Ab Initio Search for Global Minimum Structures of Pure and Boron Doped Silver Clusters

Reactivity of cationic silver clusters with O2: a probe of interplay between clusters' geometric and electronic structures

We explored the size-dependent reactivity of Agn+ (n = 2-22) with O2 under mild conditions and found that only a few sizes of Agn+, with even values of n = 4, 6, 12, 16, 18, and 22, are reactive. Possible structures of Agn+ (n = 2-22) were determined using a genetic algorithm with incomplete local optimizations at the DFT level, and the calculated bonding strengths of O2 on these structures are consistent with experimental observations. Analyses revealed a close relationship between the reactivity of Agn+ with O2 and its HOMO-LUMO gap: cationic silver clusters with a small HOMO-LUMO gap are reactive, which can be rationalized by the covalent character of chemical bonds between Agn+ and O2 involving their frontier orbitals. The peculiar size-dependent HOMO-LUMO gaps and reactivity with O2 correlate with the subtle interplay between the electronic configurations and geometric structures of these silver cluster cations.

Growth pattern and electronic and magnetic properties of Cr-doped silver clusters

Growth pattern and electronic and magnetic properties of Agn Cr (n = 1-16) clusters have been investigated via density functional theory (DFT) combined with CALYPSO structure search method. The optimized geometry shows that the growth of the global minimum structures of Agn Cr clusters have obvious rule. when n > 12, silver atoms grow around an icosahedron which is almost unchanged in each structure. Analyses of electronic properties indicate that the doped Cr atom can only enhance the stability of larger silver clusters. Optical absorption and photoelectron spectra of Agn Cr isomers have been predicted and can be used for their structural identification. The icosahedral Ag12 Cr cluster with large energy level gap can be seen as a superatom. The adsorption capacity of Cr atom in Agn Cr cluster to CO is much higher than that of free Cr atom. The intensity of IR and Ramam spectra can be dramatically enhanced when CO is absorbed on Agn Cr cluster that Cr atom is encapsulated by Ag atoms. Moreover, the red shift of IR and Raman spectra of CO adsorbed on these clusters is also very small compared to free CO. Magnetism calculations show that the magnetic moment of Agn Cr clusters decreases linearly from n = 6 to 12 and increases linearly from n = 12 to 16. The total magnetic moment of Agn Cr cluster is mainly localized on the Cr atom. The change of magnetic moment of Cr atom is related to the charge transfer between Cr and Ag atoms.

Geometric and electronic structures of medium-sized boron clusters doped with plutonium

Doping metal heteroatoms is an effective strategy to regulate the geometric and electronic structure of boron based nanoclusters. However, the exploration of the ground state structures of metal-boron-based nanoclusters is still a challenge duo to the complexity of the bonding interactions between heterogeneous atoms and boron cluster and the number of isomers on the potential energy surface increases exponentially with cluster size. Here, we use the CALYPSO cluster structural search method in combination with density functional theory calculations to study the geometries and electronic properties of anionic boron clusters doped with plutonium (PuBn-,n= 10-20). Our results show that the medium-sized PuB14-cluster exhibits excellent stability with highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap of 2.30 eV. The remarkable stability of the anionic PuB14-cluster is due to the robust interactions between the Pu metal and the B14skeleton, along with the strong covalent interactions between the B atoms. These findings enrich the geometric structure database of metal doped clusters and provide valuable insights for the future synthesis of boron based nanomaterials.

Search for the Decomposition Process of 2,4,6-Trinitrotoluene by an Evolutionary Algorithm

In this paper, we explored stable states in the system of 2,4,6-trinitrotoluene (TNT) crystal with a few additional hydrogen radicals (H_add's) using a structure-search scheme based on first-principles calculations and an evolutionary algorithm (EA) to get insights into the decomposition process of TNT. We introduced three evolutionary operators acting on H_add's and transforming only local structures of TNT molecules: "displacement", "permutation", and "mating". We searched for stable structures by increasing the number of H_add's (n) from 1 to 2, 3, 4, 6, and 8 and constructed a convex-hull diagram for the formation energy from solid TNT and solid hydrogen. We showed that the system of n = 6 had the largest energy reduction, in which five of the eight TNT molecules in the calculation cell were transformed into NO, H₂O, C₂H₃N, C₂NO₃H₃, C₈N₂O₄H₇, C₉N₂O₈H₅, and C₁₄N₇O₁₂H₁₁. Analysis of the structural transformations observed during the EA search indicates that (1) the H_add's approaching the TNT molecules react with C, forming a six-membered ring, and with N and O in nitro groups, leaving the TNT molecules as NO, H₂O, C₂H₃N, and C₂NO₃H₃, and (2) the partially decomposed TNT molecules are bonded to one another via C, N, and O.

The Au12 Gold Cluster: Preference for a Non-Planar Structure

The transition point from a two-dimensional (2D) to a three-dimensional (3D) structure in a series of small gold clusters remains a topic of continuing debate. In the present study, coupled-cluster CCSD(T) and DFT calculations are performed to re-examine the relative energies of several low-lying isomers of Au12, aiming to shed new light on this issue. At odds with many previous reports on the preference of a planar di-capped elongated-hexagon structure, the Au12 size is found to energetically prefer a globular cup-like form with C2v symmetry. While DFT results are not able to assign the most stable form of Au12 as the relative energies between the lowest-lying isomers are strongly functional-dependent, coupled-cluster theory calculations point out the preference of a 3D structure for having a D3h symmetry. Such a prediction is further supported by a comparison of the vibrational spectra computed using the revTPSS density functional with the available experimental infrared ones that were previously recorded from the far-IR multiple photon dissociation (FIR-MPD) experiment.

Growth mechanism, electronic properties and spectra of aluminum clusters

Density functional theory (DFT) and particle swarm optimization (PSO) have been applied to study the growth behavior, electronic properties and spectra of neutral, anionic and cationic aluminum clusters with 3-20 atoms. Many isomers have been obtained through a comprehensive structural search. The results indicate that the ground state structures of neutral and anionic aluminum clusters follow an identical periodic growth law. When the number of atoms is 6-11 and 13-18, Al atoms in these clusters grow around an octahedral cluster nucleus and an icosahedral cluster nucleus, respectively. For Al_n⁺ (n ≤ 14 and n ≠ 7) clusters, the most stable structure is different from that of Al_n or Al_n^-clusters. When n > 14, the ground state structure of Al_n⁺ clusters is similar to that of Al_n or Al_n^-clusters. The electronic properties of aluminum clusters have been analyzed by the averaged binding energy, second-order difference of energy, energy gap and dissociation energy. It is found that the Al₇⁺ and Al₁₃^- clusters have very high stability and a large energy gap and can be regarded as two superatoms. The aluminum cluster with 18 or 40 valence electrons are the least likely to lose an electron. The dissociation behavior of Al_n⁺ clusters caused by collision is reasonably explained by means of the dissociation energy. The optical absorption spectra of neutral aluminum clusters have been simulated by using the time-dependent density functional theory. The ground states of anionic aluminum clusters have been determined by comparing theoretical photoelectron spectra (PES) with experimental findings. Infrared and Raman spectra of cationic aluminum clusters have been forecasted and can assist in identifying the most stable structure in future experiments.

The lowest-energy structure of the gold cluster Au10: planar vs. nonplanar?

The onset of the transition from 2D to 3D structures in pure gold clusters remains a matter of continuing debate. In this theoretical study we revisit several planar and non-planar structural motifs of the size Au₁₀ with the aim to clarify this issue. Computations using a long-range corrected exchange-correlation functional LC-BLYP, coupled-cluster theories CCSD(T) and PNO-LCCSD(T)-F12 reveal that, at variance with previous reports on the preference of a planar elongated hexagon, both planar and nonplanar isomers of the neutral Au₁₀ are energetically degenerated up to 300 K. Its 3D equilibrium geometry is a core-shell structure which can be built up from a trigonal prism by capping four extra Au atoms outside. A comparison to the available experimental vibrational spectra allows us to argue that both lowest-lying 2D and 3D isomers of Au₁₀ likely coexist in the molecular beam during measurement of its FIR spectra. This result also suggests that the 2D-3D transition of neutral gold clusters occurs at the size Au₁₀.

Insights into the Structures and Bonding of Medium-Sized Cerium-Doped Boron Clusters

Since the discovery of metal-doped boron clusters attracted great significance to create a new class of materials, research interests have been directed to chemical bonding and structural evolution of lanthanide boride clusters. Here, we perform an extensive ground-state structure search for the CeB_n and CeB_n^- clusters in the size range from 9 to 18 using the Crystal structure AnaLYsis by Particle Swarm Optimization method and density functional theory optimization. It is found that the ground-state structures in both neutral and anionic series possess half-sandwich geometry. The host boron moiety in neutral series has a tendency to form borophene-like geometry. The pentagonal and hexagonal holes are more common in the larger anionic CeB_n^- series. The theoretical photoelectron spectroscopy has been simulated by applying time-dependent density functional theory calculations. The neutral CeB₁₄ cluster is identified as a magic cluster on the basis of its robust relative stability with respect to its neighbors. Electronic structure and chemical bonding analyses reveal that the CeB₁₄ cluster possesses a large HOMO-LUMO gap and enhanced stability with strong delocalized π and δ bonding via interactions between the Ce 5d- and B 2p-AOs.

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2 Mgn Q (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 Mg_n ^Q (Q = 0, -1; n = 2-11) clusters is performed. Based on the structural optimization, it is found that the Be₂ Mg_n ^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 Mg_n ^Q (Q = 0, -1; n = 1-11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.

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.

Identification of Magic Numbers in Homonuclear Clusters: The ε3 Stability Ranking Function

With the rise of cluster-assembled materials, an index that is able to rank and identify stable clusters or molecules is of great interest in materials sciences and engineering. In the present work, we applied a stability ranking function (ε³) in nanoclusters formed by simple metals (Na, Mg), main group elements (Al), or transition metals (Ti, Cu). The ε³ function parameters are molecular properties derived from the wave function. These parameters can be divided into kinetic and thermodynamic descriptors, in which the kinetic descriptors are the ionization potential and electronic excitation energy, while the atomization free Gibbs energy is the thermodynamic one. This simple ε³ function was able to identify the possible magic numbers of the studied clusters across the periodic table in a good agreement with previous experimental and theoretical works.

Dissociative chemisorption of O2 on Agn and Agn−1Ir (n = 3–26) clusters: a first-principle study

Lower dissociation barriers and higher reaction rates of O₂ on doped Ag_n−1Ir clusters, and a gradually weakened dopant effect.

Structural evolution and electronic properties of medium-sized boron clusters doped with scandium

Doping of boron-based materials with transition metal atoms allows one to tune or modify the properties and structure of the materials. In this work, an extensive search for the global minima on potential energy surfaces of ScB _n and ScB[Formula: see text] clusters has been performed using the CALYPSO method. The structural evolution of scandium doped boron clusters of this range is found to proceed in three steps; namely, the formation of half-sandwich type structures is followed by the formation of drum-like structures with the Sc atom located at the center and terminates with the cage-like structures. It is also found that highly symmetrical geometric structures are more common for the smaller size range of [Formula: see text]. The neutral ScB₁₃ cluster is identified as magic on the basis of an analysis of relative stabilities in the ScB _n series. Our analysis of chemical bonding has shown that the stability of this cluster is mainly due to the formation of several delocalized [Formula: see text]-bonding molecular orbitals composed of Sc 3d and B 2s atomic orbitals. These bonds appear to be responsible for the enhanced stability of ScB₁₃ with respect to other Sc-doped boron clusters.

Systematic Theoretical Study on Structural, Stability, Electronic, and Spectral Properties of Si2 Mg n Q (Q = 0, ±1; n = 1-11) Clusters of Silicon-Magnesium Sensor Material

By using CALYPSO searching method and Density Functional Theory (DFT) method at the B3LYP/6-311G (d) level of cluster method, a systematic study of the structures, stabilities, electronic and spectral properties of Si₂MgnQ (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material, is performed. According to the calculations, it was found that when n > 4, most stable isomers in Si₂MgnQ (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material are three-dimensional structures. Interestingly, although large size Si₂MgnQ clusters show cage-like structures, silicon atoms are not in the center of the cage, but tend to the edge. The Si₂Mg1,5,6,8-1 and Si₂Mg13,4,7,9,10+1 clusters obviously differ to their corresponding neutral structures, which are in good agreement with the calculated values of VIP, AIP, VEA, and AEA. |VIP-VEA| values reveal that the hardness of Si₂Mg_n clusters decreases with the increase of magnesium atoms. The relative stabilities of neutral and charged Si₂MgnQ (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material is analyzed by calculating the average binding energy, fragmentation energy, second-order energy difference and HOMO-LUMO gaps. The results reveal that the Si₂Mg30, Si₂Mg3-1, and Si₂Mg3+1clusters have stronger stabilities than others. NCP and NEC analysis results show that the charges in Si₂MgnQ (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material transfer from Mg atoms to Si atoms except for Si₂Mg1+1, and strong sp hybridizations are presented in Si atoms of Si₂MgnQ clusters. Finally, the infrared (IR) and Raman spectra of all ground state of Si₂MgnQ (n = 1–11; Q = 0, ±1) clusters of silicon magnesium sensor material are also discussed.

Direct observation of tunnelled intergrowth in SnO2/Ga2O3 complex nanowires

β-Ga₂O₃ intergrowths have been revealed in the SnO₂ rutile structure when SnO₂/Ga₂O₃ complex nanostructures are grown by thermal evaporation with a catalyst-free basis method. The structure is formed by a Ga₂O₃ nanowire trunk, around which a rutile SnO₂ particle is formed with [001] aligned to the [010] Ga₂O₃ trunk axis. Inside the SnO₂ particle, β-Ga₂O₃ units occur separated periodically by hexagonal tunnels in the (210) rutile plane. Orange (620 nm) optical emission from tin oxide, with a narrow linewidth indicating localised electronic states, may be associated with this β-Ga₂O₃ intergrowth.

Stability and Reactivity of Silicon Magic Numbers Doped with Aluminum and Phosphorus Atoms

The progressive scaling down of the silicon-based electronics has allowed to develop devices at nanometer scale, requiring new engineering techniques guided by fundamental chemical and physical concepts. Particularly, the nanostructured cluster systems are promising materials since their physical-chemical properties are sensitive to its shape, size, and chemical components, such that completely different materials can be produced by the simple addition or removal of a single atom. These size-tunable properties can open a new area in materials science and engineering. In the present work, quantum chemical methods were used to study the chemical substitution effects caused by subvalent (aluminum) and supervalent (phosphorus) atoms in the physical-chemical properties of some small silicon clusters, which demonstrate high stability, called magic numbers. The changes in the electronic structure and chemical acceptance to the dopants were evaluated with respect to ionization potential, electronic excitation energy, stability, and reactivity parameters. Taken together, these results enable to identify the most stable silicon-doped clusters. Regarding electrophilic reactions, Si₁₀P is the most favorable system, while for nucleophilic reactions, none of the doped clusters resulted in higher stability.

The puzzling optical-absorption and photoelectron spectra of neutral and anionic Ag8 clusters

The optical absorption and photoelectron spectra (PES) of neutral and anionic Ag₈ clusters have been studied using the particle-swarm optimization technique and time-dependent density functional theory. The results demonstrate that the enigmatic optical-absorption spectrum of neutral Ag₈ cluster is derived from the ground state structure with T_d symmetry rather than the almost degenerate isomer with D_2d symmetry. The transitions at 3.57-3.65 eV should be ascribed to the neutral fragment cluster Ag₇. Meantime, the optical-absorption and PES of neutral and anionic Ag₈ cluster are for the first time given a reasonable unified explanation.

Elucidation of the molecular and electronic structures of some magic silver clusters Agn (n = 8, 18, 20)

Density functional theory (DFT) calculations were carried out to explore the geometric, spectroscopic, and electronic properties of three magic silver clusters Ag_n (n = 8, 18, and 20) in detail. The computed results show that the global minima of these clusters are compact, near-spherical structures, while other low-lying isomers exhibit oblate or prolate shapes. Vertical ionization energies for the low-lying isomers were also computed and assigned with respect to available experimental values. Although several isomers were predicted to have similar energies, their electronic and vibrational signatures were quite distinctive, meaning that they could be used as fingerprint signals to distinguish between isomers. In addition, the electronic structures of these systems were explored using the phenomenological shell model. Calculations for the coinage metal clusters M₂₀ (M = Cu, Ag, Au) indicated that the structures and properties of the Ag cluster are similar to those of the Cu cluster in that both Cu₂₀ and Ag₂₀ prefer a compact structure whereas Au₂₀ prefers to adopt a tetrahedral form. Graphical abstract Shell Orbitals of Ag₈ Cluster.

Probing the structural, electronic and magnetic properties of AgnSc (n = 1–16) clusters

The structural, electronic and magnetic properties of Ag_nSc (n = 1–16) clusters have been studied on the basis of density functional theory and the CALYPSO structure prediction method.

Probing the Structural, Electronic, and Magnetic Properties of Ag n V (n = 1-12) Clusters

The structural, electronic, and magnetic properties of Ag _n V (n = 1-12) clusters have been studied using density functional theory and CALYPSO structure searching method. Geometry optimizations manifest that a vanadium atom in low-energy Ag_nV clusters favors the most highly coordinated location. The substitution of one V atom for an Ag atom in Ag _n + 1 (n ≥ 5) cluster modifies the lowest energy structure of the host cluster. The infrared spectra, Raman spectra, and photoelectron spectra of Ag _n V (n = 1-12) clusters are simulated and can be used to determine the most stable structure in the future. The relative stability, dissociation channel, and chemical activity of the ground states are analyzed through atomic averaged binding energy, dissociation energy, and energy gap. It is found that V atom can improve the stability of the host cluster, Ag₂ excepted. The most possible dissociation channels are Ag _n V = Ag + Ag _n - 1V for n = 1 and 4-12 and Ag _n V = Ag₂ + Ag _n - 2V for n = 2 and 3. The energy gap of Ag _n V cluster with odd n is much smaller than that of Ag _n + 1 cluster. Analyses of magnetic property indicate that the total magnetic moment of Ag _n V cluster mostly comes from V atom and varies from 1 to 5 μ _B. The charge transfer between V and Ag atoms should be responsible for the change of magnetic moment.

Structural assignment of small cationic silver clusters by far-infrared spectroscopy and DFT calculations

The structures of cationic silver clusters Ag_n⁺ (n = 3–13) are investigated by comparing measured far-IR photodissociation spectra of cluster–argon complexes with calculated harmonic vibrational spectra.

Insights into the geometries, electronic and magnetic properties of neutral and charged palladium clusters

We performed an unbiased structure search for low-lying energetic minima of neutral and charged palladium Pd_n^Q (n = 2–20, Q = 0, + 1 and –1) clusters using CALYPSO method in combination with density functional theory (DFT) calculations. The main candidates for the lowest energy neutral, cationic and anionic clusters are identified, and several new candidate structures for the cationic and anionic ground states are obtained. It is found that the ground state structures of small palladium clusters are more sensitive to the charge states. For the medium size Pd_n^0/+/– (n = 16–20) clusters, a fcc-like growth behavior is found. The structural transition from bilayer-like structures to cage-like structures is likely to occur at n = 14 for the neutral and cationic clusters. In contrast, for the anionic counterparts, the structural transition occurs at Pd₁₃^–. The photoelectron spectra (PES) of palladium clusters are simulated based on the time-dependent density functional theory (TD-DFT) method and compared with the experimental data. The good agreement between the experimental PES and simulated spectra provides us unequivocal structural information to fully solve the global minimum structures, allowing for new molecular insights into the chemical interactions in the Pd cages.

Au13−nAgn clusters: a remarkably simple trend

The planar to three dimensional transition of Au_13−nAg_n clusters is investigated.