Theoretical Study of Isomers of Doped Clusters M<Subscript>2</Subscript>Al<Subscript>42</Subscript> with Light Element Dopants M inside and on the Surface of the Aluminum Cage

Structures, energies, and spectroscopic characteristics of the isomers of the family of doubly doped М₂Al₄₂ clusters with dopants M from the first two periods and H, Cu, and Zn atoms located in different positions at the surface and in the inner cavity of the aluminum cage have been calculated by the density functional theory method. The effect of the dopant nature on the relative energies of isomers and on the energies of their dissociation along the channels М₂Al₄₂ → 2М + Al₄₂ and М₂Al₄₂ + 2Al → 2М+ Al₄₄. The results are compared with the results of previous DFT calculations of endohedral (M@Al₁₂) and exohedral (Al@)MAl₁₁) isomers of the simpler doped clusters MAl₁₂ with the same dopants M. The influence of the aluminum cage size on the relative energy stability of the surface and and internal sopant positions is considered.     

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.     

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.     

Theoretical study of model elementary reactions of dissociative addition of light hydrocarbons to the Ti-doped aluminide cluster Al<Subscript>12</Subscript>Ti

The potential energy surfaces (PES), energies E, and activation barriers h of elementary reactions of dissociative addition of CH₄ and C₂H₆ molecules to the Al₁₂Ti cluster with a marquee structure in the singlet and triplet states were calculated within the B3LYP approximation of the density functional theory using the 6-31G* basis set. The first stage of the reaction Al₁₂Ti + CH₄ leads to the adsorption complex CH₄ · Al₁₂Ti with the R(TiC) distance of ～2.4 Å. The methane molecule is coordinated as a tridentate ligand the singlet state and as a bidentate ligand in the triplet state, although both coordination modes are close in energy. In the transition state, the CH₄ molecule is coordinated through its active C-H bond to an inclined Ti-Al edge of the cluster, and the C-H bond is significantly elongated and weakened. The activation barrier height h referenced to the CH₄ complex is ～9 and ～19 kcal/mol for the singlet and triplet, respectively, and that referenced to the primary products Al₁₂Ti(CH₃)(H) is ～21 kcal/mol. The barrier to migration of the CH₃ group around the metal cluster is estimated at ～10 kcal/mol. At the initial stage of the reaction Al₁₂Ti + C₂H₆, two types of C₂H₆ · Al₁₂Ti adsorption complexes are formed. In one of them, the ethane molecule is coordinated through a methyl group (as the methane molecule); and in the other type, the coordination is through the C-C bond. This reaction can proceed through two paths by means of insertion into C-H or C-C bonds to give Al₁₂Ti(C₂H₅)(H) or Al₁₂Ti(CH₃)₂, respectively. The second path is impeded by a high barrier (～30 kcal/mol) and is possible, if at all, only at high temperatures. Conversely, the insertion into a C-H bond in ethane is somewhat more favorable than in methane. Analogously, the PES of addition of the second methane molecule to Al₁₂Ti(CH₃)(H) was calculated. The second molecule is adsorbed and dissociates by the same mechanism as the first CH₄ molecule, but with somewhat lower barriers and energy effect of formation of Al₁₂Ti(CH₃)₂(H)₂. The addition of propane and longer hydrocarbons is briefly considered. The results are compared with the results of previous analogous calculations of the PES of related reactions of dissociative adsorption of dihydrogen on the Al₁₂Ti cluster, which are more exothermic, have lower barriers, and can occur under milder conditions.     

Theoretical study of isomerism of compounds of N2 and N2H2 molecules with aluminum clusters Al13 and Al12Ti

Segments of the potential energy surfaces corresponding to successive elementary stages of multistep fragmentation of nitrogen and diimine molecules upon their reaction with the aluminum cluster Al₁₃ and its doped analogue Al₁₂Ti have been calculated by the density functional theory method. The minimum energy pathways of these reactions have been calculated for the stages of physisorption, chemisorption, and N₂ and N₂H₂ fragmentation with different ways of insertion of fragments into the Al₁₃ and Al₁₂Ti cages. Relative energies, structural characteristics, and vibrational frequencies of coordinated and fragment isomers have been calculated, the barriers separating these isomers have been evaluated, and molecular diagrams of the reactions have been constructed. The effect of doping on the relative energies of intermediates and activation barriers has been considered. A conclusion has been drawn that doping with titanium should facilitate the reactions of molecular nitrogen with aluminum clusters. Unusual isomers with a five- and six-coordinate nitrogen atom N* have been localized. The results are compared with the data of analogous previous calculations of the PES of isomers corresponding to stepwise fragmentation of an acetylene molecule in related Al₁₃C₂H₂ and Al₁₂TiC₂H₂ derivatives.     

A parallel study of Ni@Si<Subscript>12</Subscript> and Cu@Si<Subscript>12</Subscript> nanoclusters

The Ni@Si₁₂ and Cu@Si₁₂ clusters are studied in parallel within the framework of the density functional theory using the hybrid functional of Becke-Lee, Parr and Yang (B3LYP), emphasizing the differences and similarities in structural and electronic properties. The dominant structures for both clusters are a distorted hexagonal structure of C_s symmetry and a distorted octahedral structure of D_2d. For Ni@Si₁₂ the two structures are practically isonergetic whereas for Cu@Si₁₂ the energy difference of the D_2d structure from the lowest C_s structure of hexagonal origin is about 0.7 eV, at the B3LYP/TZVP level of theory. Contrary to Cu@Si₁₂ for which the well known Frank–Kasper (FK) structure of C_5v symmetry is a real local minimum of the energy hyper-surface (although higher by more than 1.6 eV from the global minimum), for Ni@Si₁₂ the FK structure is dynamically unstable. The HOMO-LUMO gaps, the binding energies per atom and the embedding energies for Cu@Si₁₂ clusters are smaller by 0.5, 0.1 and 1.1 eV, respectively compared to the Ni@Si₁₂ clusters. This is attributed to different type of bonding in the two clusters.     

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.     

Theoretical study of elementary reactions of dissociative addition of an H<Subscript>2</Subscript> molecule to doped aluminide clusters MAl<Subscript>12</Subscript> (M = Cr,Mo, and W)

The potential energy surfaces of elementary reactions of dissociative addition of one and two H₂ molecules to Cr-, Mo-, or W-doped aluminide clusters MAl12 in the states of different multiplicity have been calculated by the density functional theory method. The results are compared with the previous calculations of analogous reactions involving the singlet and triplet TiAl₁₂ cluster. The effect of the dopant nature and electronic state multiplicity on the energies and activation barriers of hydrogenation reactions is considered.     

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.     

Theoretical study of the model reaction of oxidation of methane to methyl alcohol by Fe(P)O(NH<Subscript>2</Subscript>) and related oxoferryl porphyrin complexes (P = C<Subscript>20</Subscript>H<Subscript>12</Subscript>N<Subscript>4</Subscript>)

The potential energy surfaces (PESs) of the model reactions Fe(P)O(NX₂) + CH₄ → Fe(P)(NX₂) + CH₃OH (X = H, F, Li) in the isolated state with different multiplicity have been calculated by the density functional theory B3LYP method with the 6-31G and 6-31G* basis sets. The optimized geometric, energetic, and spectroscopic characteristics of the key structures corresponding to local minima and transition states on the PES are determined; the energies and potential barriers of the reactions have been estimated, and their behavior as a function of the gas-phase states multiplicity and the electronegativity of the substituent X in the axial amino group has been studied. For all reactions, the lowest barriers are observed for the closely spaced quartet and doublet terms. The barriers considerably increase when the H atoms in the amino group are replaced by more electronegative atoms (F) and slightly decrease when H is replaced by more electropositive atoms (Li). On the basis of calculations for some structures corresponding to the stationary points on the PES of an analogous reaction of methane oxidation with the binuclear μ-N complex Fe(P)Fe(P)O, it was assumed that the effect of the second porphyrin ring on the upper active site in the binuclear μ-N complex is not too different from the effect of the amino group in the mononuclear complex Fe(P)O(NH₂) and that the role of the second ring in the μ-N complex is mainly reduced to the steric protection of the nitrogen atom from the interaction with the oxidant.     

Theoretical modeling of elementary reactions of dissociative addition of an H2 molecule to aluminum clusters MAl12 doped with early 3d and 4d transition metal atoms

The potential energy surfaces (PES) of the elementary catalytic cycle of early stages of the H₂ + MAl₁₂ reaction of dissociative addition of an H₂ molecule to aluminum clusters MAl₁₂ doped with “light” 3d and 4d transition metal atoms (Sc, Y, Ti, Zr, V, Nb) in the states of different multiplicity have been calculated by the density functional theory method. The effect of the dopant nature and the electronic state multiplicity of the cluster on the energies and activation barriers of hydrogenation reactions of aluminum clusters is considered. The calculated PES corresponding to the early stages of the H₂ + TiAl₁₂ reaction does not reveal any specific features that could be evidence of the significant preference of the titanium dopant as compared with other transitions metals like Zr or W.     

A DFT study on electronic and optical properties of aspirin-functionalized B<Subscript>12</Subscript>N<Subscript>12</Subscript> fullerene-like nanocluster

In this work, the interaction of an aspirin (AS) molecule with the external surface of a boron nitride fullerene-like nanocage (B₁₂N₁₂) is studied by means of density functional theory (DFT) calculations. Equilibrium geometry, electronic properties, adsorption energy and thermodynamic stability are identified for all of the adsorbed configurations. Four stable configurations are obtained for the interaction of AS molecule with the B₁₂N₁₂ nanocage, with adsorption energies in the range of ?10.1 to ?37.7 kcal/mol (at the M06-2X/6-31 + G** level). Our results clearly indicate that Al-doping of the B₁₂N₁₂ tends to increase the adsorption energy and thermodynamic stability of AS molecule over this nanocage. We further study the adsorption of AS over the B₁₂N₁₂ and B₁₁N₁₂Al in the presence of a protic (water) or aprotic (benzene) solvent. It is found that the calculated binding distances and adsorption energies by the PCM and CPCM solvent models are very similar, especially for the B₁₂N₁₂ complexes. According to time-dependent DFT calculations, the Al-doping can shift estimated λ _max values toward longer wavelengths (redshift). Solvent effects also have an important influence on the calculated electronic absorption spectra of AS-B₁₂N₁₂ complexes.     

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.     

Ion state of atoms and the properties of perovskite-like compound CaCu<Subscript>3</Subscript>V<Subscript>4</Subscript>O<Subscript>12</Subscript>

The binding energies and valence state of atoms in the perovskite-like compound CaCu₃V₄O₁₂ have been determined using XPS spectroscopy. The stoichiometry of this phase is formulated as Ca²⁺Cu²⁺Cu ₂ ⁺ (V ₂ ⁵⁺ V ₂ ⁴⁺ O₁₂). Under an air atmosphere, the phase interacts with water vapor and oxygen. As a result, Ca(OH)₂ is formed on its surface, the Cu⁺ and V⁴⁺ ion concentrations decrease, and the Cu²⁺ and V⁵⁺ concentrations increase in association. Raman spectra show shortened cation-anion bond lengths and cation-anion-cation bond angles in CaCu₃V₄O₁₂ compared to perovskite CuVO₃; the two structures are alike. The electrical conductivity, magnetic susceptibility, thermal and sensor properties of CaCu₃V₄O₁₂ in aqueous salt solutions have been studied.     

Geometry and electronic structure of (SiO<Subscript>2</Subscript>)<Subscript>3</Subscript> clusters

Electronic structure of (SiO₂)₃ clusters was calculated by the density functional method. Charge states were determined using various functionals, bond lengths and total energies of clusters were estimated.     

<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.     

Kinetic model of coherent synchronized ethylene monooxidation by hydrogen peroxide on a biomimetic catalyst,per-FTPhPFe<Superscript>3+</Superscript>OH/Al<Subscript>2</Subscript>O<Subscript>3</Subscript>

A kinetic model that fits the experimental data is studied on the basis of the most probable mechanism of ethylene oxidation by hydrogen peroxide over a biomimetic catalyst, perfluorinated iron (III) tetraphenylporphyrin, deposited on aluminum oxide (per-FTPhPFe³⁺OH/Al₂O₃). Effective rate constants for the catalase and oxygenase reactions and their effective activation energies are found.     

Density Functional Study of Catalytic Activity of Cu<Subscript>12</Subscript>TM for Water Gas Shift Reaction

Based on density functional theory calculations, we have systematically studied the WGS reaction on various nanosized Cu₁₂TM of Co, Ni, Cu (from the 3d row), Rh, Pd, Ag (from the 4d row), Ir, Pt, Au (from the 5d row). The reaction mechanism proposed by Langmuir–Hinshelwood has been followed, which corresponds to \({\text{CO* + OH* }} \to {\text{COOH*}} \to {\text{CO}}_{2} {\text{ + H*}}\). The comparison of the Gibbs free energy profiles of carboxyl mechanism on different Cu₁₂TM systems concludes that WGS reaction is determined by the steps of H₂ forming and OH* reacting with CO* to form COOH*. BEP relationship between activation barriers (Ea) and reaction energies (ΔH) on a series of Cu₁₂TM clusters is very good. What’s more, the activation barrier of rate-determining step of Cu₁₂Au is the smallest. TOF, with the aid of An Energetic Span Model (ESM), is used to estimate the efficiency of the different Cu₁₂TM clusters. The results show that the values of TOFs in doping Cu₁₂Rh, Cu₁₂Ir and Cu₁₂Pt are smaller than that in pure Cu. Moreover, the values of TOFs in doping Cu₁₂Co, Cu₁₂Ni, Cu₁₂Pd, Cu₁₂Ag, and Cu₁₂Au are higher than that in Cu₁₃. The higher value of TOF, the more favorable catalysts they are. This results shoud be helpful in developing efficient catalysts for WGS reaction. Finally, d-band center is used to explain the binding energy of CO and H₂O. It shows that there is a good liner relationship between d-band center and binding energy of CO but not for H₂O.     

An accurate three-dimensional potential energy surface for the He-Na<Subscript>2</Subscript> complex

An accurate three-dimensional potential energy surface (PES) for the He-Na₂ van der Waals complex was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triple (CCSD(T)) level of theory. A mixed basis set, aug-cc-pVQZ for the He atom and cc-pCVQZ for the sodium atom, and an additional (3s3p2d1f) set of midbond functions were used. The computed interaction energies in 819 configurations were fitted to a 96-parameter analytic potential model by least squares fitting. The PES has two shallow wells corresponding to the T-shaped structure and the linear configuration, which are located at 12.5a ₀ and 14 a ₀ with depths of 1.769 and 1.684 cm⁻¹, respectively. The who potential energy surface exhibits weak anisotropy. Based on the fitted PES, state-to-state differential cross sections were calculated. Supported by the Natural Science Foundation of Anhui Educational Committee (Grant No. 2006kj072A) and the Natural Science Foundation of Anhui Province (Grant No. 070416236)     

Theoretical Study of the Structure and Stability of Stepwise Hydrogenated Aluminum Clusters Al<Subscript>44</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1−24)

The energies and structural and spectroscopic characteristics of a series of model stepwise hydrogenated aluminum clusters Al₄₄H _n (n = 1?24) obtained by successive introduction of hydrogen atoms into various surface positions of the Al₄₄ cluster have been calculated by the density functional theory method (B3LYP). According to these calculations, the [Al₃₉] surface layer of the cage retains a closed “nested doll” shape with a pentaatomic inner core [Al₅]. With increasing n, both the surface layer and the core tend to experience increasing asymmetric distortions. The surface is corrugated and undergoes significant axial and equatorial extensions and contractions, some of the Al?H two-center terminal bonds are transformed into threecenter hydrogen bridges, and some Al atoms are displaced from the surface layer to the outer sphere and are bound to the surface through hydrogen bridges. The inner core [Al₅] at n = 24 loses its bipyramidal shape and shifts to the surface layer so that one or two of its atoms are “built-in” into the concave regions of the surface layer. The calculated average energies of Al?H bonds are within the range ~55.5 ± 2.5 kcal/mol. The averaged energies of the Al₄₄H _n → Al₄₄H_n–2 + Н₂ dissociation reactions with elimination of a hydrogen molecule are on the order of a few kilocalories per mole and are evidence of small exothermicity (or isothermicity) of these reactions. For the Al₄₄H, Al₄₄H₂, and Al₄₄H₆ clusters as an example, the relative stabilities of isomers with terminal Al?H bonds in various nonequivalent positions of the [Al₃₉] surface layer are compared.