A joint investigation based on an unbiased CALYPSO structure searching method and density functional theory calculation is performed to obtain the most stable structures of the neutral and anionic AlnSb (n = 1–16) clusters. The relative stability analysis reveals that the Al3Sb, Al5Sb, Al5Sb− and Al14Sb− clusters are more stable than their neighbouring clusters. The studies of electronic properties, especially in the consistency of the simulated photoelectron spectra and the experimental results for small clusters, further confirm that the predicted most stable structures are the global minima. Compared with pure aluminium (Al) clusters, the effect of impurity Sb atom on structural evolution of the neutral and anionic AlnSb(n = 1–16) clusters may be neglected, revealing that the most stable structures can be obtained by replacing one Al atom with an Sb atom in the corresponding neutral and anionic Aln+1(n = 1–16) clusters except for 8, 11 and 12. Moreover, the discussion concerning the magnetic properties indicates that the 3p state of the Al atom in the neutral and anionic AlnSb(n = 1–16) clusters is the main contributor to the total magnetic moment.
Binary alloy clusters have attracted considerable attention because of its additional advantages compared with pure metal clusters, especially with regard to relative stability and geometric configuration , , , , , , , , , , . Several studies demonstrate that the embedded transitional metal atom obviously improves the stability of the Au12W, Au12Mo, Au12M−(M = Ta, V, Nb) clusters , , , . Cu54Al− and Ag54Al− clusters doped one Al atom present more stable core-shell structures with icosahedral symmetry . More surprisingly, the magnetic properties of Mn13− and Co13− clusters may be controlled by the outer gold coating . Besides, electrical conductivity was enhanced by doping one Al atom into Si-nanowire compared to pristine Si-nanowire . Moreover, metal-aluminium (Al) alloy clusters have attracted great interest due to its good catalytic activity by absorbing small molecules CO, H2, HI, I2 and CH3I , , , , , , , . For CO oxidation on Al12X (X = Ni, Pd, Pt, Ti and Zr) clusters, lower barrier energies are obtained, indicating that the CO could be efficiently oxidised at low temperature on Al12X (X = Ni, Pd, Pt, Ti and Zr) clusters . Detailed studies of CO oxidation catalysed by AlnPt (n = 1–11) clusters reveal that the alloyed AlnPt clusters are proposed as effective nanocatalysts at lower temperatures . Moreover, results of the H2 adsorption and dissociation on small-sized AlnCr (n = 1–13) clusters indicate that Al2Cr and Al7Cr clusters can serve as highly efficient and low-cost catalysts for hydrogen dissociation, with similar activities as Al7Pt and Al12Pt clusters , . However, the premise of this study is to obtain the corresponding ground state structures of clusters.
The Al-based metal clusters are of great interest due to their potential applications in catalytic chemistry and chemical engineering , , , , , , , . Correspondingly, the characteristics of geometric structure, photoelectron spectroscopy (PES) and electric and magnetic properties were widely investigated , , , , , , , . Especially, Al13− cluster presents an icosahedral structure by a cage of 12 Al atoms on the surface and one Al atom at its centre, which is an electronic closed-shell structure with magic numbers of 40 valence electrons well described by the spherical jellium models . Note that Al13 cluster is a quasi-icosahedral structure owing to a Jahn-Teller distortion . Therefore, many studies have focussed on getting stable icosahedral structure by doping another element at the centre of the icosahedral Al12 cage , , , , , . As the geometric structures and electronic properties change strongly with size and/or composition, a large number of studies on Al-based metal alloy have mainly concentrated on the size effect , , , . Structures, stability and electronic properties of magnesium (Mg) doped Al clusters, AlnMgm−(4 < n + m < 15; 0 < m < 3) and AlnMg(n = 3–20), were investigated by Luo et al.  and Xing et al. , further showing that the size effect on geometry cannot be ignored. Hua et al.  reported the geometric transition and electronic properties of titanium-doped Al clusters containing up to 24, finding that the Ti atom is endohedrally doped from n = 20 different from the case of n < 20. Zhang et al.  found that the most stable structures of Ni-Al clusters differ from those of the corresponding pure Al clusters with the same atoms except for three atoms. Other metals (such as Pt-group metal Ni, Pd, Pt) were also added as the dopants into the Al clusters , . However, to the best of our knowledge, the structural stabilities and electronic properties of Al-Sb alloys were investigated based on the small size up to 6 only . Reports involving AlnSb clusters for n > 7 are not available yet, and the reports also revealed that the Sb can modify the microstructure and tensile properties of A356Al-silicon alloy . Thus it is worth discussing further whether Sb can modify the microstructure and electronic properties of pure Al clusters.
In this paper, we search for a number of possible structural candidates for neutral and anionic AlnSb(n = 1–16) clusters by using the CALYPSO method in combination with density functional theory (DFT) theory. To obtain the most stable structures, the binding energy per atom Eb(n), the fragmentation energy ΔE(n), the second-order differences of the total energy Δ2E(n), the highest occupied molecular orbital-lowest occupied molecular orbital (HOMO-LUMO) energy gaps, the dissociation energy (DE) and the global chemical hardness are analysed. Furthermore, the size effect on the electronic and magnetic properties of the most stable neutral and anionic AlnSb clusters is discussed. Thus, the paper is organised as follows: a brief introduction of the computational method is given in Section 2. In Section 3, we will discuss the size effect on structural stabilities, electronic and magnetic properties of neutral and anionic AlnSb clusters and in Section 4, a conclusion of our work is given.
2 Computational Method
The DFT calculation and CALYPSO structure searching method were combined to obtain the most stable structures and low-lying isomers of the neutral and anionic AlnSb(n = 1–16) clusters , , , , . Many initial structures for the neutral and anionic AlnS band pure Aln+1(n = 1–16) clusters were predicted based on the CALYPSO method , , , . We search 20 generations to achieve many structurally different isomers for each cluster size. Around 20–30 structures as candidates for each size are collected with energy difference from the lowest energy isomers less than 0.3 eV. These candidates are further optimised by using the Gaussian 09 package  (Carnegie Mellon University and Gaussiian Inc., Pittsburgh, PA, USA). In all calculations based on the Gaussian 09 package, the exchange-correlation functional B3PW91 was employed , , , , , which was successfully employed to predict the most stable structures of other metal clusters , . Here, functionals PBE0 and mPW1PW91 were assessed for pure Al clusters, which will be employed to assess the performance of the functional B3PW91 . The LANL2DZ basis set for Sb atom and the 6–311+G∗ basis set for Al atom were used . Taking the spin polarisation effect into consideration, each initial configuration was optimised at the possible spin multiplicities (singlet, doublet, triplet, quadruplet, quintet and sextet). In order to ensure that the optimised structures were corresponding to a local minima, vibration frequency calculations were performed. In the present work, the convergence thresholds are set to 6.0 × 10−5 Å for the displacement, 1.5 × 10−5 Hartree/Bohr for the forces and 10−5 Hartree for the total energy. Furthermore, a chemical-bonding analysis was carried out by means of the adaptive natural density partitioning (AdNDP) method . The corresponding nucleus-independent chemical shift and multicentre bond order are analysed based on the Multiwfn 3.3.8 program package .
3 Results and Discussion
3.1 Geometrical Structures
The unbiased CALYPSO structure searching method was carried out to get the global minima structures of neutral and anionic AlnS band pure Aln+1(n = 1–16) clusters. Using the Gaussian 09 package , the lowest-energy structures of neutral and anionic AlnSb(n = 1–16) clusters, as well as neutral and anionic Aln+1(n = 1–16) are obtained and displayed in Figure 1. Their symmetry, electronic state, binding energy Eb and HOMO-LUMO energy gap Egap are listed in Tables 1 and S1 (Supplementary Material). The corresponding lower-lying isomers of neutral and anionic AlnSb(n = 1–16) clusters are displayed in Figures S1 and S2 (Supplementary Material). Moreover, the configures of the most stable structures with the same size based on PBE0, mPW1PW91 functionals are different from those based on functional B3PW91, which are summarised in Figure S3 (Supplementary Material).
Figure 1 shows that the most stable structures retain planar for the neutral AlnSb clusters for n ≤ 4, anionic AlnSb clusters for n ≤ 3, as well as neutral and anionic Aln+1 clusters for n ≤ 4. When Al atoms n in cluster is >5, the most stable structures of AlnSb clusters and pure Aln+1 clusters display a three-dimensional structure. Moreover, one can notice that the most stable structures of the neutral and anionic AlnSb clusters are almost the same except for 4, 7 and 11. For the neutral and anionic Aln+1 clusters, their most stable structures are also the same except for 11 and 12. It is worth noting that, whether AlnSb clusters or pure Aln+1 clusters, the structural change is very small when an electron is added, which indicates the most stable structures of the anionic AlnSb and Aln+1 clusters can be obtained by attaching an electron from the corresponding neutral cluster in its ground state. By comparing the most stable structures of the AlnSb clusters with those of the corresponding same size Aln+1 clusters, we also note that the most stable structures are almost the same for the neutral and anionic AlnSb, Aln+1 clusters except for 8, 10 and 11, which further indicates that the Sb dopant will not change the structures of pure Aln+1 clusters except for 8, 10 and 11. Thus we may obtain the most stable structures of the neutral and anionic binary alloy Al-Sb clusters by substituting an Sb atom for an Al atom in the corresponding neutral and anionic Aln+1 clusters except for a handful of clusters. In the range of 1 ≤ n ≤ 6, the most stable structures of neutral and anionic AlnSb clusters are consistent with the other theoretical prediction results. This good agreement further verifies that our calculated results are reliable. However, when cluster size n ≥ 7, we have not found the related reports about the neutral and charged AlnSb clusters. For n = 7, the most stable structures of the neutral and anionic Al7Sb are similar and can be obtained by replacing an Al atom with an Sb atom in Al8 cluster. Interestingly, in the range of 8 ≤ n ≤ 11, except for 9, the most stable structures of the neutral and anionic AlnSb clusters are different from that of the neutral and anionic Aln+1 clusters, respectively, which further indicates that the impure Sb changes the structural evolution of pure Aln+1 clusters. And the same size configures of the neutral and anionic pure Aln+1(n = 8, 10 and 11) are found in low-lying isomers of AlnSb(n = 8, 11 and 12) and AlnSb−(n = 8, 11 and 12) clusters (seen in Figs. S1 and S2). Moreover, the structural transition from bilayer-like structures to cage-like structures occurs at n = 11 for neutral clusters and n = 12 for anionic clusters. The most stable structures show that Sb atom is inclined to occupy a peripheral position of the Aln+1 cluster but not an endohedral position, which is similar to other Al-Mg, Al-Ti, Al-As alloy clusters and different compared to Al-Cu alloy cluster , , , . For 12 ≤ n ≤ 16, the most stable structures are the same for neutral or anionic clusters, indicating that the impurity Sb does not change the structural evolution of pure Aln+1 clusters.
3.2 Electronic Properties and Photoelectron Spectra
The ionisation potentials, electron affinities, and detachment energies are very important quantities that are usually regarded as a signal to characterise the metallic characteristics in metal clusters. The vertical ionisation potentials (VIP) and vertical electron affinities (VEA) are used to describe the related properties of the neutral cluster, which can be estimated as follows:
VIP = E (cation at optimised neutral geometry) – E (optimised neutral)
VEA = E (optimised neutral) – E (anion at optimised neutral geometry)
The vertical detachment energy (VDE) and adiabatic detachment energy (ADE) can be evaluated as follows:
ADE = E (optimised neutral) – E (optimised anion)
VDE = E (neutral at optimised anion geometry) – E (optimised anion)
Our calculated results are listed in Table 2. One can see that the calculated VEA, VIP values of the most stable structures for pure Aln+1 clusters, and ADE, VDE values of the most stable structures for pure Aln+1− clusters are in good agreement with some experiment results , , , further indicating the B3PW91 functional is suitable to study the pure Aln clusters or Al-based metal clusters. Moreover, to further ensure the most stable structures of anionic AlnSb(n = 1–16) clusters via experimental spectra, the photoelectron spectra of anionic AlnSb(n = 1–16) clusters are simulated by adding the occupied orbital energy relative to the VDE and fitting them with a Lorentz expansion scheme and broadening factor of 0.1 eV as plotted in Figure 2. This simulated method is applied successfully in other metal clusters , . In photoelectron spectra, each peak corresponds to a transition from the ground state of the AlnSb− clusters to the ground state or an excited state of the corresponding AlnSb clusters, and the location of the first peak is corresponding to the VDE. Moreover, the ADE for the neutralclusters was measured by the corresponding intersection between the baseline and the rising edge of the first peak. The first peak of AlSb− cluster is located about 2.03 eV, which is in good agreement with the position of the first peak of the experimental photoelectron spectrum 2.13 eV. For AlnSb−(n = 2–5) clusters, position of the first peak in our simulated spectra corresponding to 2.50, 2.67, 2.51 and 2.75 eV are also consistent with the experimental results 2.57, 2.27, 2.62 and 2.87 eV, respectively. Moreover, by comparing the simulated and experimental PES, one can see that the position of the intersection between the baseline and the rising edge of the first peak with the same size is almost identical for both the simulated and experimental PES. Furthermore, we also notice that the calculated values of ADE for anionic AlnSb(n = 1–5) clusters are 1.99, 2.31, 2.00, 2.16 and 2.32 eV which are in good agreement with the experimental results 1.96, 2.39, 1.85, 1.98 and 2.03 eV, respectively . Based on the good agreement, we simulate the photoelectron spectra of AlnSb−(n = 6–16) clusters, the first peak of AlnSb−(n = 6–16) clusters are located about 2.63, 2.84, 2.66, 2.42, 2.76, 3.18, 2.81, 2.96, 3.14, 2.50 and 2.83 eV, respectively. It needs to be verified by experimental or other theoretical workers. The estimated VIP, VEA for neutral AlnSb(n = 1–5) clusters agree well with other theoretical values . These agreements further confirm that the predicted ground state structures are reliable and real global minima. Thus, the predicted values of VEA, VIP and ADE for neutral and anionic AlnSb(n = 6–16) clusters are also calculated and listed in Table 2. In order to assess further the performance of B3PW91 functional, the electronic properties of the neutral and anionic AlnSb and Aln+1(n = 1–16) are investigated based on functionals PBE0 and mPW1PW91, the results are listed in Tables S2–S5 (Supplementary Material) compared with functional B3Pw91, indicating that B3PW91 functional is also suitable to study the pure Al or Al-metal alloy clusters due to their consistency by means of functionals PBE0, mPW1PW91 and B3PW91.
3.3 Stability Analysis
The relative stabilities of the investigated clusters are discussed based on the binding energy per atom Eb(n), fragmentation energy ΔE(n), second-order differences of the total energy Δ2E(n), HOMO-LUMO energy gaps, global chemical hardness and DE.
For the neutral and anionic pure Aln+1 clusters, the Eb(n), ΔE(n), and Δ2E(n) can be estimated as the following formulas:
For the neutral and anionic AlnSb clusters, the Eb (n), ΔE(n) and Δ2E(n) can be written as follows:
where E(Al), E(Alq), E(Alnq), E(Aln−1q), E(Aln+1q), E(Sbq), E(AlnSbq), E(Aln−1Sbq), and E(Aln+1Sbq) indicate the total energies of the ground state structures of Al, Alq, Alnq, Aln−1q, Aln+1q, Sbq, AlnSbq, Aln−1Sbq, and Aln+1Sbq clusters, respectively. The Eb(n), ΔE(n), Δ2E(n) values of the neutral and anionic pure Aln+1 clusters and AlnSb(n = 1–16) clusters are plotted against n in Figure 3. The plots indicate that the binding energy per atom increases rapidly with the increasing cluster size, revealing that the Aln+1 and AlnSb(n = 1–16) clusters can continuously gain energy during the cluster evolution process. Moreover, we know that the peaks appeared in Figure 3 represent relatively more stable clusters. Some peaks are found corresponding to Aln(n = 5, 7, 13, 16), Aln−(n = 7, 9, 13), AlnSb(n = 3, 5, 9, 15), AlnSb−(n = 2, 5, 8, 12, 14) clusters, respectively, signifying that these clusters are obviously more stable than their neighbouring clusters, respectively. Moreover, the binding energy per atom Eb (n) of neutral and anionic pure Aln+1 clusters and AlnSb(n = 1–16) clusters is studied by means of a functional mPW1PW91 and PBE0 which are summarised in Table S7 compared with those based on B3PW91 functional. The consistency of results based on three functionals further indicates that the B3PW91 functional is good for pure Al and Al-antimony alloy clusters.
The HOMO-LUMO energy gap is another sensitive quantity used to reveal the relative stability of the clusters. The energy gap values of the neutral and anionic pure Aln+1 clusters and AlnSb(n = 1–16) clusters are also plotted against n in Figure 3. Some peaks are observed which correspond to Aln(n = 5, 7, 12, 14), Aln−(n = 6, 13), AlnSb with odd n and AlnSb−(n = 5, 8, 14, 16) clusters, respectively. It is worth noting that Al3Sb and Al5Sb present large HOMO-LUMO energy gaps at 2.59 and 2.09 eV, respectively, which are only slightly smaller than that of Al13− (2.74 eV). Thus, it is possible that the Al3Sb and Al5Sb are relatively more stable structures as the cluster size is up to 16. Moreover, we also noted that the HOMO-LUMO energy gaps of neutral AlnSb clusters with even n are smaller than those of Aln+1, indicating that the impurity Sb atom can improve the chemical reactivity of neutral AlnSb clusters except AlnSb(n = 2, 8, 12) clusters. Similarly, the chemical reactivity of AlnSb− with odd n as well as Al10Sb− and Al12Sb− was enhanced by doping Sb atom except for AlnSb−(n = 3, 7, 11). Moreover, the chemical hardness can be estimated in terms of the finite difference approximation between VEA and VIP values [η = (VIP–VEA)/2] for the neutral clusters , . It is plotted against n in Figure 4. One can notice the odd-even oscillations pattern for neutral AlnSb clusters. Apparently, a similar pattern is also observed for Aln clusters in the range of 10 < n < 16, but not found for n < 10. It further verifies that AlnSb with odd n and Aln(n = 2, 3, 5, 6, 7, 8, 9, 12) are more stable than their neighbouring clusters.
The thermal stability of clusters can be examined by the DE, the minimum DE corresponds to the favourable dissociation channel (DC). For the neutral and anionic pure Aln+1(n = 1–16) clusters, the DC Aln+1 ⟶ Aln+1−m + Alm and Aln+1− ⟶ Al−n+1−m + Alm are taken into account. The corresponding DE can be estimated by employing the following formulas:
Similarly, the DC AlnSb ⟶ Aln−m + AlmSb for neutral AlnSb(n = 1–16) clusters, AunSb− ⟶ Aln−m + AlmSb− (I) and AlnSb− ⟶ Al−n−m + AumSb (II) for anionic AlnSb(n = 1–16) clusters are employed. The corresponding DE can be calculated as follows:
For the neutral AlnSb(n = 1–16) clusters:
For the anionic AlnSb(n = 1–16) clusters:
where E(Aln+1−mq), E(Alm), E(Aln+1q), E(Aln−m), E(Al−n−m), E(AlmSb), E(AlmSb−) and E(AlnSb−) represent the energy of the corresponding ground state clusters. The most possible DC, the corresponding DEs of the neutral and anionic pure Aln+1(n = 1–16) cluster and AlnSb clusters are summarised in Tables S7 and S8 (Supporting Material), and the DEs are plotted against n in Figure 5. Tables S7 and S8 indicate that whether neutral Aln+1, AlnSb clusters or anionic Aln+1 clusters, the DC always tends to dissociate a neutral Al atom. For AlnSb− clusters, most DCs also prefer to dissociate a neutral Al atom except for AlSb− and Al13Sb− clusters, the DC of AlSb− and Al13Sb− dissociate a neutral Sb atom. Moreover, Tables S7 and S8 and Figure 5 show that Aln(n = 7, 13), Al13−, AlnSb(n = 3, 5, 12, 14) and AlnSb−(n = 5, 11, 14) clusters possess the larger DE, implying that those clusters have higher stability than other clusters.
|Sb||Sb (M/μB)||Al (M/μB)||Total (μB)||Sb||Sb (M/μB)||Al (M/μB)||Total (μB)|
Comprehensively considering those sensitive indicators, the relatively more stable structures Al7Al13−, Al3Sb, Al5Sb Al5Sb− and Al14Sb− clusters are determined, respectively. We also find that the more stable clusters Al7Al13−, Al3Sb, Al5Sb, Al5Sb−, Al14Sb− have 21, 40, 14, 20, 21, 48 valence electrons, respectively. It seems that Al5Sb and Al13− possess higher stability due to the magic numbers of 20 and 40 valence electrons, respectively.
3.4 Magnetic Properties
A natural bond orbital analysis is performed based on the most stable structures of neutral and anionic AlnSb clusters (n = 1–16). The total magnetic moments, and the contributions of Sb, Al to the total magnetic moments of the neutral and anionic AlnSb clusters (n = 1–16) reinvestigated as shown in Figure 6 and Table 3. Based on the natural bond orbital analysis, one can see that the nature electrons mainly locate on 3s, 3p states for Al atom and 5s, 5p, 4s states for Sb atom, respectively. For neutral AlnSb clusters (n = 1–16), we can find that, spin orbitals α and β degenerate when n is an odd number except for AlSb (2.01 μB), the total magnetic moments are 0 μB. Spin orbitals α and β do not degenerate when n is an even number, the magnetic moments can be obtained from the difference in value of the nature electron configurations between α and β spin orbitals. The total magnetic moments are found to be in the range of 0–2.01 μB for AlnSb
(n = 1–16) clusters, and vary from 0 to 1.08 μB for AlnSb−(n = 1–16) clusters. We can also notice that the total magnetic moment of AlnSb(n = 1–16) is about 1 μB for even n, and 0 μB for odd n except for AlSb (2.01 μB). The total magnetic moment presents obviously an odd-even alternative behaviour for the neutral and anionic AlnSb clusters (n = 1–16). In addition, the magnetic moment of the cluster is dominated by the spin magnetc moment, but not by the orbital magnetic moment of an electron. For AlSb cluster, the large magnetic moment 2.01 μB can be attributed to its spin multiplicity triplet. In order to further analyse the contributions of Sb and Al to the total magnetic moment of the neutral and anionic AlnSb(n = 1–16) clusters, the magnetic moment of 5s, 5p spin orbitals of the Sb atom and 3s, 3p spin orbitals of the Al atom of the most stable structures for the neutral and anionic AlnSb(n = 1–16) clusters are investigated in Figure 6 and Table S9 (Supporting Material). Figure 6 and Table S9 also indicate that the total magnetic moment is mainly derived from the contribution of the 3p state of the Al atom for the neutral and anionic AlnSb(n = 1–16) clusters, while the contribution of 5s state of the Sb atom to the total magnetic moments may be virtually neglected. Moreover, the natural charge shows that the charge is negative for Sb in AlnSb(n = 1–10, 16) clusters, implying the charge transfers from Al to Sb, while from Sb to Al for AlnSb(n = 11–15) clusters. For anionic clusters, one negative charge is assigned to Sb and Al atoms except for Al2Sb−(−1.13e) cluster.
3.5 Chemical Bonding
Al5Sb and Al13− clusters present a large energy gap (2.09 and 2.74 eV) and high stability when compared with their neighbouring clusters. It may be ascribed to their magic numbers of 20 and 40 valence electrons corresponding to a closed electronic shell. These electron configurations are well described by the spherical jellium model. We investigated the one-electron energy levels and molecular orbitals (MOs) of the most stable structures of Al5Sb and Al13− clusters, as plotted in Figures 7 and S4 (Supporting Material). For Al5Sb cluster, the HOMO occupies a d-type atomic orbital. Lower occupied levels HOMO–1 to –5, except for HOMO–2, resemble d-type atomic orbitals. HOMO–2 level corresponds to s-type molecular orbital, and so does HOMO–9. HOMO–6 to –8 levels possess p-type character. Therefore, according to the assignment of the MO based on the spherical jellium model,the electronic structure of Al5Sb is best described as 1S21P61D62S21D4. For the closed shell clusters Al13−, the HOMO are fourfold degenerate and labelled as 1F orbitals. HOMO–1 is threefold degenerate (HOMO–11, HOMO–12 and HOMO–13) and labelled as 2P orbitals, where subscripts 1, 2 and 3 serve as a mark to distinguish the degenerate orbitals. 2S and 1S orbitals are occupied as HOMO–3 and HOMO–6 orbitals. Analogously, HOMO–2, HOMO–4 and HOMO–5 are labelled as 1F, 1D and 1P orbitals, which is threefold degenerate, fivefold degenerate and threefold degenerate, respectively. The HOMO degeneracy may be attributed to the high symmetry Ih of the Al13− cluster. To further understand the bonding nature, a chemical bonding analysis based on the AdNDP method is performed as shown in Figures 7 and S4. For the Al5Sb cluster, one lone pairs (LPs), one localised bonds and eight delocalised bonds are found, and the occupation numbers (ONs) vary from 1.87 to 2.00|e|. For one LP with an occupied number ON = 1.87|e|, the main contribution is derived from the Sb but not the Al atom. While the interaction of two peripheral Al atoms plays an important role for 2c-2e σ bond with ON = 1.94|e|. Delocalised bonds are consisted of three 3c-2e σ, two 4c-2e σ, two 5c-2e π and one 6c-2e σ bonds, and the ONs of bonds are very close to the ideal values (2.00|e|). For the Al13− cluster, 21 delocalised bonds with ONs ranging from 1.77 to 1.98 |e| are found. The delocalised bonds consist of 14 3c–2e σ,six 4c-2e σ and one 6c-2e σ bonds. The delocalised 3c-2e σ bonds with ON = 1.88|e| and 1.87|e| are derived from the peripheral Al3 units, and the 4c-2e σ bonds with ON = 1.77|e| are due to the bonding between the central Al and the peripheral Al3 units. In addition, the 6c-2e σ bonds with ON = 1.98|e| present a strong interaction among six peripheral Al atoms.
The effect of Sb atom impurity on structural evolution, electronic and magnetic properties of Al-Sb alloy clusters was investigated in terms of an unbiased CALYPSO structure searching method and DFT calculation. The relative stability was analysed by means of Eb, ΔE, Δ2E, HOMO-LUMO energy gaps, DE and global chemical hardness, indicating that Al3Sb, Al5Sb, Al5Sb− and Al14Sb− clusters are relatively more stable than the other clusters. The calculated results also indicate that the most stable structures of Al-antimony alloys can be obtained by replacing one Al atom with an Sb atom in the corresponding neutral and anionic Aln+1 clusters except for AlnSb(n = 8, 10, 11) clusters. The predicted VEA, VIP and VDE are in agreement with the experimental values available for small clusters n ≤ 5. The VIP values are larger than the VEA values for all clusters. The total magnetic moments of AlnSbq(q = 0, −1; n = 1–16) clusters show a well-pronounced odd-even behaviour with respect to the number of atoms. It is located on the Al atoms especially in the 3p state, while the contribution of the Sb atom on the total magnetic moments is almost neglected. Furthermore, the chemical bonding of Al5Sb with magic numbers 20 electrons was analysed in depth, and the orbitals can be described as 1S21P61D62S21D4.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11574220
Funding statement: This work was supported by the National Natural Science Foundation of China (No. 11574220).
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