INTRODUCTION:
This type of cluster is of great importance thanks to the possibility of using them according to special requests.
Nano-sized bimetal-metal clusters have received great attention due to their promising applications in optics, magnetism and catalysis1,2, because they have physical and chemical properties that change in size as a result of surface change in size, nano clusters made of noble metals, particularly PtAun nano clusters, are attractive catalysts3,4. The physical and chemical properties of bimetal clusters depend not only on size and shape, but also on the atomic composition of the two metal elements5. The new structural and electronic variables that clusters have become enjoying due to their new size are therefore being studied.6-7.
Both gold and platinum particles have wide uses in organic chemistry, as they play an important role in protein delivery8, as well as an important role in cancer treatment9, and they also have a great ability to resist fungi10, They are optical sensors that contribute to photodynamic therapy and generally play a broad role in sensor synthesis and biomedicine11-13 Platinum particles are also included in the catalytic oxidation of blue carbon and in the general electrochemical behaviours of safe compounds and generally in many applications in other fields14-16
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 Pseudopotentials19, 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 LDA21. 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:
1. Structural properties of clusters Aun+1 and PtAun (n=1-9)
1.1. Structural characteristics:
The structural characteristics of the free gold metal clusters and platinum-doped gold depend on the structure of clusters, the locations of atoms and the average bond length between them, the DFT was chosen and using Gradient Density Approximation (GGA)and the Local Density Approximation (LDA) to reach the more stable And lower power consumption, in this work we have come up with the electronic structures of the clusters using the application of annealing simulation (SA), which is carried out through the following stages:
Phase 1: We placed a random group of atoms in the cluster simulation box.
Stage 2: The temperature of the system is raised to about 1000 K in a total of 1000 iterations.
Stage 3: The temperature of the system is stable at T = 1000 K for about 500 iterations.
Phase 4: We gradually reduce the temperature of the system to t = 0 K in 1000 iterations.
Figures 1 and 2 represent the most stable pure gold and platinum doped gold clusters, respectively.
Figure 1. The most stable Aun (n=2-10) clusters.
Figure 2. The most stable PtAun (n=1-9) clusters.
1.2. Average Bond length:
The average bond length of free gold clusters has been calculated in relation to:
Where: 
it is the length of the bond between two atoms of
gold, n is number of links in the cluster
And for gold infused with platinum corn in relation:
Where:
is the bond length between gold atoms and platinum
atom.
The length of the bond between gold and gold cluster atoms doped with platinum seed has been calculated with the XCRYSDEN program 22.
Figure3 represents the graph of the average bond length between atoms rather than the size of the cluster.
Figure 3. Average bond length for clusters Aun+1 and the PtAun cluster size allowance for (n=1-9).
According to the curve as shown in figure 3, it is clear that the average bond length increases as the size of the cluster increases whatever rounding used, as we note that clusters Au2, Au6 and Au10 characterized by an average bond length estimated at 2.62 Å, 2.77 Å and 2.86 Å by approximation (LDA) and, at 2.46 A, 2.63 Å, 2.70 Å by approximation (GGA) respectively, While the PtAu, PtAu5, and PtAu9 clusters have an average bond length approximation (LDA) of 2.40 Å, 2.64 Å, and 2.73 Å and in approximation (GGA) of 2.35 Å, 2.58 Å and 2.70 Å, comparing the above, we note a slight difference in the average values of bond length for the same cluster size from the previous clusters in the two different approximations (LDA) and (GGA).
We also recorded the average bond length for Au2, Au6 and Au8 clusters by approximation (LDA) with the values 2.62 Å, 2.77 Å, 2.85 Å, and by approximation (GGA) the values were recorded 2.46 Å, 2.63 Å, 2.71 Å, respectively, While PtAu, PtAu5, PtAu7 clusters, the average bond length values for them in (LDA) approximation are estimated at: 2.40 Å, 2.64 Å and 2.72 Å, and in (GGA) approximation they are estimated at: 2.35 Å, 2.58 Å, 2.65 Å, respectively.
For example, we notice that the average bond length of clusters Au2, Au6 and Au8 if we graft them with platinum atom decreases in the value of the average bond length, and this is through the use of both approaches (LDA) and (GGA).
We note that the largest value of the average bond length at cluster Au10 is estimated at 2.46 Å by approximation (LDA) and this value decreases to 2.73 Å by approximation (GGA).
For the grafted gold clusters, we recorded the largest value at PtAu9 with a length of 2.73 Å in (LDA) and as low as 2.70 Å in (GGA).
From the two readings we note:
The average bond length for Au10 in (GGA) is the same as for PtAu9 in (LDA) and is estimated at 2.73 Å.
As
a result of the analysis of the four curves, and in general, there has been an
increase in the average bond length of the Aun+1 and PtAun
clusters by an increase in cluster size from two to 10 atoms, with the
exception of the 
and PtAu7
cluster, where there has been a decrease in the mean bond length value, so the
Aun+1 metal cluster is the most stable than PtAun in both
LDA and GGA approximation.
1.3. Binding Energy:
Binding energy is defined as the amount of energy stored to create an interconnected cluster23, so if the structure has high binding energy (a significant correlation between its atoms), the structure is more stable.
In order to calculate the energy of linking the atoms of gold metal clusters with platinum seed gold, you should know the total energy of the cluster and the energy of the single atom, depending on the relationship:
Where:
Etot:
Total energy of the cluster, Eatis the energy of one atom, n is number of cluster atoms, 
is cluster
symbol.
Figure4 represents the value of the binding energy for the clusters Aun+1 and PtAun in terms of the size cluster.
Figure 4. Binding energy of Aun+1 and PtAun (n=1-9) clusters.
Through
Figure 4, which represents the binding energy of the cluster size, we observe
an ejection relationship between the binding energies of clusters and their
size, so that the larger the cluster size, the greater the bonding energy
between atoms, The highest values of the binding energy at the clusters 
, Au6 and Au9 respectively, is
approximately (LDA) 1.6, 2.7, 3.28 (eV/atom) and in GGA are 1.82, 2.88, 3.38
eV/atom, for clusters PtAu, PtAu5 and PtAu8 they have binding energy by approximation (LDA)
estimated at (1.82, 2.78, 3.28) (eV/atom) and rounded (GGA) are 1.83, 2.79,
3.29 (eV/atom), we note that these clusters have approximately the same binding
energy value as LDA and GGA.
In
GGA approximation, we recorded the same binding energy for Aun+1 and
PtAun clusters, with the exception of three clusters, they are 
, Au7 and Au8 different from
PtAu3, PtAu6 and PtAu7 which respectively have
the following energies: (eV/atom) 2.58, 3.18, 3.3,2.46, 3.08, 3.1. It is also
for rounding (LDA) with the exception of Au2 and Au5 clusters
where energy is different from PtAu and PtAu4 taking values: 1.6, 2.6,1.82,2.7 (eV/atom)
respectively.
In
general, we note that clusters Aun+1 and PtAun converge
in terms of binding energies except for some exceptional cases mentioned
earlier using GGA and LDA, which confirms the very high stability of clusters 
by bringing GGA closer to clusters (n=2-10). By
comparing our results for gold clusters, we find them approximately compatible
with the results 24.
2. Density of State:
Figures (5a) and (5b) represent the intensity of the density of states of clusters in terms energy, taken in order to determine the effect of introducing a platinum atom on the gold clusters and to extract the contribution made by this atom to the catalytic field.
