PHYSIOCHEMICAL PROPERTIES OF NICKEL-DOPED IRON CLUSTERS

https://doi-001.org/1025/17607776366203

Fayçal Baira  ¹, Yamina Benkrima  ², Sara Zidani ³ , Kaouther BAIRA ¹, Abdulhadi Mirdan Ghaleb ⁴

¹Department of Science and Technology, Université de Batna2.05078 Batna, Faculty of Technology, Algeria.

² Ecole normale supérieure de Ouargla, 30000 Ouargla, Algeria.

³Departement of food technology, Laboratory of food science (LSA), Institute of veterinary and agricultural sciences, University of Batna1 Hadj Lakhdar, Alleys May 19 Biskra Avenue, Batna, 05000, Algeria

⁴ Department of physics. College of Science, University of Kirkuk, Iraq

*Correspondence: E-mail: f.baira@univ-batna2.dz

Received : 11/06/2025 ; Accepted : 24/09/2025

Abstract:

In this work we present a theoretical study on the equilibrium geometry and the energetic, electronic and magnetic properties of NiFe_n (n = 1–9) using density functional theory (DFT) calculations, As well as the use of generalized gradient approximation, The larger clusters have higher binding energy, Where the results showed that the NiFe_n clusters generally indicate a greater degree of stability compared to the corresponding Fe_n clusters, We concluded from the calculated fragmentation energy, second-order energy difference, and homo-lumo energy that NiFe_2,3,4 clusters are more stable than other cluster sizes. The calculated magnetic properties for the lowest-energy NiFe_n ensembles show us a total magnetic moment between (3.35 – 4.00) μ_B, at the same time; it is greater than the values recorded in the case of pure iron clusters. We can conclude from the results of this work that it is of great use to experimental experts in order to design new nanocatalysis systems.

Keywords: Density functional theory DFT, Binding energies, homo-lumo energy, Fragmentation energy, Magnetic moment.

1. INTRODUCTION
2.  

During recent years, interest in the study of metallic clusters has increased intensely; this is due to the development of experimental techniques as well as theory that contribute to in-depth studies of this type of systems [1-4]. Nano materials have become the subject of several current research topics and experimental studies, as being performed to come up with promising results in many fields of physics, chemistry, and even biology [5-7]. These new materials are designed at the nanoscale. Nowadays, developing new materials with remarkable properties has become the main challenge for scientists over the past few years [8,9]. One of the most important motives that made researchers move in the direction of nanotechnology stems from its potential applications, thanks to which it covers a wide range of fields starting from electronics and optics to the field of biomedicine and even in anti-cancer therapies. These nanoparticles have different physicochemical properties from those of the same materials in their massive state [10-12].

Among the most intriguing elements that have brought researchers into cluster physics is iron in its pure or doped form [13]. As this work is considered the first time it has been put forward to investigate the physical and chemical properties of NiFe_n clusters. For example, the theatrical studies of Chrétien S et al. [14] Where he presented an in-depth study on neutral, cationic, and anionic iron groups up to the tetramer using corrected local and gradient functions, in which different occupation schemes for molecular orbitals with and without symmetry restrictions were presented, as well as a vibrational analysis on each optimized structure. Gutsev GL et al. [15] studied Electron Affinities, Ionization Energies, and Fragmentation Energies of Fe_n Clusters (n = 2–6) by density functional theory Study. Castro M et al [16] studied geometries, electronic and magnetic structures of Fe_n (n = 2–5) Where he highlighted that magnetism is distributed unevenly between atoms,  Leopold DG et al. [17]  He gave an interpretation of the optical electron spectrum of the cluster simply, and then the researcher explained the coherence of Fe₂ and . Luis ÁngelZárate-Hernández et al.  [18] Studied the simultaneous global geometry enhancement and total rotation of small Fen iron clusters (3 n ≤ 40) were evaluated using a DFT-based computed force-force (SA) annealing simulation on the tensile-binding theory (DFTB) level. In order to improve the overall spin, other properties such as binding energies and second energy differences were also calculated in order to compare with previously reported theoretical and experimental values.

In this paper, we focus on studying systematically the effect of nickel atom on iron clusters using NiFe_n (n = 1–9) by means of DFT-based computations, our aim is to highlight the effect of size, shape, and composition on the physicochemical properties of these clusters. Through the obtained results, we can predict the design of new nanocatalysis systems; we arranged this research paper as follows: in the second section, we present our calculation method, the various characteristics of nickel-doped iron clusters and pure iron clusters are offered in the third section together with discussions. Finally, we provide a comprehensive conclusion of the work in the fourth section.

•  
• COMPUTATIONAL DETAILS

We performed our calculations for the ground state structures within the framework of the polarized spin density functional theory [19]. The Generalized Gradient Approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) [20], functional has been used for the exchange correlation energy as implemented in the SIESTA code [21]. This program is used for all types of Troullier-Martins non-local pseudo-standards preservation method [22]. In order to improve the obtained geometries without any symmetry constraints, we resort to the self-consistent field (SCF) solution of the Kohn-Sham equations with a approximation of 10^-4a.u. on electron density and energy. We also used the cubic supercell of 20 Å space in order to avoid the interaction between neighboring groups and the conjugate gradient (CG) algorithm. Using the Γ point approximation, the k grid integration was carried out. Geometrical optimizations were considered as converged when the residual forces were smaller than 10^-2eV/Å. We employed the double zeta polarize ξ(DZP) basis with polarization function for nickel and iron atoms. First, we relax a large number of possible elementary structures of pure iron clusters with a size of n = 2-10 atoms, and then choose the most stable clusters for each size. Then we searched for the most stable clusters of structure in NiFe_n by searching the different possible isomers. The most stable putative structures of NiFe_n were obtained by in situ relaxation after replacing one iron atom by a nickel atom in several isomers of the original pure iron clusters.

• RESULTS AND DISCUSSION
• 3.1. Structural Properties
•  

We have searched for a large number of isomers and specified the ground-state structure of all NiFe_n (n =1–9) clusters using the computation scheme mentioned above. The most favourable structures obtained with lower energy are shown in Fig. 1. In general, a nickel atom is always located on the surface, the calculated bond length of NiFe dimer is 2.16 Å and its binding energy per atom of 2.26 eV larger than the Fe₂ dimer 1.98 Å bond lengths and 1.40 eV binding energy per atom.

     Fig. 1 The lowest energy structures of Fe_n (n = 2–10) and NiFe_n (n = 1–9) clusters, the red color indicates the iron atom, blue color indicates nickel atom.

• 3.2. Relative Stability

We report the calculated binding energies of NiFe_n (n = 1–9) clusters are plotted for the lowest-energy of each cluster in Fig. 2. Generally, we observe a binding energy increases with increasing the cluster size. This approach means that the blocks can obtain energy continuously during the growth process. We see that the binding energies of pure iron clusters are smaller than those of Ni-doped nickel clusters; this means that doping of a Ni atom always enhances the stability of iron clusters. This means that the Ni atom presents a strong covalent character and a greater ability to form chemical bonds. For NiFe_n clusters with n > 8, a land sliding value of 3.16 eV for binding energy is detected at n=9 .

Fig 2. Binding energy for the more stable structures of Fe_n+1 and NiFe_n  (n = 1–9) clusters.

The fragmentation energy among the indicators predicting the relative stability of clusters.in Fig 3, we present the growth of E_F as a function of the size cluster n. Through the general shape, a fluctuating behaviour of the amount of energy is observed at the clusters. The NiFe_n clusters show larger values compared to pure iron clusters, except for the cluster sizes (n = 7, 8 and 9), this result indicates that Ni atom vaccination reinforces the stability of pure Fe_n+1 clusters with large values obtained for NiFe, NiFe₂, NiFe₃, NiFe₄, NiFe₅ and NiFe₆ clusters. Consequently, these clusters are relatively more powerful in terms of thermodynamic stability.

Fig. 3. Fragmentation energy for the more stable structures of Fe_n+1 and NiFe_n  (n = 1–9) clusters.

In addition to both the fragmentation energy and the binding energy, another variable that can be studied is the quadratic energy difference, which is also another factor that can reflect the relative stability of the clusters. Through Fig. 4 we show the growth of Δ₂E in terms of changing cluster size. Positive values of Δ₂E are observed in (n = 6,8) for Fe_n+1 clusters, which indicates that these clusters may have special stabilities. As can be also seen, other noticeable positive values of Δ₂E are obtained for NiFe₄, NiFe₆ and NiFe₉.

Fig. 4. Second energy difference for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

3.3    Electronic Properties

When the value of the energy gap HOMO–LUMO (ΔE) is small, the chemical reactivity is high, whereas a considerable value is ascribed to an even higher chemical stability. Because of this, the HOMO-LUMO energy the vacuole is an important milestone and criterion for the chemical stability of small clusters. Values of change of ΔE in terms of cluster size variation n, for the most suitable structures are shown in Fig. 5.

       Fig. 5. HOMO-LUMO energy for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

As expected, an oscillating behavior is detected in the growth of the ΔE when the size increases. From the general shape of the curve, we can see that the energy ΔE of the NiFe_n clusters is smaller than that of the related pure iron clusters. Thus, this demonstrates that the Ni atom doping favors the emergence of more metallic behavior and increases the interaction of related clusters, except for sizes (n = 1 and 9), where larger values of 2.843 eV and 1.172 eV are obtained. From this point of view, it means that these clusters come with greater stability and very low reactivity compared to their neighbors, and they can be suitable for certain fields, such as using them mainly in the development of new materials.Another key factor is the vertical electronic affinity (VEA) and vertical ionization potential (VIP), which also determine the chemical stability behavior of the clusters. We report the results in relation to their developments in Figure 6 and 7 as a function of cluster size, along with those for the Fe_n+1clusters. In Fig. 6, we record an oscillatory behavior in the evolution of the VIP values of the Fe_n+1 and NiFe_n clusters, these last clusters are larger than those of Fe_n+1 clusters. What appears clearly is that the effect of Ni stimulants is very prominent, as an atom of Ni stimulates an increase in the value of VIP. We found the highest values for n= 2.

Fig. 6. Vertical ionization potential (VIP) for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

In Fig. 7, higher VEA values were recorded for Fe_n+1 clusters than those obtained for Ni-doped iron clusters. Except for the case of (n = 4), which indicates that an electron will be captured more easily. In general, and with the same observations recorded in the solution of the vertical ionization potential, we find that the values of VEA increase non-monotically with the size of the cluster.

             Fig. 7. Vertical electron affinity (VEA) for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

Pearson [23] proposed the principle of maximum hardness (PMH) in order to distinguish between the relative stability of the clusters. In general, if clusters have the highest value of chemical hardness, they are the least reactive and most stable. In Fig. 8 we highlight the change of η values for lower-energy structures as a function of η cluster size. The values in the Ni-doped iron clusters are greater than those in the Fe_n+1 clusters and this effect is clearly visible for 7> n, where the inclusion of a Ni atom leads to a significant elevation of the chemical hardness η.

Fig. 8. Chemical hardness η for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

3.4.  Magnetic Characteristics

       The magnetic behavior is also an important signature of small clusters. In fact, we can find small clusters with specific magnetic moments that qualify them to be used in many important applications in nanotechnology. The magnetic moment results are shown in the figure 9. In general, we see that the total magnetic torque ranges between (3 – 3.38 ) μ_B  values for Fen clusters, while the values of the magnetic moment for NiFe_n clusters range  at (3.70 – 4 ) μ_B.  So the process of grafting iron clusters with a nickel atom seed has a significant impact on changing the values of the magnetic moment of the clusters Fen this makes the NiFe_n clusters a strong candidate for magnetic uses.

Fig. 9. Magnetic moment for the more stable structures of Fe_n+1 and NiFe_n (n = 1–9) clusters.

• CONCLUSIONS

The equilibrium geometries, energetic, electronic and magnetic characteristics of NiFe_n (n = 1–9) clusters have been performed by using DFT calculations, with the use of generalized gradient approximation. The geometric structures of the clusters are in good agreement with previous computational studies; the reported binding energy for the dimer is closest to the experimental and theoretical value available. Furthermore, we find that the decay behavior of the binding energy curve indicates that the obtained cluster structures are the ground states. Larger Ni doped-Fe_n+1 clusters revealed higher binding energy, suggesting their greater stability compared to the corresponding pure iron clusters.The calculated fragmentation energy, second-order energy difference, and HOMO-LUMO energy gap revealed that the NiFe_2,3,4clusters are more stable than other cluster sizes. Compared to experimental and theoretical data, all of our VIP and VEA results are sometimes underestimated and sometimes overstated. The NiFe_2,3 cluster corresponds to the most stable structure in the chemical hardness analysis. The calculated magnetic properties of The lowest energy Fe_n+1 clusters exhibited a total magnetic torque of (3.00 – 3.384) μ_B, except for the Fe₁₀ cluster, which takes the value 3.385 μ_B, while the process of inoculating with a nickel atom seed added greater values to the magnetic moment of the Fe_n+1 clusters to the best, and that’s how the clusters NiFe_n became more magnetically moment, yet been calculated with siesta code Therefore, the results obtained from this fundamental work will be useful to guide future experiments, particularly in the fabrication of new nanocatalysts.

ORCID Ids

BENKRIMA Yamina   https://orcid.org/0000-0001-8005-4065;

BAIRA Faycal           https://orcid.org/0009-0008-0869-8614

Sara ZIDANI              https://orcid.org/0009-0004-3604-2437

BAIRA KAOUTHER   https://orcid.org/0000-0001-5530-1570

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