve as a benchmark for performance assessment of several density functional theory (DFT) methods frequently used in beryllium cluster chemistry. We observe that, from Be10 clusters on, the deviation from CCSD(T) benchmarks is stable with respect to size, and fluctuating within 0.02 eV error bar for most examined functionals. This opens up the possibility of scaling the DFT binding energies for large Be clusters using CCSD(T) benchmark values for smaller clusters. We also tried to find analogies between the performance of DFT functionals for Be clusters and for the valence-isoelectronic Mg clusters investigated recently in Truhlar's group. We conclude that it is difficult to find DFT functionals that perform reasonably well for both beryllium and magnesium clusters. Out of 12 functionals examined, only the M06-2X functional gives reasonably accurate and balanced binding energies for both Be and Mg clusters.

First principles electron-correlated calculations of optical absorption in magnesium clusters

In this paper, we report large-scale configuration interaction (CI) calculations of linear optical absorption spectra of various isomers of magnesium clusters Mg$_{n}$ (n=2--5), corresponding to valence transitions. Geometry optimization of several low-lying isomers of each cluster was carried out using coupled-cluster singles doubles (CCSD) approach, and these geometries were subsequently employed to perform ground and excited state calculations using either the full-CI (FCI) or the multi-reference singles-doubles configuration interaction (MRSDCI) approach, within the frozen-core approximation. Our calculated photoabsorption spectrum of magnesium dimer (Mg$_{2}$) isomer is in excellent agreement with the experiments both for peak positions, and intensities. Owing to the sufficiently inclusive electron-correlation effects, these results can serve as benchmarks against which future experiments, as well as calculations performed using other theoretical approaches, can be tested.

A series of alkaline earth metal coordination polymers constructed from two newly designed imidazole-based dicarboxylate ligands containing pyridinylmethyl groups

Two new imidazole-based dicarboxylate ligands, which are 2-(pyridin-4-ylmethyl)-1H-imidazole-4,5-dicarboxylic acid (H3pPyMIDC) and 2-(pyridin-3-ylmethyl)-1H-imidazole-4,5-dicarboxylic acid (H3mPyMIDC), have been designed and successfully synthesized. Both these multidentate ligands are then used to react with different kinds of alkaline earth metal ions under solvothermal conditions, leading to the construction of a series of new coordination polymers (CPs), namely, [Ba(μ5-HpPyMIDC)(H2O)]n (1), [Sr(μ5-HpPyMIDC)(H2O)]n (2), [Ca2(μ4-HpPyMIDC)2(H2O)2]n (3), {[Ca2(μ3-HpPyMIDC)(μ4-HpPyMIDC)(H2O)2]·H2O}n (4), [Ba(μ5-HmPyMIDC)(H2O)]n (5), {[Mg10(μ3-mPyMIDC)3(μ4-mPyMIDC)3(H2O)21]·SO4·12H2O}n (6) and {[Sr(μ2-H2mPyMIDC)2(DMF)2]n·H2O}n (7). Compounds 1 and 2 are isostructural, exhibiting two-dimensional (2D) network structures with a hexagonal honeycomb (6,3) topology if the corresponding metal ions are seen as 3-connected nodes. Compound 3 displays another type of 2D network, which is built by the connection of μ4-HpPyMIDC ligands and Ca(II) centres. Compound 4 is a binodal (3,4)-connected 3D framework with the Schläfli symbol of (6·82)(65·8). The 2D structure of compound 5 is similar to those of compounds 1 and 2, although different kinds of ligands are employed. Compound 6 exhibits an interesting 3D framework with a pcu topology by considering each unusual heptanuclear magnesium cluster as a 6-connected node. In compound 7, connection of μ2-H2mPyMIDC ligands with Sr(II) ions results in the formation of an uncommon 3D chiral framework containing two different types of 1D helical chains. The present results reveal that both these new imidazole-based dicarboxylate ligands containing flexible pyridinylmethyl groups show versatile coordination abilities and are good candidates for fabricating new CPs. Moreover, the thermogravimetric and solid-state luminescence properties of all the compounds have also been studied.

Theoretical Study of Cu/Mg Core-shell Nanocluster Formation.

In a recently reported helium droplet-mediated deposition experiment to produce copper-coated magnesium core-shell nanoclusters, structural inversion was observed, which resulted in copper in the nanocluster interior, surrounded by oxidized magnesium on the copper surface. This study utilizes density functional theory methods to model the migration of copper atoms into the interior of a magnesium nanocluster to probe the energetics of this process and to compare it to the complementary process of magnesium atom migration into the interior of a copper nanocluster. Potential energy surfaces describing the forced migration of copper (magnesium) atoms into the interior of a 30-atom magnesium (copper) cluster were generated using the B3PW91 hybrid generalized gradient approximation functional with the augmented correlation consistent core-valence polarized triple-ζ basis set for magnesium and a pseudopotential plus valence-only basis set for copper. The estimated barrier for atomic copper to penetrate the surface of Mg30 is 0.6 kcal mol-1. In contrast, the migration of atomic magnesium into the interior of Cu30 crosses an estimated barrier of 6 kcal mol-1. These results are qualitatively consistent with the observed structural inversion of copper-coated magnesium nanoclusters and also suggest that inversion of a magnesium-coated copper cluster is less likely to occur.

Thermodynamics of Metal Nanoparticles: Energies and Enthalpies of Formation of Magnesium Clusters and Nanoparticles as Large as 1.3 nm

The major obstacle that prevents reliable electronic structure studies of nanoparticles is the rapid increasing computational cost for benchmark calculations using coupled-cluster methods. We show that a CCSD(T) scheme with an MP2/CBS correction can reproduce accurate cohesive energies for magnesium clusters, and this scheme is much less computationally demanding than other reliable methods, so it is applied to Mgn with n up to 19, which enters the realm of nanoparticles. (The diameters of all Mg clusters n ≥ 11 are >1 nm). With the extended benchmark data, we validate exchange–correlation functionals into the nanoparticle regime and use the two best-validated functionals to calculate the enthalpy of formation of Mg28, with a diameter of 1.30 nm. We also calculated the enthalpy of formation of all Mg clusters and nanoparticles from Mg2 to Mg19. This kind of reliable thermodynamic data on size-selected metal nanoparticles has been hard to come by, either experimentally or theoretically, but it is badly nee...

The Study of the Dissolution AlZr2 Ligatures in the Liquid Alloy AlMg6Mn1

We studied the dissolution of zirconium in the molten alloy AlMg6Mn1. Zirconium is introduced into the melt in the form of the ligature AlZr2. It is established that during 10 minutes at 750 °C complete Zr dissolution occurs. The study of the structure and phase composition of the samples allowed setting the dendrite structure of the samples; presence of clusters of magnesium, manganese, iron and silicon in the interdendritic space. Zirconium is injected into the melt in a stable particulate form (D023) Al3Zr phase is uniformly distributed in grains α - Al as a metastable (L12) Al3Zr phase. After some time, increasing of the density distribution of the metastable (L12) Al3Zr in the aluminum matrix phase is detected in the selected samples after 10 and 60 minutes after the introduction of zirconium. It has been established that after some time, an increase of the aluminum lattice parameter occurs in the samples selected after the addition ligature of zirconium.

Geometries, Binding Energies, Ionization Potentials, and Electron Affinities of Metal Clusters: Mgn0, ± 1, n = 1–7

Equilibrium geometries, binding energies, adiabatic ionization potentials, and adiabatic electron affinities for neutral and singly charged magnesium clusters, Mgn0, ± 1, n = 1–7, have been computed using 39 exchange-correlation (XC) functionals in Kohn–Sham density functional theory and several coupled-cluster methods with single, double, and triple excitations, including CCSD(T) for all species, CCSD(2)T and CR-CC(2,3) for species with n = 1–3, and CCSDt, CC(t;3), and CCSDT for species with n = 1 and 2. We have used augmented polarized–valence and polarized–core–valence correlation-consistent basis sets. We have found that the geometry and binding energy of the weakly bound Mg2 dimer requires a robust treatment of connected triple excitations, represented in this work by the CR-CC(2,3), CC(t;3), and full CCSDT methods, which are more accurate than the popular quasi-perturbative CCSD(T) approximation, but CCSD(T) is sufficiently accurate to be applied to other Mg clusters. We have also demonstrated that ...

Unusual behavior in magnesium-copper cluster matter produced by helium droplet mediated deposition.

We demonstrate the ability to produce core-shell nanoclusters of materials that typically undergo intermetallic reactions using helium droplet mediated deposition. Composite structures of magnesium and copper were produced by sequential condensation of metal vapors inside the 0.4 K helium droplet baths and then gently deposited onto a substrate for analysis. Upon deposition, the individual clusters, with diameters ∼5 nm, form a cluster material which was subsequently characterized using scanning and transmission electron microscopies. Results of this analysis reveal the following about the deposited cluster material: it is in the un-alloyed chemical state, it maintains a stable core-shell 5 nm structure at sub-monolayer quantities, and it aggregates into unreacted structures of ∼75 nm during further deposition. Surprisingly, high angle annular dark field scanning transmission electron microscopy images revealed that the copper appears to displace the magnesium at the core of the composite cluster despite magnesium being the initially condensed species within the droplet. This phenomenon was studied further using preliminary density functional theory which revealed that copper atoms, when added sequentially to magnesium clusters, penetrate into the magnesium cores.

Diffusion and growth of aluminum adatoms on magnesium clusters with hexahedral structure

The surface diffusion and growth of Al atoms on Mg clusters with hexahedral structure was investigated using molecular dynamics simulations. The diffusion pathways and the corresponding energy barriers were determined via the nudged elastic band method. Two diffusion paths from a (0001) facet to a neighboring (11¯01) facet and between two adjacent (11¯01) facets were considered. The energy barriers on the (11¯01) facets and between the two (11¯01) facets were remarkably increased. As such, the adatom's mobility became limited at low temperatures. The growth of small Al–Mg nanoclusters was modeled via the one-by-one atom deposition technique to form an anomalous core–shell structure. The Mg atoms with lower surface energy and larger atomic radius occupied the core and the Al atoms with higher surface energy and smaller atomic radius occupied the shell.

Nano-scale energetic films by superfluid helium droplet assembly

The helium droplet technique has been utilized to study a wide range of topics in chemical physics such as atomic scale manifestations of superfluidity, chemistry at ultra-low temperatures, and the assembly of exotic Van der Waals complexes. Our efforts have transitioned the helium droplet methodology from a cryogenic nano-scale matrix to a film deposition technique capable of creating nano-structured films of composite metal-based energetic materials (EM). Such materials are ideal candidates to study propagation of reactions at small scale, and could be alternatives to organic based EM due to their higher energy densities. The helium droplet methodology may also provide a solution overcoming issues of reaction-limiting effects such as the formation of oxide layers by exploiting 'magic-number' cluster sizes and core-shell cluster mechanisms. This proceeding describes our previously reported efforts to model and characterize the deposition of magnesium clusters by superfluid helium droplet assembly, our efforts to produce magnesium-Fomblin core-shell EM cluster-based films, and our early attempts at making intermetallic cluster-based films.