First-principles Investigation of the Structural, Magnetic, and Optical Pure and Gold-Doped Platinum Clusters

https://doi-001.org/1025/17630191906048

Hazem Bouraoui 1, 2, Yamina Benkrima 3*, Mohammed Seyf Eddine Bougoffa4, Sebti Khodja5, Mohamed Atoui 5

1Faculty of Hydrocarbons, Renewable Energies, Earth and Universe Sciences, Kasdi Merbah – Ouargla University, Ouargla 30000, Algeria

2Crystallography Laboratory, Department of Physics, Frères Mentouri – Constantine 1 University, 25000 Constantine, Algeria

3 Ecole normale supérieure de Ouargla, 30000 Ouargla, Algeria

4 laboratory of Materials Technology, Department of Materials Science, University of Science

and Technology Houari Boumediene, Bp 32 El Alia, Bab Ezzouar, 16111, Algeria

5Radiation, Plasma, and Surface Physics Laboratory, Kasdi Merbah – Ouargla University, Ouargla 30000, Algeria

*Corresponding author: b-amina1@hotmail.fr

Received : 08/07/2025  ; Accepted : 02/11/2025

Abstract

In this study, we conduct a systematic computational investigation using density functional theory (DFT) to explore the effects of introducing a platinum (Pt) atom into gold clusters (Aun). The objective is to determine how Pt doping influences the structural, magnetic, and optical properties of PtAun clusters (n = 1–9). For each cluster size, the isomer with the lowest total energy is identified and selected as the most stable configuration.

The optimized low-energy structures indicate that the clusters adopt three-dimensional geometries starting from n = 6. While doping gold clusters with a Pt atom does not enhance their overall stability, it significantly alters their magnetic and optical characteristics. All computed properties including magnetic moment, absorption, reflectivity, optical conductivity, refractive index, and damping coefficient were analyzed and compared with previous related studies, showing notable trends with cluster size. The results obtained using the generalized gradient approximation (GGA) were also benchmarked against those from the local density approximation (LDA). Overall, the findings demonstrate that Pt doping induces substantial modifications in the physical properties of Aun clusters.

KEYWORDS: Density Function Theory (DFT), doping, Cluster, Structural Properties, Magnetic Properties, Optical Properties.

  1. INTRODUCTION

Over the past years, the physics and chemistry of nanocluster science has become very important to researchers. The researchers’ work was directed to research to find the unique properties of these clusters, whose unique structure between the molecule and the size (mass) was the main reason for the theoretical researcher to delve into the understanding of the transition from atoms to clusters, molecule and finally to solid state.

Where in recent years, a lot of attention has been paid to the structural and chemical properties of mixed bimetallic clusters, this type of cluster is very important in its uses thanks to the possibility of using it according to special requests.

Nano-sized bimetallic groups have received great attention, due to their wide applications in many fields, including optics, magnetism and catalysis [1,2], and because they have physical and chemical properties that change in size as a result of the surface change in size, The nanoclusters made of noble metals, especially the PtAun nanocluster, are attractive catalysts [3,4]. The physical and chemical properties of bimetallic clusters depend not only on the size and shape, but also on the atomic structure of the two metallic elements [5]. Therefore, the researchers were interested in conducting the current studies to find the new structural and electronic variables possessed by the groups due to their new size [6,7].

Both particles of noble metals such as gold and platinum have wide uses, whether in organic chemistry, where they play an important role in protein delivery [8], or their important role in cancer treatment [9], It also has a great ability to resist fungi [10], Because of their potential as optical sensors contributing to phototherapy, they generally play a broad role in sensor synthesis and biomedicine [11-13], Platinum particles are also included in the catalytic oxidation of blue carbon, as well as in the general electrochemical behaviors of amino compounds, and generally in many applications in various fields [14-16].

  • DETAIL OF CALCULATIONS

The electronic structure calculations of PtAun (n = 1–9) clusters were performed using the density functional theory (DFT) [17], as implemented in the SIESTA program [18]. This code uses norm-conserving Troullier-Martins nonlocal Pseudopotentials [19], and employs flexible basis sets of localized Gaussian-type atomic orbitals. The exchange correlation energy was evaluated using the generalized gradient approximation (GGA) parameterized by Perdew, Burke, and Ernserh of (PBE) [20], and local density approximation LDA [21]. The self-consistent field (SCF) calculations were carried out with convergence criterion of 1 × 10−4 a.u. for total energy; we used a double ζ (DZ) basis with polarization function for Pt and Au atoms. With energy shift parameter of 50 meV, the change density was calculated in regular real-space grid with cut-off energy of 170 Ry. The simulated clusters were placed in a big cubic supercell with a parameter of 30 Å, including enough vacuums between neighboring clusters and periodic boundary conditions were imposed. To sample the Brillouin zone, only a single k-point centred at Γ was used because of the extended size of the super cell. The conjugated gradient method within Hellmann-Feynman forces was used and all the forces after structural relaxation were less than 10−3 eV/Å.

We first searched for the lowest-energy structures of pure Aun clusters in the (2–10) atoms. Secondly, the most stable ground state structures obtained for Aun clusters were doped through substitution with one Pt atom. Then, the obtained Pt-Aun clusters were optimized until reaching their ground states. In order to get lowest-energy structures of the PtAun clusters, several initials isomeric structures, including some high and low symmetries, were optimized by placing one Pt atom in substitution in different possible sites of the pure corresponding Aun in order to get as close as possible to the low energy structure. Then, we cannot be sure that a more stable structure than those found in our calculations does not exist. We aim of our study is to highlight the variation of the properties of gold cage clusters due to the Pt doping atom. We hope that this work would be useful to understand the influence of the Pt atom on the properties of gold clusters and provide some guidelines for the probable future experimental studies. Our calculated results were found to be in line with the literature, confirming the reliability of our protocol to simulate small Au clusters.

  • RESULTS AND DISCUSSION
  • Structural properties of clusters Aun+1  and PtAun (n = 1-9)

The calculated structural properties of pure gold and platinum-doped gold clusters depend on the groups structure, in addition to the positions of the atoms and the average bond length between them, the density function theory (DFT) was chosen. Using generalized gradient approximation (GGA) and local density approximation (LDA) to reach the most stable structures with lower energy. In this work we have come up with the electronic structures of the most stable groups using the application of annealing simulation (SA), which has gone through the following stages:

  • The first stage: a random group of atoms is placed in the block simulation box.
  • Stage 2: We raise the temperature of the system until it is about 1,000 K in a total of 1,000 iterations.
  • Stage 3: System temperature is stable at T = 1000 K for about 500 iterations.
  • Stage 4: We gradually lower the temperature of the system until t = 0 K in 1,000 iterations.

Figures 1 and 2 represent the most stable pure gold and platinum-doped groups, respectively.

Figure 1. The most stable Aun (n=2-10) clusters.

Figure 2. The most stable PtAun (n=1-9) clusters.

  • Magnetic Properties

It is defined as the difference between the total sum of the up-spin electrons and the total downward spin charge. All the calculated magnetic moment results for pure gold Aun+1 and platinum doped gold PtAun clusters are shown in Figures (4a) and (4b), Where the two figures represent the magnetic moment of clusters Aun+1 and PtAun in terms of cluster size in both approximations used (GGA) and (LDA) respectively.

(A)

(B)

Figure 3. Magnetic moment of Aun+1 and PtAun clusters, (A) in approximation (GGA), (B)                      in approximation (LDA).

We note that Aun+1clusters have magnetic moment except for Au4, Au8 and Au10 clusters, while we find that doping gold with platinum PtAun clusters also have magnetic moment values except for (n= 2,3,4,6,8) clusters which are zero magnetic moment, Also the magnetic moment values recorded for all studied clusters range from (1-2) μβ ,our results are also fairly close to the results [22].

  • Optical propertiesAbsorbance

Absorption occurs when electromagnetic radiation falls on a material and the energy of the photons is converted into internal energy. The absorption coefficient α is defined as the percentage of decrease in the radiation energy per unit distance in the direction of propagation within the medium [22].

It is calculated by the relationship:

α=4πk/λ                                                                 (1)

Where λ is wave length (cm-1),

Figure 4 represents the absorbance in terms of energy changes for the Au2 and PtAu clusters.

Figure 4. Absorbance of Au2 and PtAu cluster.

Through the analysis of the trend, we record for Au2 cluster in the range of [0-0.9] eV that no light absorption occurs, which is there is a value for the upper and lower limits of the energy gap estimated at 0.9 eV, which means that no direct electronic transitions occur from the valence band to conduction band .

As for the fields [0.9 – 2.5] eV, [7.5 – 8.55] eV, [10.8 – 11.5] eV which correspond to [0-5000] cm-1, [0-12000] cm-1, [0-11000]cm-1 respectively, we recorded low absorptions. , Except for these areas, we recorded peaks with high absorption, where the highest peak was recorded is 90000 cm-1 at 7 eV energy.

For the PtAu cluster, we notice that when the cluster is exposed to minimum energy values, absorption occurs with a value estimated at 12000 cm-1 and then decreases to notice its increase and decrease at other times, To record its highest value at energy 5.5 eV with a value estimated at 78000 cm-1 followed by two peaks of lowest intensity corresponding to energies 8.5 eV, 11 eV with values estimated at 30000 cm-1 and 35000 cm-1 respectively, it is also seen that the two absorbance in figure 4 are identical based on the energy of 11.25 eV. Finally, we conclude that Au2 cluster is characterized by a high absorbance in the field [4.5-7. 5] eV.

  • Optical conductivity

It is an electrical phenomenon in which a material becomes more conductive of electricity as a result of absorbing electromagnetic radiation such as light, and thus the increase in electron gaps, it was reached by the relationship:

First-principles Investigation of the Structural, Magnetic, and Optical Pure and Gold-Doped Platinum Clusters                                                      (2)

Figure 5, represents the changes in the optical conductivity value of Au2 and PtAu clusters in terms of the energy applied to them.

Figure 6. The optical conductivity of Au2 and PtAu clusters.

Figure 6, shows that in the energy field [0-0.9] eV there is no optical conductivity for the pure gold Au2 cluster, while the opposite is recorded for PtAu with a small peak at 0.5 eV of 27,000 Ω/cm-1. As for the Au2 cluster, the photoconductivity experiences either increase or decrease, starting from 0.9 eV, where the optical conductivity registers its highest intensity with a peak estimated at 22500 Ω ⁄ cm-1 and this is at energy 6.5 eV, followed by two least intense peaks within this field estimated at 200 Ω/cm-1 and 9500 Ω/cm-1 respectively, While the PtAu cluster recorded the highest intensity of the optical conductivity value estimated at 20000 Ω/cm-1.

 Starting from energy 11.3 eV, it is observed that the optical conductivity curves of both clusters are similar.

  • Refraction index

The n0 refractive index is defined as changing the path of light rays from one transparent medium to another [24].

First-principles Investigation of the Structural, Magnetic, and Optical Pure and Gold-Doped Platinum Clusters                                            (3)

The following figure 7, represents the refractive index spectra of light in terms of photon energy for Au2 and PtAu clusters.

Figure 7. Refractive index of  Au2 and PtAu clusters.

From the figure, we notice that the Au2 cluster, as the energy of the photons falling on it increases, the refractive index remains almost constant at the value (1.0), except for some changes in the value at the energy 4.8 eV and 6.4 eV where a very slight increase in the value of the refractive index is seen, As for the PtAu cluster, at energy 0.1 eV, the index of refraction was at its highest value, estimated at about (1.8) to start decreasing to reach the value (0.89), and this is within the energy range [0-0.5] eV.

The value of the refractive index gradually increases by increasing the energy of the photons to reach a peak less intense than the previous one estimated at (1.1), and starting from 7 eV, fluctuations are seen in the refractive index around the value 1 for both clusters.

  • damping coefficient

The damping coefficient K is defined as the amount of energy of incident radiation photons absorbed by the electrons of the material [23] and is determined according to the relationship:

First-principles Investigation of the Structural, Magnetic, and Optical Pure and Gold-Doped Platinum Clusters                                                          (4)

Figure 8, was obtained, which represents the changes of the damping coefficient in terms of energy for Au2 and PtAu clusters.

Figure 8. damping coefficient of Au2 and PtAu clusters.

We note from the figure 8, that for PtAu cluster recorded in the range [0-0.9] eV the highest peak reached by the damping coefficient which is 0.43 corresponding to 0.4 eV, while in the range [0.9-10] eV Fluctuations are observed in the damping coefficient spectrum, except for its peak at 5.2 eV corresponding to 0.15. From the comparison of the curves in the figure, we notice that the damping coefficient is inversely proportional to the absorption spectra of PtAu clusters.

From figure 8, the Au2 cluster in the field [0-0.9] eV no spectrum of the damping coefficient was recorded because there is no absorption spectrum, but in the fields [0.9 – 2.2] eV, [4.2 -5.2] eV, [5.8 – 7.2] eV, [8.8 -9.8] eV Four peaks were recorded with values of 0.04, 0.1, 0.14, 0.05 corresponding to the energies 1.4 eV, -4.8 eV, -6.4 eV, 9.3 eV respectively. From it, we conclude that the spectra of the damping coefficient correspond to the spectra of the absorption.

Conclusion

In present work, the structural, magnetic and optic properties of Aun+1 and PtAu clusters with n=1-9 are investigated by density functional calculations with generalized gradient approximation (GGA) and local gradient approximation (LDA), Clusters with total number of atoms up to five were found to have planar structures, The results show that new structures are obtained for each cluster size comparatively for those reported in the literature. The results of the magnetic moment showed that gold clusters Aun+1 have this property more than PtAun (n=1-9) clusters, the calculated optical properties clearly show the field of use of these clusters

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