Comprehensive study of sodium, copper, and silver clusters over a wide range of sizes 2≤N≤75

Accelerating Global Search of Large-Sized Silver Clusters Using Cluster Graph Attention Network

Great efforts have been devoted to understanding the stability and reactivity of silver clusters, which usually depend on geometric structures, electronic configuration, and cluster size. Despite the fact that the jellium model and Wulff construction rule have successfully rationalized the stable clusters with "magic number" behavior, some experiments imply that silver clusters with 48 valence electrons also possess puzzling enhanced stability. In this work, using a recently developed deep learning technology, i.e., cluster graph attention network (CGANet), combined with a homemade comprehensive genetic algorithm (CGA) program, we searched the global minimum (GM) structures of Agn (n = 30-60) clusters with graphics processing unit acceleration, whose efficiency is about 2 orders of magnitude higher than that of the conventional density functional theory (DFT) calculations. GM structures and some representative isomers are reported at each size, revealing the competitive structural patterns based on truncated octahedra and icosahedra as well as the icosahedra-based layer-by-layer growth mode of large-sized Ag clusters. Most importantly, the size-dependent evolution behavior of structural and electronic properties of Agn (n = 30-60) clusters can successfully explain the observed stability at Ag48. Therefore, CGANet provides a powerful tool for rapidly exploring the potential energy surface of atoms with an accuracy comparable to that of DFT.

Understanding and controlling the formation of single-atom site from supported Cu10 cluster by tuning CeO2 reducibility: Theoretical insight into the Gd-doping effect on electronic metal-support interaction

Controlling the formation of single-atom (SA) sites from supported metal clusters is an important and interesting issue to effectively improve the catalytic performance of heterogeneous catalysts. For extensively studied CO oxidation over metal/CeO2 systems, the SA formation and stabilization under reaction conditions is generally attributed to CO adsorption, however, the pivotal role played by the reducible CeO2 support and the underlying electronic metal-support interaction (EMSI) are not yet fully understood. Based on a ceria-supported Cu10 catalyst model, we performed density functional theory calculations to investigate the intrinsic SA formation mechanism and discussed the synergistic effect of Gd-doped CeO2 and CO adsorption on the SA formation. The CeO2 reducibility is tuned with doped Gd content ranging from 12.5 % ∼ 25 %. Based on ab initio thermodynamic and ab initio molecular dynamics, the critical condition for SA formation was identified as 21.875 % Gd-doped CeO2 with CO-saturated adsorption on Cu10. Electronic analysis revealed that the open-shell lattice Oδ- (δ < 2) generated by Gd doping facilitates the charge transfer from the bottom-corner Cu (Cubc) to CeO2. The CO-saturated adsorption further promotes this charge transfer process and enhances the EMSI between Cubc and CeO2, leading to the disintegration of Cubc from Cu10 and subsequent formation of the active SA site.

Band edges positions prediction of the of Ag nanocluster-decorated titania surfaces and their relationship to NO and NO2 interaction from first-principles calculations

Metal nanoclusters deposited on oxides have been widely used in photocatalysis playing an important role in the design of model catalysts with applications in heterogeneous catalysis. In particular, we are interested in the potential activity of these cluster-supported systems for the removal of nitrogen oxides either by possible catalytic reduction and/or by their adsorption. In this work, using first-principles methods, we evaluate the main characteristics of Agn (n = 1-4) nanoclusters isolated and deposited on anatase TiO2(101) and rutile TiO2(110) surfaces. Our results indicate that they are preferably adsorbed on rutile surface. The different formation energy at each surface can be explained using a Bader charge analysis. Particularly for Ag4 the lowest formation energy is obtained for tetrahedral geometry while the isolated Ag4 geometry is planar. Small silver deposits placed superficially on titania surfaces modify its electronic structures and improve the conduction band edges positions for possible NO reduction. Band edges positions with respect to the vacuum potential have been studied. The comparison of the conduction band minimum with the reduction potentials of NO/N2O and N2O/N2 shows that they are higher, being Ag3 on rutile and Ag1, Ag2 and Ag4P on anatase better for NO reduction. To complete the analysis, the calculation of work function, energy gap, ionization energy and electron affinity are relevant since they allow the location of semiconductor band edges at point of zero charge. Finally, the adsorption of nitrogen oxides is studied where the NO2 adsorption is favored over NO.

Structural transformations in Cu, Ag, and Au metal nanoclusters

Finite-temperature structures of Cu, Ag, and Au metal nanoclusters are calculated in the entire temperature range from 0 K to melting using a computational methodology that we proposed recently [M. Settem et al., Nanoscale 14, 939 (2022)]. In this method, Harmonic Superposition Approximation (HSA) and Parallel Tempering Molecular Dynamics (PTMD) are combined in a complementary manner. HSA is accurate at low temperatures and fails at higher temperatures. PTMD, on the other hand, effectively samples the high temperature region and melts. This method is used to study the size- and system-dependent competition between various structural motifs of Cu, Ag, and Au nanoclusters in the size range 1-2 nm. Results show that there are mainly three types of structural changes in metal nanoclusters, depending on whether a solid-solid transformation occurs. In the first type, the global minimum is the dominant motif in the entire temperature range. In contrast, when a solid-solid transformation occurs, the global minimum transforms either completely to a different motif or partially, resulting in the co-existence of multiple motifs. Finally, nanocluster structures are analyzed to highlight the system-specific differences across the three metals.

The global minimum of Ag30: a prolate spheroidal structure predicted using a genetic algorithm with incomplete local optimizations at the DFT level

Genetic algorithms have been widely used to explore global minimum points of atomic clusters, and their incorporation with ab initio calculations (including density functional theory methods) as local optimization approaches increases their ability to accurately locate the global minimum points on complicated potential energy surfaces. However, the local optimizations using ab initio calculations significantly increase the computational cost relative to those based on empirical or semi-empirical calculations. Herein, we develop a genetic algorithm program with an incomplete local optimization strategy at the DFT level. Using several representative clusters as test examples, this program showed high efficiency in locating their global minimum points. The low-lying isomers of Ag₃₀ were explored using this program, and the determined global minimum is a prolate spheroidal structure. The elongated spheroidal shape causes degeneracy lifting of the free electron shells, and endows Ag₃₀ with a large HOMO-LUMO gap. The sharp increase of silver clusters' reactivity around the sizes with 30 valence electrons observed in our previous experiments could be correlated with this theoretical figure.

Single atom alloy clusters Agn-1X- (X = Cu, Au; n = 7-20) reacting with O2: Symmetry-adapted orbital model

Single atom alloy AgCu catalysts have attracted great attention, since doping the single Cu atom introduces narrow free-atom-like Cu 3d states in the electronic structure. These peculiar electronic states can reduce the activation energies in some reactions and offer valuable guidelines for improving catalytic performance. However, the geometric tuning effect of single Cu atoms in Ag catalysts and the structure-activity relationship of AgCu catalysts remain unclear. Here, we prepared well-resolved pristine Ag_n ^- as well as single atom alloy Ag_n-1Cu^- and Ag_n-1Au^- (n = 7-20) clusters and investigated their reactivity with O₂. We found that replacing an Ag atom in Ag_n ^- (n = 15-18) with a Cu atom significantly increases the reactivity with O₂, while replacement of an Ag with an Au atom has negligible effects. The adsorption of O₂ on Ag_n ^- or Ag_n-1Cu^- clusters follows the single electron transfer mechanism, in which the cluster activity is dependent on two descriptors, the energy level of α-HOMO (strong correlation) and the α-HOMO-LUMO gap (weak correlation). Our calculation demonstrated that the cluster arrangements caused by single Cu atom alloying would affect the above activity descriptors and, therefore, regulates clusters' chemical activity. In addition, the observed reactivity of clusters in the representative sizes with n = 17-19 can also be interpreted using the symmetry-adapted orbital model. Our work provides meaningful information to understand the chemical activities of related single-atom-alloy catalysts.

Relative Populations and IR Spectra of Cu38 Cluster at Finite Temperature Based on DFT and Statistical Thermodynamics Calculations

The relative populations of Cu38 isomers depend to a great extent on the temperature. Density functional theory and nanothermodynamics can be combined to compute the geometrical optimization of isomers and their spectroscopic properties in an approximate manner. In this article, we investigate entropy-driven isomer distributions of Cu38 clusters and the effect of temperature on their IR spectra. An extensive, systematic global search is performed on the potential and free energy surfaces of Cu38 using a two-stage strategy to identify the lowest-energy structure and its low-energy neighbors. The effects of temperature on the populations and IR spectra are considered via Boltzmann factors. The computed IR spectrum of each isomer is multiplied by its corresponding Boltzmann weight at finite temperature. Then, they are summed together to produce a final temperature-dependent, Boltzmann-weighted spectrum. Our results show that the disordered structure dominates at high temperatures and the overall Boltzmann-weighted spectrum is composed of a mixture of spectra from several individual isomers.

Computational Modeling of the Interaction of Silver Clusters with Carbohydrates

Silver nanoparticles are recognized for their numerous physical, biological, and pharmaceutical applications. In the present study, the interaction of silver clusters with monosaccharide molecules is examined to identify which molecule works better as a reducing agent in the application of a green synthesis approach. Geometry optimization of clusters containing one, three, and five silver atoms is performed along with the optimization of α-d-glucose, α-d-ribose, d-erythrose, and glyceraldehyde using density functional theory. Optimized geometries allow identifying the interaction formed in the silver cluster and monosaccharide complexes. An electron localization function analysis is performed to further analyze the interaction found and explain the reduction process in the formation of silver nanoparticles. The overall results indicate that glyceraldehyde presents the best characteristics to serve as the most efficient reducing agent.

Synthesis of hydrophilic Ag2Se quantum dots optically optimized by multivariate strategies: an easy one-pot approach

A simple and fast aqueous synthesis of silver selenide quantum dots is proposed with the aid of multivariate optimization.

Effects of Temperature on Enantiomerization Energy and Distribution of Isomers in the Chiral Cu13 Cluster

In this study, we report the lowest energy structure of bare Cu₁₃ nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu₁₃ cluster, employing a genetic algorithm coupled with density functional theory. Moreover, we discuss the energetic ordering of isomers computed with various density functionals. Based on the computed thermal population, our results show that the chiral putative global minimum strongly dominates at room temperature.

Systematic Investigation of the Structure, Stability, and Spin Magnetic Moment of CrM n Clusters (M = Cu, Ag, Au, and n = 2-20) by DFT Calculations

Binary clusters of transition-metal and noble-metal elements have been gathering momentum for not only advanced fundamental understanding but also potential as elementary blocks of novel nanostructured materials. In this regard, the geometries, electronic structures, stability, and magnetic properties of Cr-doped Cu _n , Ag _n , and Au _n clusters (n = 2-20) have been systematically studied by means of density functional theory calculations. It is found that the structural evolutions of CrCu _n and CrAg _n clusters are identical. The icosahedral CrCu₁₂ and CrAg₁₂ are crucial sizes for doped copper and silver species. Small CrAu _n clusters prefer the planar geometries, while the larger ones appear as on the way to establish the tetrahedral CrAu₁₉. Our results show that while each noble atom contributes one s valence electron to the cluster shell, the number of chromium delocalized electrons is strongly size-dependent. The localization and delocalization behavior of 3d orbitals of the chromium decide how they participate in metallic bonding, stabilize the cluster, and give rise to and eventually quench the spin magnetic moment. Moreover, molecular orbital analysis in combination with a qualitative interpretation using the phenomenological shell model is applied to reveal the complex interplay between geometric structure, electronic structure, and magnetic moment of clusters. The finding results are expected to provide greater insight into how a host material electronic structure influences the geometry, stability, and formation of spin magnetic moments in doped systems.

Comment on 'Structural characterization, reactivity and vibrational properties of silver clusters: a new global minimum for Ag16' by P. L. Rodríguez-Kessler, A. R. Rodríguez-Domínguez, D. MacLeod Carey and A. Muñoz-Castro, Phys. Chem. Chem. Phys., 2020, 22, 27255, DOI: D0CP04018E

A recent paper by Rodríguez-Kessler et al., Phys. Chem. Chem. Phys., 2020, 22, 27255-27262, reported not only results of quantum chemical computations (using the PW91 density functional) on Ag₁₆ clusters as emphasized in the article's title, but also on the Ag₁₅ size. These authors confirmed previous results obtained by McKee and Samokhvalov (J. Phys. Chem. A, 2017, 121, 5018-5028 using the M06 density functional) that the most stable isomer of Ag₁₅ is a C_2v structure. We wish to point out that two low symmetry isomers of Ag₁₅ that have a similar energy content are even lower in energy than their reported C_2v global minimum. The relative energies between low-lying Ag₁₅ isomers were again found to be method-dependent, and within the expected accuracy of DFT and CCSD(T) methods they could be considered as energetically degenerate, and likely coexist in a molecular beam. The new lower-energy Ag₁₅ isomers appear to fit more consistently within the structural evolution of small silver clusters.

Systematic cluster growth: a structure search method for transition metal clusters

The systematic cluster growth (SCG) method is a biased structure search strategy based on a seeding process for investigating the structural evolution and growth pattern of transition metal clusters.

Passivating Nucleobases Bring Charge Transfer Character to Optically Active Transitions in Small Silver Nanoclusters

DNA-wrapped silver nanoclusters (DNA-AgNCs) are known for their efficient luminescence. However, their emission is highly sensitive to the DNA sequence, the cluster size, and its charge state. To get better insights into photophysics of these hybrid systems, simulations based on density functional theory (DFT) are performed. Our calculations elucidate the effect of the structural conformations, charges, solvent polarity, and passivating bases on optical spectra of DNA-AgNCs containing five and six Ag atoms. It is found that inclusion of water in calculations as a polar solvent media results in stabilization of nonplanar conformations of base-passivated clusters, while their planar conformations are more stable in vacuum, similar to the bare Ag₅ and Ag₆ clusters. Cytosines and guanines interact with the cluster twice stronger than thymines, due to their larger dipole moments. In addition to the base-cluster interactions, hydrogen bonds between bases notably contribute to the structure stabilization. While the relative intensity, line width, and the energy of absorption peaks are slightly changing depending on the cluster charge, conformations, and base types, the overall spectral shape with five well-resolved bands at 2.5-5.5 eV is consistent for all structures. Independent of the passivating bases and the cluster size and charge, the low energy optical transitions at 2.5-3.5 eV exhibit a metal to ligand charge transfer (MLCT) character with the main contribution emerging from Ag-core to the bases. Cytosines facilitate the MLCT character to a larger degree comparing to the other bases. However, the doublet transitions in clusters with the open shell electronic structure (Ag₅ and Ag₆⁺) result in appearance of additional red-shifted (<2.5 eV) and optically weak band with negligible MLCT character. The passivated clusters with the closed shell electronic structure (Ag₅⁺ and Ag₆) exhibit higher optical intensity of their lowest transitions with much higher MLCT contribution, thus having better potential for emission, than their open shell counterparts.

Thermal Stability of Ag13- Clusters Studied by Ab Initio Molecular Dynamics Simulations

Identification of the geometric structures of silver clusters is of great importance in future nanotechnologies due to their superior properties. Nevertheless, some ground-state structures are still in academic debate, partly because the experiments and theoretical calculations are not performed at the same temperatures. For example, silver clusters usually have compact configurations. However, a combined experimental and theoretical study proposed that the most stable structure of Ag₁₃^- had a two-coordinated atom. By using the CALYPSO approach for the global minima search followed by first-principles calculations, we discovered that a more compact trilayer Ag₁₃^- cluster was the ground state, in accordance with another three works published recently. In addition, its O₂ adsorption structure is also energetically favored. By tracing characteristic bond changes in ab initio molecular dynamics (MD) simulations, we confirmed that, compared with other isomers, this trilayer structure and its O₂ adsorption structure also had the highest thermal stability. This work emphasized the thermal stability concept in theoretical calculations, which may be a necessary supplement to explain the experimental observations on cluster science.

Structural characterization, reactivity, and vibrational properties of silver clusters: a new global minimum for Ag16

In the present work, the lowest energy structures and electronic properties of Agn clusters up to n = 16 are investigated using a successive growth algorithm coupled with density functional theory calculations (DFT).

Static and dynamical isomerization of Cu38 cluster

The lowest-energy geometrical and electronic structures of Cu₃₈ cluster are investigated by density-functional calculations combined with a genetic algorithm based on a many body semi-empirical interatomic potential, the traditional FCC-truncated Octahedron (OH) and an incomplete-Mackay icosahedron (IMI) are recognized as the two lowest energy structures (energetically degenerate isomers) but with different electronic structures: a semiconductor-type with the energy-gap of 0.356 eV for the IMI and a metallic-type with negligible gap for the OH, which is in good agreement with the experimental results. The electron affinity and ionization potential of Cu₃₈ are also discussed and compared with the observations of the ultraviolet photoelectron spectroscopy experiments. The dynamical isomerization of the OH-like and IMI-like structures of Cu₃₈ is revealed to dominate the pre-melting stage through the investigation by the molecular dynamics annealing simulations.

Catalysis of Cu Cluster for NO Reduction by CO: Theoretical Insight into the Reaction Mechanism

Density functional theory calculations here elucidated that Cu₃₈-catalyzed NO reduction by CO occurred not through NO dissociative adsorption but through NO dimerization. NO is adsorbed to two Cu atoms in a bridging manner. NO adsorption energy is much larger than that of CO. N-O bond cleavage of the adsorbed NO molecule needs a very large activation energy (ΔG°^‡). On the other hand, dimerization of two NO molecules occurs on the Cu₃₈ surface with small ΔG°^‡ and very negative Gibbs reaction energy (ΔG°) to form ONNO species adsorbed to Cu₃₈. Then, a CO molecule is adsorbed at the neighboring position to the ONNO species and reacts with the ONNO to induce N-O bond cleavage with small ΔG°^‡ and very negative ΔG°, leading to the formation of N₂O adsorbed on Cu₃₈ and CO₂ molecule in the gas phase. N₂O dissociates from Cu₃₈, and then it is readsorbed to Cu₃₈ in the most stable adsorption structure. N-O bond cleavage of N₂O easily occurs with small ΔG°^‡ and significantly negative ΔG° to form the N₂ molecule and the O atom adsorbed on Cu₃₈. The O atom reacts with the CO molecule to afford CO₂ and regenerate Cu₃₈, which is rate-determining. N₂O species was experimentally observed in Cu/γ-Al₂O₃-catalyzed NO reduction by CO, which is consistent with this reaction mechanism. This mechanism differs from that proposed for the Rh catalyst, which occurs via N-O bond cleavage of the NO molecule. Electronic processes in the NO dimerization and the CO oxidation with the O atom adsorbed to Cu₃₈ are discussed in terms of the charge-transfer interaction with Cu₃₈ and Frontier orbital energy of Cu₃₈.

Combined Automated Reaction Pathway Searches and Sparse Modeling Analysis for Catalytic Properties of Lowest Energy Twins of Cu13

In nanocatalysis, growing attention has recently been given to investigation of energetically low-lying structural isomers of atomic clusters, because some isomers can demonstrate better catalytic activity than the most stable structures. In this study, we present a comparative investigation of catalytic activity for NO dissociation of a pair of the energetically degenerated isomers of Cu₁₃ cluster having C₂ and C _s symmetries. It is shown that although these isomers have similar structural, electronic, and optical properties, they can possess very different catalytic activities. The effect of isomerization between cluster isomers is considered using state-of-the-art automated reaction pathway search techniques such as an artificial force induced reaction (AFIR) method as a part of a global reaction route mapping (GRRM) strategy. This method allows effectively to locate a large number of possible reaction pathways and transition states (TSs). In total, 12 TSs for NO dissociation were obtained for Cu₁₃, of C₂, C _s, as well as I _h isomers. Sparse modeling analysis shows that LUMO is strongly negatively correlated with total energy of TSs. For most TSs, LUMO has the antibonding character of NO, consisting of the interaction between π* of NO and SOMO of Cu₁₃. Therefore, an increase in the strength of interaction between NO molecule and Cu₁₃ cluster causes the rise in energy of the LUMO, resulting in lowering of the TS energy for NO dissociation. The combination of the automated reaction pathway search technique and sparse modeling represents a powerful tool for analysis and prediction of the physicochemical properties of atomic clusters, especially in the regime of structural fluxionality, where traditional methods based on random geometry search analyses are difficult.

Sub nanometer clusters in catalysis

Sub nanometer transition metal clusters composed of a small number of atoms exhibit unexpected electronic, optical, magnetic and catalytic properties that often change substantially as a function of cluster atomicity. Several factors influence their unique catalytic behavior, including their discrete electronic structure of molecular-like orbitals and the accessibility of their low-coordinated atoms. In addition, these factors are strongly correlated so that changes in their morphology may provoke large modifications to their electronic structure and vice versa. The thermodynamic instability of clusters makes it necessary to stabilize them with protective ligands in solution or to support them on solid matrices for practical applications, which introduces non-negligible modifications into their properties. Understanding their cause and extent is the key point to potentially achieve a fine tuning of their catalytic behavior. Selected examples are discussed illustrating important points on this matter, such as the influence of cluster morphology on reactivity, the need of anchoring clusters to avoid sintering and deactivation, and the possible formation of clusters in solution or under reaction conditions, with the associated difficulty to identify them as the true active species.

Electronic processes in NO dimerization on Ag and Cu clusters: DFT and MRMP2 studies

Experimentally observed NO dimerization on Cu and Ag surfaces is surprising because binding energy of NO dimer is very small in gas phase. MRMP2, MP2 to MP4, CCSD(T), and DFT studies of NO dimerization on Ag₂ and Cu₂ clusters disclosed that the CCSD(T) method could be applied to this reaction on Ag₂ and Cu₂ unlike NO dimerization in gas phase which exhibits significantly large nondynamical electron correlation effect. Charge-transfer (CT) from Ag₂ and Cu₂ to NO moieties plays important role in NN bond formation between two NO molecules. This CT considerably decreases nondynamical correlation effect. Also, the DFT method could be applied to this NO dimerization, if appropriate DFT functional is used; all pure functionals examined here and most of the hybrid functionals underestimated the activation barrier (E_a ), while only ωB97X provided E_a similar to CCSD(T)-calculated value. NO dimerization on similar Cu₂ and Cu₅ needs moderately larger E_a than those on Ag₂ and Ag₅ , because frontier orbital participating in the CT exists at lower energy in Cu₂ and Cu₅ than in Ag₂ and Ag₅ . The E_a decreases in the order Ag₂ >> Ag₃₈ > Ag₇ ∼ Ag₅ and the reaction energy (ΔE) is positive (endothermic) in Ag₂ but significantly negative in Ag₃₈ , Ag₇ , and Ag₅ , indicating that various Ag clusters could be effective for NO dimerization except for Ag₂ . The decreasing order of E_a and increasing order of exothermicity are attributed to increasing order of the frontier orbital energy of Ag₂ < Ag₃₈ < Ag₇ ∼ Ag₅ . © 2018 Wiley Periodicals, Inc.

The stability of Cu clusters and their adsorption for CH4 and CH3 by first principle calculations

Two-dimensional (2D) and three-dimensional (3D) Cu _n clusters (n indicates the atom number) and their adsorption behaviors for both methane (CH₄) and methyl (CH₃) are studied in this work using the density functional theory method, where n ranges from 6 to 20. In these small clusters, it is found that the CH₄ molecule is always adsorbed on the top site with the adsorption energy between -0.05 eV and -0.21 eV. Considering methane dehydrogenation, stronger adsorption for CH₄ is required, so 2D clusters with n = 7, 14, 15, and 16 and 3D clusters with n = 6, 10, 12, and 17 are found to have relatively stronger adsorption. However, for the adsorption of CH₃, there is an obvious even-odd oscillation change in the size of 3D clusters, while it is not clear in 2D clusters since one cannot find an even-odd change as n > 14. The weaker adsorption for CH₃ occurs on 3D clusters when n is even except 6 and also on 2D clusters when n = 6, 7, 10, and 12 with higher carbon poisoning resistance. Based on these calculated results, some Cu clusters which show good potential ability for methane dehydrogenation are provided, especially when n = 10 and 12 for 3D structures, and n = 7 for the 2D ones.

Evolution of the Structural and Electronic Properties of Medium-Sized Sodium Clusters: A Honeycomb-Like Na20 Cluster

Sodium is one of the best examples of a free-electron-like metal and of a certain technological interest. However, an unambiguous determination of the structural evolution of sodium clusters is challenging. Here, we performed an unbiased structure search among neutral and anionic sodium clusters in the medium size range of 10-25 atoms, using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method. Geometries are determined by CALYPSO structure searches, followed by reoptimization of a large number of candidate structures. For most cluster sizes the simulated photoelectron spectra of the lowest-energy structures are in excellent agreement with the experimental data, indicating that the current ground-state structures are the true minima. The equilibrium geometries show that, for both neutral and anionic species, the structural evolution from bilayer structures to layered outsides with interior atoms occurs at n = 16. A novel unprecedented honeycomb-like structure of Na₂₀ cluster with C₃ symmetry is uncovered, which is more stable than the prior suggested structure based on pentagonal structural motifs.

A Systematic Investigation on CrCun Clusters with n = 9-16: Noble Gas and Tunable Magnetic Property

A systematic investigation on structure, dissociation behavior, chemical bonding, and magnetic property of Cr-doped Cun clusters (n = 9-16) is carried out using the mean of density functional theory calculations. It is found that CrCu12 is a crucial size, preferring an icosahedral Cu12 cage with the central Cr dopant. Smaller cluster sizes appear as on the way to form the CrCu12 icosahedron while larger ones are produced by attaching additional Cu atoms to the CrCu12 core. The presence of Cr dopant obviously enhances the stability of CrCun clusters in comparison to that of pure counterparts. Exceptionally stable CrCu12 has an 18-electron closed-shell electronic structure, mimicking a noble gas in the viewpoint of superatom concept. Analysis on cluster electronic structure shows that the interplay between 3d orbitals of Cr and 4s orbitals of Cu has a vital role on the magnetic properties of CrCun clusters.

STABILITIES AND FRAGMENTATION BEHAVIORS OF Agn CLUSTERS (n = 2–34)

A global search on the lowest-energy structures of the medium-sized silver clusters Ag n(n = 21–34) was performed by using a genetic algorithm (GA) coupled with a tight-binding (TB) method. Structures, binding energies per atom, second differences in energies, the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO), and fragmentation behaviors of Ag n(n = 21–34) are investigated by using DFT method. The calculated results show that the neutral silver clusters prefer to decay by evaporation of a monomer except a small sized silver cluster ( Ag 4), which favors a dimmer evaporation. For the collision induced dissociation of cationic silver clusters, decaying a silver atom is found to be the dominant fragmentation channel. But for some small sized cationic silver clusters, a neutral dimmer evaporation is found to be energetically favorable. Our calculated results are consistent with previous studies.

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.

Density functional investigations on structural and electronic properties of anionic and neutral sodium clusters Na(N) (N = 40-147): comparison with the experimental photoelectron spectra

Density functional calculations have been carried out to obtain low energy equilibrium geometries of anionic and neutral sodium clusters over a wide range of sizes 40 ≤ N ≤ 147, where N is the number of atoms. An exhaustive search for the low energy equilibrium geometries has been carried out. The density of states of the lowest energy geometries are compared with the experimental photoelectron spectra (Huber et al 2009 Phys. Rev. B 80 235425; Kostko et al 2007 Phys. Rev. Lett.98 043401) for N > 41. The agreement between theory and experiment is good for almost all the clusters and the changes in the spectrum with size correlate very well with the changes in the shapes as observed in the evolutionary trend of the ground state geometries.