Finding all‐nonmetal transition‐metal‐like superatom and its magnetic building block

In novel superatom chemistry, it is very attractive that all‐metal clusters can mimic the behaviors of nonmetal atoms and simple nonmetal molecules. Wizardly all‐metal halogen‐like superatom Al₁₃ with 2P⁵ sub shell (corresponding to the 3p⁵ of chlorine) is the most typical example. In contrast, how to mimic the behaviors of magnetic transition‐metal atom using all‐nonmetal cluster is an intriguing challenge for superatom chemistry. In response to this based on human intuition, using quantum chemistry methods and extending jellium model from metal cluster to all‐nonmetal cluster, we have found out that all‐nonmetal octahedral B₆ cluster with characteristic jellium electron configuration 1S²1P⁶2S²1D⁸ in the triplet ground state can mimic the behaviors of transition‐metal Ni atom with electron configuration 3s²3p⁶4s²3d⁸ in electronic configuration, physics and chemistry. Interestingly, the characteristic order of 1S1P2S1D for the B₆ nonmetal cluster with short B‐B lengths is different from that of the traditional jellium model—1S1P1D2S for metal clusters with long M‐M lengths, which exhibits a novel size effect of nonmetal cluster on jellium orbital ordering. Based on the jellium electron configuration, the B₆ with the spin moment value of 2μ_B is a new all‐nonmetal transition‐metal nickel‐like superatom exhibiting a new kind of all‐nonmetal magnetic superatom. Finding the application of the all‐nonmetal magnetic superatom, we encapsulate the magnetic superatom B₆ inside fully hydrogenated fullerene forming a clathrate B₆@C₆₀H₆₀ with the spin moment value of 2μ_B. As the C₆₀H₆₀ cage as a polymerization unit can conserve the spin moment of endohedral B₆, the clathrate B₆@C₆₀H₆₀ is a new all‐nonmetal magnetic superatom building block. Naturally, magnetic superatom structures of the B₆ and B₆@C₆₀H₆₀ may be metastable.     

Stabilities of Al<Subscript>n</Subscript>Cu (n = 1–19) Clusters and Magnetic Properties of Three Cu-Doped Al Clusters

By using the Amsterdam Density Functional program, we have studied the geometric features, stabilities and magnetic properties of Al_nCu (n = 1–19) clusters. The magnetic structures of Al₁₇Cu₂ and Al₁₉Cu clusters are found. Although the high spin ground state of Al₁₂Cu cluster is in accordance with the Hund’s rule under spherical Jellium model (SJM), it is difficult to explain why the Al₁₇Cu₂ and Al₁₉Cu clusters exhibit larger magnetic moments by the model. A superatom model under equivalent charge distribution is proposed. The magnetic properties of the Cu-doped Al clusters can be explained well by combination of the superatom model with SJM.     

Theoretical study of isomerism in nitrogen- and phosphorus-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript> (M = N,P)

More than 20 М₆Al₃₈ isomers and several М₁₂Al₃₂ isomers for nitrogen- and phosphorus-substituted clusters with six and twelve dopant atoms M = N and P substituted for Al atoms in different positions at the surface of the aluminum cage and inside it have been studied by the density functional theory method. In the preferred N₆Al₃₈ isomer, all N atoms are substituted for Al atoms initially located in one outer layer of the cluster. In the course of geometry optimization, the nitrogen atoms are incorporated into positions in the neighboring intermediate layer, thus converting it into a 12-atom face consisting of three vertex-sharing adjacent six-membered rings with short N–Al bonds. For Р₆Al₃₈, a distribution of the dopant either in both surface layers or in the intermediate space between the surface layers and the inner core of the cluster is preferred. Optimization of alternative structures of the N₁₂Al₃₂ cluster with N atoms substituted for Al atoms in both outer layers is evidence in favor of the isomer in which the dopants are dispersed as separated monatomic anions N–. Together with their bridging Al atoms, these anions form the inner [N₁₂Al₁₄] cage with an unusual dumbbell-like structure in which the upper and lower halves are linked through N–Al bonds with the equatorial aluminum atoms. In the next low-lying isomer being ~23 kcal/mol higher on the energy scale, there is observed the “microclustering” of the dopant to form three covalently bonded diatomic dianions N₂^2-; the latter, together with the bridging Al atoms are combined into a [N₆Al₆] “subcluster” inside the severely distorted outer cage. In P₁₂Al₃₂, the aluminum cage is subjected only to moderate distortions: the phosphorus atoms remain in the outer layers and form two three-membered rings [Р₃]. The estimated energies of the model substitution reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ (1) and Al₄₄ + 2M₆ → M₁₂Al₃₈ + 2A_l6 (2) demonstrate that all these reactions are exothermic; however, for the nitrogen-containing clusters, the decrease in energy with increasing number of substitutions increases from 66 (1) to 113 (2) kcal/mol, while in the case of phosphorus, it decreases from 45 (1) to 4 (2) kcal/mol. The results obtained for N₆Al₃₈, N₁₂Al₃₂, Р₆Al₃₈, and Р₁₂Al₃₂ are compared with the previous calculations for the C₆Al₃₈, C₁₂Al₃₂, Si₆Al₃₈, and Si₁₂Al₃₂ clusters.     

First‐principles study of molecular hydrogen dissociation on doped Al12X (X = B,Al, C,Si, P,Mg, and Ca) clusters

Inspired by the concept of superatom via substitutionally doping an Al₁₃ magic cluster, we investigated the H₂ molecule dissociation on the doped icosahedral Al₁₂X (X = B, Al, C, Si, P, Mg, and Ca) clusters by means of density functional theory. The computed reaction energies and activation barriers show that the concept of superatom is still valid for the catalysis behavior of doped metal clusters. The hydrogen dissociation behavior on metal clusters characterized by the activation barrier and reaction energy can be tuned by controllable doping. Thus, doped Al₁₂X clusters might serve as highly efficient and low‐cost catalysts for hydrogen dissociation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Theoretical study of isomerism of carbonand silicon-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript>

More than twenty M₆Al₃₈ isomers and several M₁₂Al₃₂ isomers of carbon- and silicon-substituted aluminum clusters with six and twelve dopant atoms of general formula M_nA_l44–n(M = C and Si, n = 6 and 12) have been studied by the density functional theory method. Calculations predict that, in the lowest-lying M₆Al₃₈, isomer, all substitutions of C atoms for Al are localized in one outer surface layer of the aluminum cage. In the course of optimization, the C atoms with a negative charge of about 1e are incorporated into positions of the intermediate layer to transform it into a 12-atom face composed of three adjacent vertex-sharing six-membered rings with short C–Al bonds. In the favorable isomer of M₆Al₃₈, the dopants are scattered as individual Si atoms located in both outer layers or in the subsurface space between the outer layers and the inner core of the cluster. Optimization of low-lying isomers with twelve starting substitutions of C and Si for Al in both outer layers has localized two preferable C₁₂Al₃₂ isomers. One of them contains three covalently bonded diatomic C₂ anions, which are combined through bridging aluminum atoms in the three-dimensional [C₆Al₇] cluster inside the severely distorted outer cage. In the second, most favorable, isomer, the dopants are distributed as isolated C anions; together with the bridging Al atoms, they form the [M₁₂Al₃₂] inner cage with an unusual dumbbell-like structure. For M₁₂Al₃₂, the aluminum cage undergoes moderate distortions. The silicon atoms remain in the outer layers and form five-membered ring subclusters [Si₅] and [Si₂Al₃] bound to the neighboring intermediate layers through elongated and weakened Si–Al bonds. Evaluation of the energies of the model exchange reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ and Al₄₄ + 2M₆ → M₁₂Al₃₂ + 2A_l6 shows that for M= C both reaction are exothermic, whereas for M = Si the former reaction is nearly isothermal and the second reaction is endothermic and requires significant energy inputs. The differences between the equilibrium structures and the relative positions on the energy scale of the isomers of the C₆Al₃₈–Si₆Al₃₈ and C₁₂Al₃₈–Si₁₂Al₃₈ clusters are examined.     

Ligand-field regulated superalkali behavior of the aluminum-based clusters with distinct shell occupancy

Protecting clusters from coalescing by ligands has been universally adopted in the chemical synthesis of atomically precise clusters. Apart from the stabilization role, the effect of ligands on the electronic properties of cluster cores in constructing superatoms, however, has not been well understood. In this letter, a comprehensive theoretical study about the effect of an organic ligand, methylated N-heterocyclic carbene (C₅N₂H₈), on the geometrical and electronic properties of the aluminum-based clusters XAl₁₂ (X = Al, C and P) featuring different valence electron shells was conducted by utilizing the density functional theory (DFT) calculations. It was observed that the ligand can dramatically alter the electronic properties of these aluminum-based clusters while maintaining their structural stability. More intriguingly, different from classical superatom design strategies, the proposed ligation strategy was evidenced to possess the capability of remarkably reducing the ionization potentials (IP) of these clusters forming the ligated superalkalis, which is regardless of their shell occupancy. The charge transfer complex formed during the ligation process, which regulates the electronic spectrum through the electrostatic Coulomb potential, was suggested to be responsible for such an IP drop. The ligation strategy highlighted here may provide promising opportunities in realizing the superatom synthesis in the liquid phase.     

Reactions with a Metalloid Tin Cluster {Sn10[Si(SiMe3)3]4}2−: Ligand Elimination versus Coordination Chemistry

Chemistry that uses metalloid tin clusters as a starting material is of fundamental interest towards understanding the reactivity of such compounds. Since we identified {Sn₁₀[Si(SiMe₃)₃]₄}^2? 7 as an ideal candidate for such reactions, we present a further step in the understanding of metalloid tin cluster chemistry. In contrast to germanium chemistry, ligand elimination seems to be a major reaction channel, which leads to the more open metalloid cluster {Sn₁₀[Si(SiMe₃)₃]₃}^? 9 , in which the Sn core is only shielded by three Si(SiMe₃)₃ ligands. Compound 9 is obtained through different routes and is crystallised together with two different countercations. Besides the structural characterisation of this novel metalloid tin cluster, the electronic structure is analysed by ¹¹⁹Sn Mössbauer spectroscopy. Additionally, possible reaction pathways are discussed. The presented first step into the chemistry of metalloid tin clusters thus indicates that, with respect to metalloid germanium clusters, more reaction channels are accessible, thereby leading to a more complex reaction system.     

Models of Molecular Structures of Al<Subscript>2</Subscript>Cr<Subscript>3</Subscript> and Al<Subscript>2</Subscript>Mo<Subscript>3</Subscript> Metal Clusters according to Density Functional Theory Calculations

The geometrical parameters of the molecular structures of aluminum–chromium and aluminum–molybdenum clusters Al₂Cr₃ and Al₂Mo₃ have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 programL package. It has been found that each of these metal clusters can exist in twenty structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

Cage Structure Formation of Singly Doped Aluminum Cluster Cations Al<Subscript><Emphasis Type="BoldItalic">n</Emphasis></Subscript><Emphasis Type="BoldItalic">TM</Emphasis><Superscript>+</Superscript> (<Emphasis Type="BoldItalic">TM</Emphasis> = Ti,V, Cr)

Structural information on free transition metal doped aluminum clusters, Al _n TM ⁺ (TM = Ti, V, Cr), was obtained by studying their ability for argon physisorption. Systematic size (n = 5 – 35) and temperature (T = 145 – 300 K) dependent investigations reveal that bare Al _n ⁺ clusters are inert toward argon, while Al _n TM ⁺ clusters attach one argon atom up to a critical cluster size. This size is interpreted as the geometrical transition from surface-located dopant atoms to endohedrally doped aluminum clusters with the transition metal atom residing in an aluminum cage. The critical size, n _crit , is found to be surprisingly large, namely n _crit = 16 and n _crit = 19 – 21 for TM = V, Cr, and TM = Ti, respectively. Experimental cluster–argon bond dissociation energies have been derived as function of cluster size from equilibrium mass spectra and are in the 0.1–0.3 eV range.     

Synthesis of Two‐Electron Bimetallic Cu–Ag and Cu–Au Clusters by using [Cu13(S2CNnBu2)6(C≡CPh)4]+ as a Template

Atomically precise Cu‐rich bimetallic superatom clusters have been synthesized by adopting a galvanic exchange strategy. [Cu@Cu₁₂(S₂CNⁿBu₂)₆(C≡CPh)₄][CuCl₂] ( 1 ) was used as a template to generate compositionally uniform clusters [M@Cu₁₂(S₂CNⁿBu₂)₆ (C≡CPh)₄][CuCl₂], where M=Ag ( 2 ), Au ( 3 ). Structures of 1 , 2 and 3 were determined by single crystal X‐ray diffraction and the results were supported by ESI‐MS. The anatomies of clusters 1 – 3 are very similar, with a centred cuboctahedral cationic core that is surrounded by six di‐butyldithiocarbamate (dtc) and four phenylacetylide ligands. The doped Ag and Au atoms were found to preferentially occupy the centre of the 13‐atom cuboctahedral core. Experimental and theoretical analyses of the synthesized clusters revealed that both Ag and Au doping result in significant changes in cluster stability, optical characteristics and enhancement in luminescence properties.     

Study on the Geometric and Electronic Structures of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Si<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> (n = 3, 4, 5; m = 1, 2, 3, 4) Clusters

Genetic algorithm combined with the semi-empirical Hamitonian AM1/PM3 is used to search the low energy isomers of Al _n Si _m (n = 3, 5, m ≤ 3 and n = 4, m ≤ 4) and the charged clusters with 20 and 28 valence electrons. The candidate structures were optimized by the density functional theory PBE0 and B3LYP models with the triply split basis sets including polarization functions. The electronic structures show that Al–Si binary clusters behave like metal clusters. The molecular orbitals accord with that predicted by the jellium model, and the electron localization function shows the valence electrons are delocalized over the entire clusters. The clusters having 20 and 28 valence electrons exhibit pronounced stabilities and large energy gaps. The 20 valence electrons of Al₄Si₂ and Al₃Si₃ ⁺, Al₅Si^? form closed shells 1S ²1P ⁶2S ²1D ¹⁰. Al₄Si₄ and Al₅Si₃ ^? have oblate structures and the P, D, F levels spilt considerably in these clusters. The electron density distributions suggest that doping silicon in the aluminum clusters enhances the stability considerably.     

Extraordinary superatom containing double shell nucleus: Li(HF)3Li connected mainly by intermolecular interactions

The structure and properties of the Li(HF)₃Li cluster with C_3h symmetry are investigated using ab initio calculations. This Li(HF)₃Li is a metal–nonmetal–metal sandwich‐like cluster connected mainly by the intermolecular interactions. In the special cluster, the (HF)₃ containing the triangular F ring with the negative charges is sandwiched between two Li atom. It is interesting that under the action of the triangular F ring with the negative charges, the valence electrons of two Li atoms are pushed out to form the distended excess electron cloud that surrounds the Li(HF)₃Li as a core. So the Li(HF)₃Li cluster shows not only the electride characteristic, but new superatom characteristics as well. Several characteristics of the special superatom are found. First, the superatom contains the double shell nucleus. The internal nucleus is the regular triangular ring made of three F atoms with the negative charge and the outer‐shell nucleus is made up of three H and two Li atoms with the positive charge. Second, the bonding force of this superatom framework is mainly the intermolecular interaction force, the lithium bond, which is different from that (covalent bond or ionic bond) of the general superatom. Third, the interaction between the outer‐shell nucleus and the excess electron cloud is mainly the anti‐excess‐electron hydrogen bond. Fourth, the special superatom exhibits the new aromaticity (NICS = ?8.37 ppm at the center of the regular triangular F ring), which is the aromaticity found in the cluster of the intermolecular interaction. This is the new knowledge of the aromaticity. Fifth, the large polarizability of the superatom is revealed. Further, the vertical ionization energy (VIE) of the superatom is low, 4.51 eV (<5.210 eV of the alkaline–earth metal Ba) so that it may be viewed as a superalkaline–earth metal atom. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

<Superscript>27</Superscript>Al NMR Study of the Metal Cluster Compound Al<Subscript>50</Subscript>C<Subscript>120</Subscript>H<Subscript>180</Subscript>

We present an ²⁷Al NMR study of the metal cluster compound Al₅₀Cp*₁₂ which is composed of (identical) Al₅₀ clusters, each surrounded by a Cp* ligand shell, and arranged in a crystalline 3D array (here Cp* = pentamethylcyclopentadienyl = C₅(CH₃)₅). The compound is found to be non-conducting, the nuclear spin-lattice relaxation in the temperature range 100–300 K being predominantly due to reorientational motions of the Cp* rings. These lead to a pronounced maximum in the relaxation rate at T ∼ 170 K, corresponding to an activation energy of about 850 K. Data for the related compound Al₄Cp*₄, containing very much smaller Al₄ clusters are also presented. A comparison is drawn with the quadrupolar relaxation recently observed for the non-conducting fraction of Ga₈₄ molecules in the metal cluster compound Ga₈₄[N(SiMe₃)₂]₂₀-Li₆Br₂(thf)₂₀·2toluene. It is our pleasure to dedicate this paper to our colleague professor Günter Schmid at the occasion of his 70th birthday.     

Theoretical study of aluminide clusters Al13X, Al13X−, and Al13X 2 − (X=H, Hal, OH, NH2, CH3, and C6H5)

The structural, electronic, energy, and vibrational characteristics of the Al₁₃X^? and Al₁₃X ₂ ^? clusters, with an aluminum-centered (Al_c) icosahedral cage Al₁₃ and with one or two outer-sphere ligands X=H, F, Cl, Br, OH, NH₂, CH₃, C₆H₅, have been calculated within the B3LYP approximation of the density functional theory using the 6-31G* and 6-311+G* basis sets. In all Al₁₃X^? radicals, the unpaired electron is localized at the cage atom Al* located opposite the Al-X bond. This Al* atom is the most favorable site for attaching the second X ligand of any nature (trans-addition rule). According to the previously suggested molecular model of the valence state of the [Al ₁₃ ^? ] “superatom,” the calculated energies D ₁(Al ₁₃ ^? -X) of addition of the first ligand to the Al ₁₃ ^? anion are about 1 eV lower than the corresponding energies of addition of the second ligand D ₂(XAl ₁₃ ^? -X). The structure of the Al₁₃ cage depends on the nature of the nature of the substituent X and can radically change in going from anions to their neutral congeners. In the lowest-lying Al₁₃X isomer with electronegative substituents X (Hal, OH, NH₂, CH₃, etc.), the aluminum cage has a marquee structure (1, symmetry C _s) with a hexagonal base and a pentagonal “roof.” For Al₁₃X analogues with electropositive ligands X (Al, Li, Na), a tridentate isomer (T, C _3v ) with the X substituent coordinated to a face of the Al₁₃ icosahedron is preferable. In the case of moderately electronegative X ligands (of the H type), the marquee (1) and icosahedral (T) isomers are close in energy. The stretching vibration frequencies of isomers 1 and T differ significantly in magnitude and intensity so that vibrational spectroscopy methods can be especially applicable to their experimental identification.     

Does the "superatom" exist in halogenated aluminum clusters?

We have shown that Aln clusters do not show any characteristics of a superatom in halogenated aluminum clusters. The enhanced stability of halogenated Al clusters can be explained by the magic nature of the clusters, not by superatom chemistry. The presence of even a few electronegative elements provides significant perturbation to the molecular orbitals of Al clusters and stabilizes the electropositive Al cluster cores, closely correlating with metal cluster-ligand chemistry. Our work provides significant chemical insights into the understanding of the structure and stability of halogenated aluminum clusters, and these new insights are applicable to other metal cluster-ligand systems.     

Models of molecular structures of aluminum–iron clusters AlFe<Subscript>3</Subscript>, Al<Subscript>2</Subscript>Fe<Subscript>3</Subscript>, and Al<Subscript>2</Subscript>Fe<Subscript>4</Subscript> according to quantum-chemical DFT calculations

The geometrical parameters of molecular structures of three types of aluminum–iron clusters containing in total four, five, and six Al and Fe atoms in structural units have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 program package. It has been found that the AlFe₃, Al₂Fe₃, and Al₂Fe₄ clusters can have four, eight, and nine structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

Magnesium(I) Reduction of Aluminum(III) Hydride Complexes: Generation of Mixed Valence Aluminum (AlI/Al0) Hydride Cluster Compounds, [Al6H8(NR3)2{Mg(β-diketiminate)}4]**

Reduction of a range of amido- and aryloxy-aluminum dihydride complexes, e.g. [AlH₂(NR₃){N(SiMe₃)₂}] (NR₃=NMe₃ or N-methylpiperidine (NMP)), with β-diketiminato dimagnesium(I) reagents, [{(^ArNacnac)Mg}₂] (^ArNacnac=[HC(MeCNAr)₂]⁻, Ar=mesityl (Mes) or 2,6-xylyl (Xyl)), have afforded deep red mixed valence aluminum hydride cluster compounds, [Al₆H₈(NR₃)₂{Mg(^ArNacnac)}₄], which have an average Al oxidation state of +0.66, the lowest for any well-defined aluminum hydride compound. In the solid-state, the clusters are shown to have distorted octahedral Al₆ cores, having zero-valent Al axial sites and mono-valent AlH₂⁻ equatorial units. Several novel by-products were isolated from the reactions that gave the clusters, including the Mg−Al bonded magnesio-aluminate complexes, [(^ArNacnac)(Me₃N)Mg−Al(μ-H)₃[{Mg(^ArNacnac)}₂(μ-H)]]. Computational analyses of one aluminum hydride cluster revealed its Al₆ core to be electronically delocalized, and to possess one unoccupied, and six occupied, skeletal molecular orbitals.     

Altering Charges on Heterobimetallic Transition-Metal Carbonyl Clusters

The homoleptic group 5 carbonylates [M(CO)₆]⁻ (M=Nb, Ta) serve as ligands in carbonyl-terminated heterobimetallic Ag_mM_n clusters containing 3 to 11 metal atoms. Based on our serendipitous [Ag₆{Nb(CO)₆}₄]²⁺ ( 4 a ²⁺) precedent, we established access to such Ag_mM_n clusters of the composition [Ag_m{M(CO)₆}_n]^x (M=Nb, Ta; m=1, 2, 6; n=2, 3, 4, 5; x=1−, 1+, 2+). Salts of those molecular cluster ions were synthesized by the reaction of [NEt₄][M(CO)₆] and Ag[Al(OR^F)₄] (R^F=C(CF₃)₃) in the correct stoichiometry in 1,2,3,4-tetrafluorobenzene at −35 °C. The solid-state structures were determined by single-crystal X-ray diffraction methods and, owing to the thermal instability of the clusters, a limited scope of spectroscopic methods. In addition, DFT-based AIM calculations were performed to provide an understanding of the bonding within these clusters. Apparently, the clusters 3 ⁺ (m=6, n=5) and 4 ²⁺ (m=6, n=4) are superatom complexes with trigonal-prismatic or octahedral Ag₆ superatom cores. The [M(CO)₆]⁻ ions then bind through three CO units as tridentate chelate ligands to the superatom core, giving overall structures related to tetrahedral AX₄ ( 4 ²⁺) or trigonal bipyramidal AX₅ molecules ( 3 ⁺).     

Calculated properties of neutral and charged Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> clusters by density functional theory

Density functional calculations are performed to study the structures and electronic properties of Al _n Co _m clusters with n = 1–7 and m = 1–2. Frequency analysis is also performed after structural optimization to make sure that the calculated ground states are real minima. The corresponding total and binding energies, adiabatic electron affinities and ionization potentials are presented and discussed to aid the identification of our calculations. The BSSE correction is also considered in our calculation. Among Al _n Co _m , Al _n Co _m ⁻, and Al _n Co _m ⁼ clusters (n = 1–7 and m = 1–2), Al₄Co⁻, Al₆Co⁻, Al₂Co₂, and Al₆Co₂ are predicted to be more stable. Our results are consistent with the available experimental data.