A density functional study of small copper clusters: Cun (n⩽5)

Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics

We performed parallel-tempering molecular dynamics simulations to predict the temperature- and size-dependent equilibrium shapes of a series of Cu nanocrystals in the 100- to 200-atom size range. Our study indicates that temperature-dependent, solid-solid shape transitions occur frequently for Cu nanocrystals in this size range. Complementary calculations with electronic density functional theory indicate that vibrational entropy favors nanocrystals with a shape intermediate between a decahedron and an icosahedron. Overall, we find that entropy plays a significant role in determining the shapes Cu nanocrystals, so studies aimed at determining minimum-energy shapes may fail to correctly predict shapes observed at experimental temperatures. We also observe significant shape changes with nanocrystal size - sometimes with changes in a single atom. The information from this study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

Comparison of Cu3, Cu5, and Cu7 clusters as potential antioxidants: A theoretical quest

CONTEXT

Herein, we compare and contrast the dual roles of Cun clusters (n = 3, 5, and 7 atoms) in scavenging or generating RO• free radicals from ROH at the theoretical levels (where R = H, methyl, ethyl, n-propyl, i-propyl, n-butyl, t-butyl, and phenyl). This investigation is performed in water media to mimic the actual environment in the biological system. In the presence of the Cun clusters, bond dissociation energy (BDE) of RO-H and R-OH is reduced. This is clear evidence for the increased possibility of both the RO-H and R-OH bonds breakage and scavenging of RO• radicals. The nature of anchoring bonds responsible for the interaction of Cun clusters with ROH and RO• are interpreted using the quantum theory of atoms in molecules (QTAIM) and the natural bond orbital (NBO) analysis. The DFT results indicate that the O•⋅⋅⋅•Cu bond is stronger and has more covalent character in RO•⋅⋅⋅•Cun radical complexes than in ROH⋅⋅⋅•Cun. Therefore, the interactions of Cun clusters with RO• radicals (antioxidant) are more pronounced than their interactions with ROH non-radicals (pro-oxidant).

METHODS

The GAMESS software package was utilized in this paper. The B3LYP and M06 functions with the 6-311 +  + G(d,p), and LANL2DZ/SDD basis sets was used to perform the important geometrical parameters of RO•⋅⋅⋅•Cun and ROH⋅⋅⋅•Cun, binding energy (Eb), and bond dissociation energy (BDE).

Reaction Mechanism and Kinetics for the Selective Hydrogenation of Carbon Dioxide to Formic Acid and Methanol over the [Cu2]0,±1 Dimer

With the rapid growth of industrialization, deforestation, and burning of fossil fuels, undeniably there has been an incredible escalation of the CO2 concentration in the atmosphere. In order to mitigate the problem, the capture and utilization of CO2 in different value-added chemicals have thus remained topics of concerned research for more than a decade. Accordingly, we have performed molecular -level catalytic hydrogenation of CO2 to formic acid using bare [Cu2]0,±1 dimers as catalysts. The entire investigation has been performed using a density functional theory (DFT) method employing the Perdew-Burke-Ernzerhof (PBE) functional with the def2TZVPP basis set to explore the different possible routes and efficiency of the catalysts. Results reveal the feasibility of H2 dissociation on all three Cu2, Cu2+, and Cu2- dimers. The negatively charged hydride formed during H2 dissociation on Cu2 and Cu2+ dimers facilitates the formation of the HCOO* intermediate over COOH*, thereby providing product selectivity for HCOOH above CO. However, the reaction on the Cu2- dimer forms both HCOO* and COOH* intermediates, but HCOO*, being kinetically more favorable, results in HCOOH production. The free-energy change suggests that the complete reaction on Cu2 and Cu2+ dimers forms a stable product compared to the Cu2- dimer. Furthermore, H3COH production is studied using the title catalysts via the obtained HCOOH* intermediate from the reaction channel. Transition state theory (TST) has been considered to evaluate the rate constants for each step of the reaction. Overall results suggest Cu2 to be better compared to Cu2+ and Cu2- dimers for HCOOH formation and Cu2+ over Cu2 and Cu2- dimers to be more efficient for H3COH formation. This work opens the way for further investigation of the reaction mechanism and development of an efficient catalyst for CO2 hydrogenation.

Structure and formation of copper cluster ions in multiply charged He nanodroplets

The structure of cationic and anionic Cu clusters grown in multiply charged superfluid He nanodroplets was investigated using He tagging as a chemical probe. Further, the structure assignment was done based on the magic-numbered ions, representing the most energetically favorable structures. The exact geometry of the cluster and positions of He is verified by calculations. It was found that the structure of the clusters grown in the He droplets is similar to that produced with a laser ablation source and the lowest energy structures predicted by theoretical investigations. The only difference is the structure of the Cu₅⁺, which in our experiments has a twisted-X geometry, rather than a bipyramid or planar half-wheel geometry suggested by previous studies. This might be attributed to the different cluster formation mechanisms, the absence of the Ar-tag and the ultracold environment. It was also found that He tends to bind to partially more electro-negative or positive areas of the anionic or cationic clusters, respectively.

Synthesis of photocatalytic cysteine-capped Cu≈10 clusters using Cu5 clusters as catalysts

We report an easily scalable synthesis method for the preparation of cysteine-capped Cu_≈10 clusters through the reduction of Cu(II) ions with NaBH₄, using Cu₅ clusters as catalysts. The presence of such catalytic clusters allows controlling the formation of the larger Cu_≈10 clusters and prevents the production of copper oxides or Cu(I)-cysteine complexes, which are formed when Cu₅ is absent or at lower concentrations, respectively. These results indicate that small catalytic clusters could be involved, as precursor species before the reduction step, in the different methods developed for the synthesis of clusters. The visible light-absorbing Cu_≈10 clusters, obtained by the cluster-catalysed method, display high photocatalytic activities for the decomposition of methyl orange with visible light.

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.

DFT insights into structural effects of Ni-Cu/CeO2 catalysts for CO selective reaction towards water-gas shift

The water-gas shift (WGS) reaction is a key step in hydrogen production, particularly to meet the high-purity H2 requirement of PEM fuel cells. The catalysts currently employed in large-scale WGS plants require a two-step process to overcome thermodynamic and kinetic limitations. Ni-Cu/CeO2 solids are promising catalysts for the one-step process required for small-scale applications, as the addition of Cu hinders undesired methanation reactions occurring on Ni/CeO2. In this work, we performed calculations on Ni4-xCux/CeO2(111) systems to evaluate the influence of cluster conformation on the selectivity towards water-gas shift. The structure and miscibility of CeO2-supported Ni4-xCux clusters were investigated and compared with those of gas-phase clusters to understand the effect of metal-support interactions. The adsorption of CO onto apical Ni and Cu atoms of Ni4-xCux/CeO2(111) systems was studied, and changes in the C-O bond strength were confirmed at the electronic level by investigating shifts in the 3σ and 1π orbitals. The selectivity towards WGS was evaluated using Brønsted-Evans-Polanyi relations for the C-O activation energy. Overall, a strengthening of the C-O bond and an increase in CO dissociation energy were verified on Cu-containing clusters, explaining the improvement in selectivity of Ni4-xCux/CeO2(111) systems.

Quantifying electron-correlation effects in small coinage-metal clusters via ab initio calculations

We investigate many-electron correlation effects in neutral and charged coinage-metal clusters Cun, Agn, and Aun (n = 1-4) via ab initio calculations using fixed-node diffusion Monte Carlo (FN-DMC) simulations, density functional theory (DFT), and the Hartree-Fock (HF) method. From very accurate FN-DMC total energies of the clusters and the HF results in the infinity large complete-basis-set limit, we obtain correlation energies in these strongly correlated many-electron clusters involving d orbitals. The obtained bond lengths of the clusters, atomic binding and dissociation energies, ionization potentials, and electron affinities are in satisfactory agreement with the available experiments. In the analysis, the electron correlation effects on these observable physical quantities are quantified by relative correlation contributions determined by the difference between the calculated FN-DMC and HF results. We show that the correlation contribution is not only significant for the quantities related to electronic structures of the coinage-metal clusters, such as electron affinity, but it is also essential for the stability of the atomic structures of these clusters. For example, the electron correlation contribution is responsible for more than 90% of the atomic binding energies of the small neutral copper clusters. We also demonstrate the orbital-occupation dependence of the correlation energy and electron pairing of the valence electrons in these coinage-metal clusters from the electron correlation-energy gain and spin-multiplicity change in the electron addition processes, which are reflected in their ionization potentials and electron affinities.

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.

Effect of atomicity on the oxidation of cationic copper clusters studied using thermal desorption spectrometry

The resistivity to oxidation of small copper clusters, Cun+ (n ≤ 5), in the gas phase with a precise atomicity at the molecular level was investigated using a combination of thermal desorption spectrometry and mass spectrometry. Oxide clusters, CunOm+, with more O atoms than those present with a stoichiometry of n : m = 1 : 1 were produced at room temperature in the presence of O2, and the weakly bound excess oxygen atoms involved in the clusters were removed by post heating. Non-oxidized Cu2+ and Cu3+ clusters were formed in the range of 323-923 K, whereas partially oxidized clusters, Cu4O2+ and Cu5O2+, were generated for n = 4 and 5. Considering the fact that CunOm+ (m = n/2 + 1) tends to be generated for n ≥ 6, the small copper clusters were concluded to be resistive to oxidation. The possible reaction paths for the oxidation of Cu2+ and Cu4+ clusters were obtained by density functional calculations, which were consistent with the experimental findings. The oxidation states of the Cu atoms in the clusters were discussed based on the natural charges of the atoms.

Structures of Cu n+ ( n = 3-10) Clusters Obtained by Infrared Action Spectroscopy

Coinage metal clusters are of great importance for a wide range of scientific fields, ranging from microscopy to catalysis. Despite their clear fundamental and technological importance, the experimental structural determination of copper clusters has attracted little attention. We fill this gap by elucidating the structure of cationic copper clusters through infrared (IR) photodissociation spectroscopy of Cu _n⁺-Ar _m complexes. Structures of Cu _n⁺ ( n = 3-10) are unambiguously assigned based on the comparison of experimental IR spectra in the 70-280 cm^-1 spectral range with spectra calculated using density functional theory. Whereas Cu₃⁺ and Cu₄⁺ are planar, starting from n = 5, Cu _n⁺ clusters adopt 3D structures. Each successive cluster size is composed of its predecessor with a single atom adsorbed onto the face, giving evidence of a stepwise growth.

A comparative study of CunX (X = Sc, Y; n = 1–10) clusters based on the structures, and electronic and aromatic properties

The MO diagrams and orbital contributions of the HOMO and LUMO for the Cu₇Sc and Cu₇Y clusters.

Cu3-Cluster-Doped Monolayer Mo2CO2 (MXene) as an Electron Reservoir for Catalyzing a CO Oxidation Reaction

The catalytic oxidation of CO on Cu₃-cluster-decorated pristine and defective Mo₂CO₂ (MXene) monolayers (Cu₃/p-Mo₂CO₂ and Cu₃/d-Mo₂CO₂) was investigated by first-principles calculations. The stability of the designed catalysts was comprehensively demonstrated via analysis of the energies, geometry distortion, and molecular dynamics simulations at finite temperatures. The difference in the individual adsorption energies, as well as the oxidation and poisoning of Cu₃/p(d)-Mo₂CO₂ under CO and O₂ gas atmospheres, was tested to estimate the catalytic ability. We found that Cu₃/d-Mo₂CO₂ might be a superior catalyst with good stability and reactivity for CO oxidation. The active sites of the Cu₃ cluster acting as an electron reservoir governed its electron-donating and -accepting ability. Different adsorption configurations of O₂ on Cu₃/d-Mo₂CO₂ also gave rise to different reaction activities. The facile rate-limiting energy barrier was attributed to the charge buffer capacity of the Cu₃ cluster that mediates the reaction. Our results may provide clues to fabricate MXene-based materials by depositing small clusters on MXenes and exploring the advanced applications of these materials.

Insights into the structures and electronic properties of Cun+1μ and CunS μ (n = 1-12; μ = 0, ±1) clusters

ABSTARCT

The stability and reactivity of clusters are closely related to their valence electronic configuration. Doping is a most efficient method to modify the electronic configuration and properties of a cluster. Considering that Cu and S posses one and six valence electrons, respectively, the S doped Cu clusters with even number of valence electrons are expected to be more stable than those with odd number of electrons. By using the swarm intelligence based CALYPSO method on crystal structural prediction, we have explored the structures of neutral and charged Cu_n+1 and Cu_nS (n = 1-12) clusters. The electronic properties of the lowest energy structures have been investigated systemically by first-principles calculations with density functional theory. The results showed that the clusters with a valence count of 2, 8 and 12 appear to be magic numbers with enhanced stability. In addition, several geometry-related-properties have been discussed and compared with those results available in the literature.

An insight into the structures, stabilities, and bond character of B(n)Pt (n=1∼6) clusters

We perform a systematical investigation on the geometry, thermodynamic/kinetic stability, and bonding nature of low-lying isomers of BnPt (n=1-6) at the CCSD(T)/[6-311+G(d)/LanL2DZ]//B3LYP/[6-311+G(d)/LanL2DZ] level. The most stable isomers of BnPt (n=1-6) adopt planar or quasi-planar structure. BnPt (n=2-5) clusters can be generated by capping a Pt atom on the B-B edge of pure boron clusters. However, For B6Pt with non-planar structure, a single doped Pt atom significantly affects the shape of the host boron cluster. The dopant of the Pt atom can improve the stability of pure boron clusters. The valence molecular orbital (VMO), electron localization function (ELF), and Mayer bond order (MBO) are applied to gain insight into the bonding nature of BnPt (n=2-6) isomers. The aromaticity for some isomers of BnPt (n=2-6) is analyzed and discussed in terms of VMO, ELF, adaptive natural density partitioning (AdNDP), and nucleus-independent chemical shift (NICS) analyses. Results obtained from the energy and cluster decomposition analyses demonstrate that B2Pt and B4Pt exhibits as highly stable. Importantly, some isomers of BnPt (n=2-5) are stable both thermodynamically and kinetically, which are observable in future experiment.

A density functional study of Rh13

A density functional study was performed for the Rh13 cluster using the linear combination of Gaussian-type orbitals density functional theory (LCGTO-DFT) approach. The calculations employed both the local density approximation (LDA) as well as the generalized gradient approximation (GGA) in combination with a quasi-relativistic effective core potential (QECP). Initial structures for the geometry optimization were taken along Born–Oppenheimer molecular dynamics (BOMD) trajectories. The BOMD trajectories were performed at different temperatures and considered different potential energy surfaces (PES). As a result, several hundred isomers of the Rh13 cluster in different spin multiplicities were optimized with the aim to determine the lowest energy structures. All geometry optimizations were performed without any symmetry restriction. A vibrational analysis was performed to characterize these isomers. Structural parameters, relative stability energy, harmonic frequencies, binding energy, and most relevant Kohn–Sham (KS) molecular orbitals are reported. The obtained results are compared with available data from the literature. This study predicts a low symmetry biplanarlike structure as the ground-state structure of Rh13 with 11 unpaired electrons. This isomer was first noticed by inspection of first-principle Born–Oppenheimer molecular dynamics (BOMD) simulations between 300 and 600 K. This represents the most extensive theoretical study on the ground-state structure of the Rh13 cluster and underlines the importance of BOMD simulations to fully explore the PES landscapes of complicated systems.

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.

MOLECULAR DYNAMICS STUDY OF Tin, Vn AND Crn CLUSTERS

Using a Morse type pair potential, molecular-dynamics simulations have been performed to investigate the atomic geometries, growing patterns, structural stabilities, energetics and magic sizes of Ti n, V n and Cr n (n = 2-50) clusters. Following rearrangement collision of the atom–cluster system in fusion process, and absorbing their energies step by step down to 0 K, possible optimal equilibrium geometries of the clusters have been generated to tackle the structural determination problem. This approach serves an efficient alternative to the growing path identification and the optimization techniques. It has been found that titanium, vanadium and chromium clusters prefer to form three-dimensional compact structures in the determined configurations and the appearances of medium sizes are, in general, five-fold symmetry on the spherical clusters. Moreover, relevant relations between atomic arrangements in the clusters and the magic sizes have been observed.

A new magnetron based gas aggregation source of metal nanoclusters coupled to a double time-of-flight mass spectrometer system

A new magnetron based gas-aggregation source for continuous production of metal nanoclusters has been built and coupled to a double time-of-flight mass spectrometer system. The capability of the source to produce neutral, positive, and negative nanoclusters within one production cycle, particularly under the same optimized experimental conditions, has been tested. The source performs steadily for continuous long operations and has high beam intensity that would be preferable for size selective measurements in gas phase on individual nanoclusters. This paper describes on the instrumentation of the integrated complete experimental setup for gas-phase measurement on nanoclusters including the source. It reports on the production of copper nanoclusters using the source. Mass abundances of neutral and charged clusters have been investigated and the results are discussed with respect to reported results using various other types of sources. The experimental isotopic distributions of (63)Cu versus (65)Cu within individual cluster mass peaks have been derived and compared to corresponding theoretical profiles.

Growth mechanism and chemical bonding in scandium-doped copper clusters: experimental and theoretical study in concert

Size matters! The electronic structure and size-dependent stability of neutral and cationic scandium-doped copper clusters have been investigated by mass spectrometric studies (for the cations) and also quantum chemical computations. The proposed reaction paths ultimately lead to the most stable Frank-Kasper-shaped Cu(16)Sc(+) cluster (shown here), which could be the germ of a new crystallization process.Electronic structure and size-dependent stability of scandium-doped copper cluster cations, Cu(n)Sc(+), were investigated by using a dual-target dual-laser vaporization production scheme followed by mass spectrometric studies and also quantum chemical computations in the density functional theory framework. The neutral species also were studied by using computational methods. Enhanced abundances and dissociation energies were measured in the case of Cu(n)Sc(+) for n=4, 6, 8, 10 and 16, the last of these identified as being extraordinary stable. Neutral clusters are stable with n=5, 7, 9 and 15, which are isoelectronic with respect to the number of the valence s electrons with the stable cationic clusters; hence a simple electron count determines cluster properties to a great extent. The Cu(17)Sc cluster was found to be a superatomic molecule, containing Cu(16)Sc(+) and Cu(-) units; however, the charge separation is not as pronounced as in the case of CuLi. Cu(15)Sc was found to be a stable cluster with a large dissociation energy and a closed electronic structure; hence this can be regarded as a superatom, analogous to the noble gases. The main factors determining the growth patterns of these clusters are the central position of the scandium atom and the successive filling of the shell orbitals. For smaller clusters, the reaction paths appear to diverge yielding various products; however all paths ultimately lead to the most stable Frank-Kasper shaped Cu(16)Sc cluster, which in turn can be the germ of the crystallization process.

Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters

Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (n<or=5), using the linear combination of Gaussian-type orbital density functional theory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems

Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.

CO adsorption on pure and binary-alloy gold clusters: a quantum chemical study

We performed density-functional theory analysis of nondissociative CO adsorption on 22 binary Au-alloy (Au(n)M(m)) clusters: n=0-3, m=0-3, and m+n=2 (dimers) or 3 (trimers), M=Cu/Ag/Pd/Pt. We report basis-set superposition error corrections to adsorption energies and include both internal energy of adsorption (DeltaU(ads)) and Gibbs free energy of adsorption (DeltaG(ads)) at standard conditions (298.15 K and 1 atm). We found onefold (atop) CO binding on all the clusters except Pd2 (twofold/bridged), Pt2 (twofold/bridged), and Pd3 (threefold). In agreement with the experimental results, we found that CO adsorption is thermodynamically favorable on pure Au/Cu clusters but not on pure Ag clusters and also observed the following adsorption affinity trend: Pd>Pt>Au>Cu>Ag. For alloy dimers we found the following patterns: Au2>M Au>M2 (M=Ag/Cu) and M2>M Au>Au2 (M=Pd/Pt). Alloying Ag/Cu dimers with (more reactive) Au enhanced adsorption and the opposite effect was observed for PdPt dimers. The Ag-Au, Cu-Au, and Pd-Au trimers followed the trends observed on dimers: Au3>M Au2>M2Au>M3 (M=Ag/Cu) and Pd3>Pd2Au>PdAu2>Au3. Interestingly, Pt-Au trimers reacted differently and alloying with Au systematically increased the adsorption affinity: PtAu2>Pt2Au>Pt3>Au3. A strikingly different behavior of Pt is also manifested by the triplet spin state and onefold (atop) binding in Pt3-CO which is in contradiction with the singlet spin state and threefold binding in Pd3-CO. We found a linear correlation between CO binding energy (BE) and elongation of the CO bond. For Ag-Au and Cu-Au clusters, the increase in CO BE (and elongation of the C-O bond which is probably due to the back donation) is accompanied by the decrease in the cluster-CO distance suggesting that the donation (from 5sigma highest occupied molecular orbital in CO to cluster lowest unoccupied molecular orbital) mechanism also contributes to the BE. For Pd-Au clusters, the cluster-CO distance (and CO bond length) increases with increase in the BE, suggesting that the donation mechanism may not be important for those clusters. No clear trend was observed for Pt-Au clusters.

Ab Initio Study of Structure and Stability of M2Al2 (M = Cu, Ag, and Au) Clusters

Coinage metal aluminium clusters M2Al2 (M = Cu, Ag, and Au) were studied by Hartree–Fock (HF) and second-order Møller–Plesset perturbation theory (MP2) with pseudopotentials. It was found that the butterfly structure with C2v (1A1) symmetry is more stable than the planar structure, and Au2Al2 is the most stable of the title species. The binding energies and the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO) gap are evaluated, which indicates that doping clusters M2Al2 are more stable than the pure clusters M4 (M = Cu, Ag, and Au). Electron correlation and relativistic effects stabilize the present species.

Analysis of O2 Adsorption on Binary−Alloy Clusters of Gold: Energetics and Correlations

We report a B3LYP density-functional theory (DFT) analysis of O(2) adsorption on 27 Au(n)M(m) (m, n = 0-3 and m + n = 2 or 3; M = Cu, Ag, Pd, Pt, and Na) clusters. The LANL2DZ pseudopotential and corresponding double-zeta basis set was used for heavy atoms, while a 6-311+G(3df) basis set was used for Na and O. We employed basis-set superposition error (BSSE) corrections in the electronic adsorption energies at 0 K (deltaE(ads)) and also calculated adsorption thermodynamics at standard conditions (298.15 K and 1 atm), i.e., internal energy of adsorption (deltaU(ads)) and Gibbs free energy of adsorption (deltaG(ads)). Natural Bond Orbital (NBO) analysis showed that all the clusters donated electron density to adsorbed O(2) and we successfully predicted intuitive linear correlations between the NBO charge on adsorbed O(2), O-O bond length, and O-O stretching frequency. Although there was no clear trend in the O(2) binding energy (BE = -deltaE(ads)) on pure and alloy dimers, we found the following interesting trend for trimers: BE (MAu(2)) < BE (M(3)) < or = BE (M(2)Au). The alloy trimers containing only one Au atom are most reactive toward O(2) while those with two Au atoms are least reactive. These trends are discussed in the context of the ensemble effect and coulomb interactions. We found an approximate linear correlation between the O(2) BE and charge transfer to O(2) for all 27 clusters. The clusters having strongly electropositive Na atoms (e.g., Na(3) and Na(2)Au) donated almost one full electron to adsorbed O(2), and the BE is maximum on these clusters. Although O(2) dissociation is likely in such cases, we have restricted this study to trends in the adsorption of molecular O(2) only. We also found an approximate linear correlation between the charge transfer and BE versus energy difference between the bare-cluster HOMO and O(2) LUMOs, which we speculate to be a fundamental descriptor of the reactivity of small clusters toward O(2). Part of the scatter in these correlations is attributed to the differences in the O(2) binding orientations on different clusters (geometric effect). Relatively higher bare-cluster HOMO energy eases the charge transfer to adsorbed O(2) and enhances the reactivity toward O(2). The Frontier Orbital Picture (FOP) is not always useful in predicting the most favorable O(2) binding site on clusters. It successfully predicted the cluster-O(2) ground-state configurations for 10 clusters, but failed for the others. Finally, the energetics of fragmentation suggest that the bare and O(2)-covered clusters reported here are stable.

Stable Tin (n = 2−15) Clusters and Their Geometries: DFT Calculations

We present a detailed structural analysis for small Tin (n = 2-15) clusters based on ab initio quantum mechanical calculations of their binding energies, frontier orbital gaps, and second energy derivatives. Local density approximation calculations revealed that while the smaller clusters (n < or = 8) prefer hexagonal atomic arrays with bulklike crystal symmetry, the bigger clusters prefer pentagonal atomic arrays. From the stability criteria of the magic number clusters we could identify three magic number clusters Ti7, Ti13, and Ti15. While the most stable configuration of Ti7 is a decahedral bipyramid induced by tetrahedral atomic arrays, the most stable configuration of Ti13 is an icosahedron. The other stable cluster Ti15 takes a closed-shell icosahedron-like configuration with both pentagonal and hexagonal symmetries. The stability of the Tin clusters strongly depends on their geometries and charge states. The HOMO-LUMO gap of the Tin clusters approaches its bulk value for n > 8. While there is not much difference between the HOMO and LUMO isosurface charge distributions for the Ti7 and Ti13 clusters in their most stable configurations, they are very different in the case of Ti15. Such a distinct charge distribution in Ti15 indicates its singular chemical selectivity over the other two magic number clusters.

Real space pseudopotential calculations for copper clusters

Neutral and anion clusters of copper, Cu(n) (n=3-11), are examined using real space pseudopotentials constructed within the local spin density approximation. We predict the ground state structure for each cluster, the binding energy, and the corresponding photoelectron spectra, which we compare to experiment. We find strong final state effects in the photoelectron spectra, especially for the smaller clusters. The binding energy as a function of cluster size tracks well with the measured values, although the magnitude of the binding energy exceeds the experimental values by approximately 20%, as expected for the local spin density approximation.

Molecular Structure and Bonding of Copper Cluster Monocarbonyls CunCO (n = 1−9)

In this work we analyze CO binding on small neutral copper clusters, Cun (n = 1-9). Molecular structures and reactivity descriptors of copper clusters are computed and discussed. The results show that the condensed Fukui functions and the frontier molecular orbital theory are useful tools to predict the selectivity of CO adsorption on these small clusters. To get further insight into the CO binding to copper clusters, an energy decomposition analysis of the CO binding energy is performed. The Cs symmetry of the formed CunCO clusters (n = 1-8) allows the separation between the orbital interaction terms corresponding to donation and back-donation. It is found that, energetically, the donation is twice as important as back-donation.