Gold clusters have been intensively studied during the past two decades due to the potential value of their catalytic, electronic, and optical properties. Pure Au_n clusters in the small-to-medium size range have been intensively investigated experimentally and theoretically.^{[1– 19]} In addition, a considerable amount of research work has been carried out on bimetallic gold clusters to enhance the stabilities of gold clusters and extend the potential applications. Most of these works focused on the doping transition-metal (TM) atoms into gold clusters.^{[20– 29]} Some studies on gold clusters doped with non-transition elements have also been carried out.^{[30– 37]} The above work shows that gold clusters doped with a proper element have distinctive structures and interesting properties.

However, studies on both structures and properties of trimetallic nanoclusters are extremely challenging because of the drastically increased complexity due to the presence of a third-part atom. There are numerous changes of structures in FeAlAu_n clusters. To the best of our knowledge, no systematical theoretical study of MN-doped gold clusters FeAlAu_n (M = Fe, N = Al) has been reported. In our previous work, ^{[38– 41]} the geometries, electronic and magnetic properties of FeAu₆ and AlAu_n clusters were studied using the relativistic all-electron density functional theory. In this work, we extend our investigation on FeAlAu_n (n = 1– 6) clusters to explore their geometrical structures, electronic and magnetic properties. It is hoped that the present research will be conducible to experimental realizations and verifications on the ternary metal clusters.

Structure optimizations and property calculation in this work are performed using DFT implemented in the DMol³ package.^[42] Relativistic calculations are carried out via pseudopotentials with scalar relativity (VPSR) to valence orbitals relevant to atomic bonding properties. All-electron spin-unrestricted calculations with double numerical plus d-functions (DND) are employed. Generalized gradient approximation in the Perdue– Burke– Ernzerhof (PBE) functional form is chosen.^[43] Spin multiplicity ranging from 1 to 8 of this system is considered. The convergence threshold for the maximum energy change is set to be 2× 10^{− 5}  Hartree (1  Hartree = 27.2114  eV) in the geometry optimization. The convergence thresholds are set to be 0.004  Hartree/Å for the force, and 0.005  Å for the displacement. Harmonic vibrational frequency analysis is also carried out at the same level of theory to confirm that the energies of isomers are truely minimal values.

The quality of the current computational method (PBE/DND/VPSR) is tested by the calculations on Au₂, , AlAu, Au₇, and clusters. The results are given in Table  1. All the properties of these clusters computed in our work are in good agreement with available experimental data.^{[9– 19]} This indicates that our method is reliable and accurate enough to describe the structures and properties of FeAlAu_n clusters.

Table 1.

Table 1.

Table 1. Calculated ground-state parameters and properties of Au2, , AlAu, Au7, and clustersa. System Property This work Experimental[9– 19] Au2 d 2.51 2.47 ω e 173 191 Eb 1.15 1.15, 1.18 IP 9.44 9.50, 9.22 d 2.63 2.58 VDE 1.98 2.01 AlAu ω e 313 333 Eb 1.66 1.67 Au7 ω e1 153 165 ω e2 172 185 ω e3 185 203 VDE 3.39 3.46 ADE 3.35 3.4 ad: bond distance (in unit Å , 1  Å 0.1  nm); ω e: vibrational frequency (cm− 1); Eb: binding energy per atom (eV); VDE: vertical electron detachment energy (eV); ADE: adiabatic electron detachment energy (eV); IP: ionization potential (eV).

Table 1. Calculated ground-state parameters and properties of Au2, , AlAu, Au7, and clustersa.

To discover the stable structures of FeAlAu_n (n = 1– 6) clusters, we use the computational methods described in Section 2 and consider extensive two-dimensional (2D) and three-dimensional (3D) structures to optimize each FeAlAu_n cluster structure. The obtained lowest-energy structures and some low-lying isomers are shown in Fig.  1. The symmetries and the differences in total energy between the lowest-energy and the low-lying isomers are listed. The lowest-energy structures of the corresponding bare Au_{n+ 2} clusters are also given in Fig.  1 for comparison. The optimized geometries reveal that small pure gold clusters prefer 2D structures, and the ground-state structures of FeAlAu_n clusters are all 2D configurations, except for FeAlAu₄. A single Au atom edge-capped structure of the FeAlAu_{n− 1} cluster is a dominant growth pattern. Previous studies showed that unlike alkali metal clusters, pure Au_n clusters favor 2D structures due to the strong relativistic effect of Au, and adding one Au atom to the Au_{n− 1} cluster is its main structural evolution for its small size.^{[7, 44]} The tendency to retain the overall structural integrity of the gold clusters is the possible explanation of the growth pattern in FeAlAu_n.

Fig.  1.

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Fig.  1. Lowest-energy structures and low-lying isomers with the relative energies (in unit eV) of FeAlAun (n = 1– 6) clusters, optimized with PBE/DND/VPSR (DMol3). The ground-state geometries of the corresponding bare Aun + 2 clusters are also given on the left. See Table  2 for the corresponding energetic and structural information. Red, gray, and yellow circles represent aluminum, iron, and gold atoms, respectively.

Fig.  2.

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	Fig.  2. Average binding energies per atom (Eb) of the FeAlAun, AlAun + 1, FeAun + 1, and bare Aun+ 2 clusters (n = 1– 6) for the lowest-energy structures.

Table 2.

Table 2.

Table 2. Values of HOMO– LUMO energy gap Egap (eV), vertical ionization potential VIP (eV), vertical electron affinity VEA (eV), and atomic charges (in atomic unit a.u.) on Fe and Al atoms of FeAlAun (n = 1– 6) clusters, for the lowest-energy structures. Cluster Egap VIPs VEAs Charge (Fe) Charge (Al) FeAlAu1 0.91 7.83 0.80 0.12 0.20 FeAlAu2 0.76 6.63 0.18 0.24 0.34 FeAlAu3 0.72 6.56 1.48 0.25 0.54 FeAlAu4 0.59 6.65 1.46 0.36 0.42 FeAlAu5 0.75 7.07 2.00 0.38 0.56 FeAlAu6 0.64 7.49 1.53 0.52 0.59

Table 2. Values of HOMO– LUMO energy gap Egap (eV), vertical ionization potential VIP (eV), vertical electron affinity VEA (eV), and atomic charges (in atomic unit a.u.) on Fe and Al atoms of FeAlAun (n = 1– 6) clusters, for the lowest-energy structures.

The triangle structure (1a) with C_s symmetry is found to be the most stable structure for the FeAlAu cluster. The angular isomer (1b) with C_2v symmetry is 0.53  eV higher in energy than the lowest-energy structure. The most stable structure of the FeAlAu₂ cluster is a C_2v rhombic planar structure (2a), which relates to the lowest-energy structure of the Au₄ cluster. The 3D geometries are all higher in energy. Like the lowest-energy structure of a pure Au₅ cluster, the most stable structure of FeAlAu₃ is a planar trapezoid configuration (3a), which can be obtained by adding one Au atom to the structure (2a). Another isomer (3b) with an Fe atom sitting in the center is only 0.04  eV higher in energy than the structure (3a). A 3D trigonal bipyramid (3c) with C_3v symmetry is 0.34  eV higher in energy than the structure (3a). Unlike other mall size of FeAlAu_n (n = 1– 6) clusters, the ground-state structure (4a) of the FeAlAu₄ cluster is not a planar structure, but a 3D quadrilateral bipyramid structure with C_4v symmetry. The Fe and Al impurities occupy the two opposite apex positions. The first low-lying isomer (4b), which is a planar geometry with C_s symmetry by subsequent addition of one Au atom to isomer (3a), is only 0.06 eV higher than the most stable structure. The lowest-energy structure of the FeAlAu₅ cluster (5a) is a planar irregular hexagon with C₂v symmetry. The Al atom occupies the top position, and the Fe atom occupies the central position. Figure  1 shows that the 3d Fe atom in FeAlAu₅ and FeAlAu₆ is likely to be surrounded by the host gold atoms. The hexagon structure can be seen as a distorted isomer of the ground-state structure of FeAu₆ with an Fe atom sitting in the center of the Au₆ ring.^[40] To further analyze the stabilities of clusters, the average binding energies per atom (E_b) of the FeAlAu_n, AlAu_{n+ 1}, FeAu_{n+ 1}, and bare Au_{n+ 2} for the lowest-energy structures are calculated and depicted in Fig.  2 each as a function of the number of Au atoms. It can be seen from Fig.  2 that the values of E_b for the ground state of FeAlAu_n clusters are significantly higher than those of the corresponding pure Au_{n+ 2}, AlAu_{n+ 1}, and FeAu_{n+ 1} clusters, respectively. This indicates that doping with two different types of metal atoms (Al and Fe) can effectively enhance the stabilities of the Au_n clusters.

Fig.  3.

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	Fig.  3. Variations of HOMO– LUMO energy gap Egap (eV), vertical ionization potential VIP (eV), and vertical electron affinity VEA (eV) with the number of Au atoms, of the FeAlAun, AlAun+ 1, FeAun+ 1, and bare Aun+ 2 clusters (n = 1– 6) for the lowest-energy structures.

According to the frontier molecular orbital theory, to a certain extent, the energy gap between HOMO and LUMO determines the charge transfer in a cluster, which affects the chemical activity. The vertical ionization potential (VIP) and the vertical electron affinity (VEA) reflect the capacities of losing or gaining electrons, respectively. The calculated results of E_gap, VIP, VEA, and the atomic charge on Fe and Al atoms of the lowest-energy structures of FeAlAu_n (n = 1– 6) clusters are given in Table  2 and plotted in Fig.  3. These electronic properties of the lowest-energy structures of AlAu_{n+ 1}, FeAu_{n+ 1}, and pure Au_{n+ 2} clusters are also plotted in Fig.  3 for comparison. It can be seen from Fig.  3 that there are obvious odd– even oscillations in the spectra of the E_gap, VIP, and VEA in AlAu_{n+ 1}, FeAu_{n+ 1}, and pure Au_{n+ 2} clusters, while this phenomenon disappears in FeAlAu_n clusters. Both VIPs and VEAs of FeAlAu_n clusters are smaller than those of the AlAu_{n+ 1}, FeAu_{n+ 1}, and pure Au_{n+ 2} clusters. It reveals that the electronic structures of FeAlAu_n clusters are more unstable, and doping Fe and Al atoms into Au_n clusters can enhance the chemical activities of the gold clusters.

In what follows, we will discuss the magnetic properties of the FeAlAu_n clusters. The local magnetic moments of Fe, Al, and Au atoms, and total magnetic moments of FeAlAu_n clusters for the lowest-energy structure are listed in Table 3 and plotted in Fig.  4. The Mulliken population analysis in Table 3 shows that the total magnetic moment of the clusters is localized mainly in the Fe atom. A small quantity of magnetic moment is found in the Al atom and host Au atoms, which shows that the 3d Fe atom plays a decisive role in the magnetic moment of Au clusters. The total magnetic moment of bare Au_{n+ 2} clusters shows a pronounced odd– even alternation (0  μ _B and 1  μ _B, respectively) with the number of Au atoms. A single Fe atom has four unpaired electrons with an atomic configuration of 3d⁶4s², and the d electrons are localized. The electronic shell structure of a single Au atom is 5d¹⁰6s¹. When an Fe atom with the partially filled 3d orbital is doped into Au_n clusters, one unpaired s electron from the Au_n clusters will reduce an offset of 1  μ _B magnetic moment of the Fe atom. So the formed FeAlAu_n clusters generate a large magnetic moment (3  μ _B or 4  μ _B) with the even or odd number of Au atoms. This suggests that the FeAlAu_n clusters have potential applications in new nanomaterials with tunable magnetic properties by adding even or odd number of Au atoms.

Fig.  4.

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	Fig.  4. Local magnetic moments of Fe, Al, Au atoms, and total magnetic moments of FeAlAun, FeAln+ 1, and bare Aun+ 2 (n = 1– 6) clusters for the lowest-energy structures.

Table 3.

Table 3.

Table 3. Local magnetic moments of Fe, Al, and Au atoms, and the total magnetic moment of FeAlAun (n = 1– 6) clusters for the lowest-energy structures. Cluster Moment/μ B Fe Al Au Total FeAlAu1 3.756 0.046 0.29 4 FeAlAu2 3.162 0.153 0.01 3 FeAlAu3 3.312 0.312 0.377 4 FeAlAu4 3.272 0.081 0.191 3 FeAlAu5 3.37 0.204 0.426 4 FeAlAu6 3.223 0.003 0.225 3

Table 3. Local magnetic moments of Fe, Al, and Au atoms, and the total magnetic moment of FeAlAun (n = 1– 6) clusters for the lowest-energy structures.

In order to explain the phenomenon of the magnetic properties in FeAlAu_n, figure  5 shows an example of the schematic molecular orbitals (MOs) and MO energy level correlation diagram of the FeAlAu₄. The d orbit characteristic of an Fe atom is marked in the figure. Two d orbitals (d_xz and d_yz) of the Fe atom are degenerate and occupied both by α electrons (spin-up) and β electrons (spin-down), and other three orbitals d_z², d_xy, and d_{x² − y²}, are singly occupied by three α electrons with spin-up, respectively, resulting in 3  μ _B of the total magnetic moment in FeAlAu₄. In addition, we also give the partial densities of states (PDOSs) in Fig.  6. It can be found that the shapes of α and β PDOSs of s, p, and d orbitals for FeAlAu_n clusters are always different, which explains why these FeAlAu_n each have a large magnetic moment. Figure  6 also shows that the electronic states below the Fermi level are contributed mainly from the d state.

Fig.  5.

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	Fig.  5. Molecular orbitals (MOs) and their energy level correlation diagram of the FeAlAu4 for the lowest-energy structures. Continuous lines correspond to the filled levels and the dotted lines correspond to the unfilled states. The surface isovalue for molecular orbital plotting is 0.02  e/Å 3.

Fig.  6.

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	Fig.  6. PDOSs of s, p, and d orbitals for FeAlAun (n = 1– 6) clusters. Spin-up (positive) and spin-down (negative) densities are given in each case. The dashed lines indicate the location of the Fermi level.

A density functional theory is investigated to study the geometric structures, relative stabilities, electronic and magnetic properties of the ternary metal clusters FeAlAu_n (n = 1– 6). A number of new isomers are obtained and discussed. All the lowest-energy structures of FeAlAu_n clusters prefer planar structures, except for the FeAlAu₄ cluster. It is found that a single Au atom edge-capped structure of the FeAlAu_{n− 1} cluster is a dominant growth pattern. Doping with Al and Fe atoms can greatly enhance stabilities of geometric structures, but reduce stabilities of electronic structures in gold clusters. FeAlAu_n clusters have tunable magnetic properties of odd– even oscillations by adding an even or odd number of Au atoms. This suggests that the stable FeAlAu_n clusters may have the potential to be utilized in new nanomaterials as building blocks.