Formation of pyramidal structures through mixing gold and platinum atoms: the AuxPty2+ clusters with x + y = 10

The geometric and electronic structures of a small series of mixed gold and platinum AuxPty2+ clusters, with x + y = 10, were investigated using quantum chemical methods. A consistent tetrahedral pyramid structure emerges, displaying two patterns of structural growth by a notable critical point at y = 5. This affects the clusters' electron population, chemical bonding, and stability. For the Pt-doped Au clusters with y values from 2 to 5, the bonds enable Pt atoms to assemble into symmetric line, triangle, quadrangle, and tetragonal pyramidal Pty blocks, respectively. For the Au-doped Pt clusters, with larger values of y > 5, the structures are more relaxed and the d electrons of Pt atoms become delocalized over more centers, leading to lower symmetry structures. A certain aromaticity arising from delocalization of d electrons over the multi-center framework in the doped Pt clusters contributes to their stability, with Pt102+ at y = 10 exhibiting the highest stability. While the ground electronic state of the neutral platinum atom [Xe]. 4f145d96s1 leads to a triplet state (3D3), the total magnetic moments of AuxPty2+ are large increasing steadily from 0 to 10 μB and primarily located on Pt atoms, corresponding to the increase of the number of Pt atoms from 0 to 10 and significantly enhancing the magnetic moments. An admixture of both Au and Pt atoms thus emerges as an elegant way of keeping a small pyramidal structure but bringing in a high and controllable magnetic moment.


Introduction
The element gold and gold-based clusters have several unique electronic, 1-3 optical, 4-8 chemical, 9,10 and catalytic [11][12][13][14][15] properties that have been, and still are, triggering an explosive growth in both experimental and theoretical studies so far.Gold has an electronic conguration of 5d 10 6s 1 but in contrast to other coinage metal atoms, the gold atom exhibits a typical sd hybridization, resulting from a strong relativistic effect of the heavy element 16 and emphasizing numerous specic and customized properties, particularly in its geometric and electronic structures.As a result, stable frameworks of pure gold clusters with intriguing structures have emerged such as 2D-planar, 17 at cage, 18,19 tubular, 20 icosahedral, [21][22][23][24] core-shell, 25 star-like shape, 26,27 and tetrahedral structures.][30] Through the use of a combination of photoelectron spectroscopic techniques and relativistic density functional theory (DFT) calculations, a tetrahedral cluster of 20 gold atoms was identied as an ideal building block for gold surfaces. 31The distinctive Au 20 cluster exhibits a notably large HOMO-LUMO energy gap (1.8 eV) exceeding that of the well-known C 60 fullerene.This characteristic contributes to the cluster's exceptional inertness and stability in both its geometric and electronic structures.The Au 20 pyramid can also be considered as a superatom with an electronic shell-closure.Its distinctive features include a (16c-16e) superatomic Au-core connected to four vertical Au atoms via a SD 3 hybridization, 16 resulting in a closed electron shell conguration of (1S 2 1P 6 2S 2 1D 10 ) of Au 20 giving rise to its magic number of 20 valence electrons. 28This pyramidal superatomic cluster could be used as building blocks for assembling cluster-based materials.
The Au 10 clusters in different charge states were expected to also have a tetrahedral skeleton like Au 20 .However, it was found that the neutral Au 10 favors a 2D planar structure of elongated hexagon 17 (Scheme 1).Recently, Nhat et al. 32 reported that both the 2D elongated hexagonal and 3D tetra-capped trigonal prism (TTP) isomers of Au 10 are likely to exist together in experimental molecular beams at temperatures between 100 and 300 K. 32 On the other hand, the Au 10 − monoanion was observed to prefer a 2Dplanar structure, 1,33,34 whereas the Au 10 + monocation possesses a quasi-tetrahedral TTP shape [35][36][37] (Scheme 1).It is well known that while the negative charge tends to favour the planar form of atomic clusters, the positive charge induces 3D shapes.
For its part, the dicationic Au 10 2+ cluster is of particular interest due to its magic number of 8 valence electrons, which forms a closed electron shell of (1S 2 1P 6 ) and an exceptionally large HOMO-LUMO energy gap of 3.9 eV. 29The geometrical structure of Au 10 2+ dication has theoretically been determined to be a tetrahedral pyramid with T d symmetry 29 (Scheme 1) and is considered as a tetravalent SP 3 -Au 6 core decorated with four capping Au atoms. 38The coincidence of both the same geometric symmetry and a magic electron shell makes both Au 10 2+ and Au 20 clusters equivalent superatoms. 30However, this magic character invariably causes these clusters to have no magnetic properties.In order to induce magnetism in these clusters, the possibility of incorporating additional elements, particularly transition metals, into the gold tetrahedral Au 20 and Au 10 2+ clusters was considered. 30,39,40While doping of some transition metals can cause signicant geometric transformations to form endohedral structures, the M@Au 19 having 19-Au atoms doped with lighter transition metals such as Cr, Mn, Fe, Co, Ni and Cu still maintain their tetrahedral framework. 39Among these clusters, CrAu 19 exhibits the largest magnetic moment of 5 m B with its 20 delocalized valence electrons forming a stable electron shell of (1S 2 1P 6 2S 2 1D 10 ) and the 3d-Cr atomic shell is partially lled by its ve remaining localized electrons, resulting in a total magnetic moment of 5 m B . 40A recent investigation 29 explored the effects of rst-row transition metal M doping on the Au 9

2+
dication and found that the total spin magnetic moment of the metal doped MAu 9 2+ dication is induced mainly by electrons on the 3d-AOs of dopant M atoms and is, as expected, strongly dopant-dependent, varying from the smallest value of 0 m B for ScAu 9 2+ to the largest value of 5 m B for CrAu 9 2+ . 30Despite shape variations in ScAu 9 2+ and TiAu 9 2+ , the tetrahedral framework is maintained in the remaining MAu 9 2+ clusters.
The platinum element which has an electronic conguration of [Xe]4f 14 5d 9 6s 1 and a triplet ground state ( 3 D 3 ), is located next to gold on the Periodic Table .Unlike the gold Au 10 , the pure platinum Pt 10 cluster exhibits a highly stable tetrahedral shape and is regarded as a magic cluster 41 at a nonet spin state. 42,43A planar isomer of Pt 10 is much higher in energy.For its part, the Pt 10 − anion has been reported to follow the [Pt 6 @Pt 4 ] − model, 44 which, similar to Au 10 2+ , imitates the tetrahedral arrangement of the methane molecule with the Pt 6 core substituting for the carbon center.][47] This suggests that Pt could be a suitable dopant which could either preserve the tetrahedral framework and/or improve the magnetic moment of gold cluster through its unpaired electrons.In other words, substitution of Au atom(s) in the pure Au 10 2+ dication by Pt atom(s) in a stepwise manner, could open the Au 10 2+ closed electron shell and thereby increase its magnetic moment while keeping the pyramidal shape.In this context, we set out to perform a detailed and systematic investigation on the binary Au x Pt y 2+ clusters with x + y = 10, making use of quantum chemical computations to scrutinize their geometries as well as their corresponding electronic and magnetic properties.It is clear that when x < y, the Au atom plays the role of dopant on Pt clusters.Our goal is to understand the factors governing the formation of a tetrahedral pyramid as the most stable isomer following mixture of a small number of Au and Pt atoms.

Computational methods
All standard electronic structure calculations are performed using the Gaussian 09 package. 48In theoretical studies of the heavy atoms and their cluster systems, it is important to properly account for relativistic effects, 15,23,37,[49][50][51] in particular that of the gold atom. 15,23,52This is in fact an issue of concern, because in density functional theory (DFT) methods, even they are favored over wavefunction methods thanks to their lower computational cost and decently accurate outcome, there is no global functional which can accurately describe the properties of both Au and Pt atoms. 37,53Several DFT functionals have been applied to these metals including the BP86, 33,35 TPSS, 54 BPE, 55,56 Scheme 1 Shapes of the Au 10 cluster in the anionic, neutral, cationic and dicationic states.
][56][57] In previous studies of dicationic gold clusters 29 as well as both pure and doped Pt clusters, 42,[60][61][62][63] the hybrid B3PW91 functional has been extensively used.This functional has been well calibrated and has demonstrated good agreement with experimental results for doped Pt clusters. 61Furthermore, the BP86 and revTPSS functionals are also commonly employed when studying Au and transition metal (TM)-doped Au clusters, 32,64 while the TPSSh functional has been utilized for Pt n clusters. 43,65Hence to ensure consistency and facilitate comparison, we employ the B3PW91, BP86, TPSSh, and revTPSS functionals in our current investigation to explore stable species of the binary clusters Au x Pt y 2+ with x + y = 10.
The low-lying isomers of a cluster are located on the corresponding potential energy surface which is explored using an intensive search procedure covering as many atomic arrangements as possible.Our search for energy minima of clusters is conducted using two different approaches.First, all possible structures of Au x Pt y 2+ clusters are generated using a stochastic algorithm 66 which was improved from the previously reported random kick procedure. 67By another way, initial structures of Au x Pt y 2+ are manually built by either replacing y Pt atoms into various positions belonging to local minimum structures of both neutral and charged states of Au 10 , 1,17,29,[32][33][34][35] or doping y Pt atoms onto the surfaces of the pure Au x +/0/− clusters, 1,2,17,[33][34][35] and conversely by doping x Au atoms into the Pt y +/0/− clusters alike. 42,60These initial structures are rst optimized at different multiplicities using the B3PW91, BP86, TPSSh, and revTPSS functional in conjunction with the small LANL2DZ basis set.Subsequently, the local energy minima identied from both search approaches with relative energies of <5 eV with respect to the lowest-lying minimum of each size are all re-optimized using the same functional but with the larger aug-cc-pVTZ-PP basis set, in which PP stands for an effective core potential including the relativistic effects for heavy atoms.Harmonic vibrational frequencies are then calculated at the same level to identify equilibrium geometries and evaluate their zero-point energy (ZPE) corrections.
The natural bond orbital (NBO) analysis is performed by the NBO 5.0 program 68 to investigate the electronic congurations and populations thereby the chemical bonding and magnetic properties of the clusters considered.The results of NBO calculation are further analyzed 69 using the Multiwfn program 70 to study bonding characteristics of the Au x Pt y 2+ clusters.

Lower-lying structures
Let us rst evaluate the performance of difference density functionals on the relative energies between isomers.Fig. 1 illustrates the assessment of low-lying structures within the Au 10 2+ cluster, by combining the CCSD(T) method with the cc-pVDZ-PP basis set and the B3PW91, BP86, TPSSh, and revTPSS functionals in conjunction with the aug-cc-pVTZ-PP basis set.
The results unequivocally support the conclusion that the pyramidal conguration stands out as the sole and most stable structure for the Au 10 2+ clusters.
For the Au x Pt y 2+ (x + y = 10), due to the abundance of local minima on the potential energy surface for each cluster size, we selectively include only the lowest-lying isomers with relative energies in proximity to the most stable structure (with a difference of <1.00 eV in relative energy). 71,72The shapes of the Au x Pt y 2+ equilibrium structures, their spin states and their relative energies obtained at the B3PW91, BP86, TPSSh, or revTPSS with the aug-cc-pVTZ-PP basis set and ZPE corrections are displayed in Fig. 2, S1 and S2 (ESI le).† As for a convention, the Au x Pt y

2+
.Z label is used to denote the isomers where x is the number of Au atoms, y the number of Pt atoms and Z = A, B, C,. accords to the isomers with increasing  In general, regardless of the specic numbers of Au or Pt atoms (represented by x and y) and the calculation methods employed, it has been observed that the most stable isomer for each size (x, y) consistently exhibits a tetrahedral pyramid structure (Fig. 2).This indicates a strong preference for this geometric skeleton within this series of small binary clusters.Previous studies suggested that Au 10 2+ comprises a hybridized tetravalent SP 3 -Au 6 2+ core with an octahedral central structure, adorned by four extra Au atoms on the Au 3 faces of this core (Scheme 1). 29,38However, in the case of Pt-doped Au clusters, the use of a [Au 6 X 4 ] 2+ model 38 cannot adequately explain the shapes of these Au x Pt y 2+ dications.This is due to the fact that Au atoms in core positions are successively replaced by Pt atoms, even before the Au atoms at the top positions of the tetrahedron (cf.Fig. 2).This is because (i) the Pt-Pt bond is stronger than the Au-Au bond (cf.section "thermodynamic stability" hereaer) and (ii) d-electrons of Au atoms do not join to a formation of multi-center bonds, but d-electrons of Pt atoms do (cf.section "chemical bonding" hereaer).In other words, Pt atoms tend to gather into small groups in such a way that their electrons can move more freely around them.Such a preference for Pt atoms placed in the core and Au atoms at the surface can also explain why the core Au 6 is not xed in place.Accordingly, two tendencies emerge in the formation of binary structures with a critical point at size x = y = 5.In the rst trend, the Pt y blocks in the lowest-lying structures Au 9 Pt 2+ .A, Au 8 Pt 2 2+ .A, Au 7 Pt 3 2+ .A, Au 6 Pt 4 2+ .A and Au 5 Pt 5 2+ .A regularly develop from a spot, a line, a triangle, a quadrangle and a tetragonal pyramid as y increases from 1 to 5, respectively (cf.Fig. 2).Each of these blocks constitutes the octahedral center which is located inside the pyramid.However, in the second trend of y = 6-9, replacement of Pt no longer follows the same pattern of structural growth as that of y = 1-5, and some Pt atoms tend to occupy outer vertices rather than apexes of the inner core (cf.Fig. 2).In fact, in this series where y > x, the mixed systems can better be regarded as Au    the expected error margin of ±0.3 eV, typically associated with energetic parameters derived from DFT computations. 71,72To further validate these ndings, the energies of these two isomers are also calculated using the CCSD(T)/cc-pVDZ-PP method, yielding results consistent with an energy difference of ∼0.1 eV.This additional analysis reinforces the assumption of energy degeneracy between the two geometric structures.
In the transitional size, ve Au atoms of Au 5 Pt 5 2+ .B are arranged as a triangle corner, where two atoms reside at the core, while the remaining three atoms occupy the outer vertices.This triangular arrangement forms one of the three faces of a tetrahedron (cf.Fig. 2).Following the same framework as .A and the Pt 10 2+ clusters (cf.Fig. 2).

Thermodynamic stability
The B3PW91/aug-cc-pVTZ-PP + ZPE method is utilized to investigate the thermodynamic stability of the clusters.The inherent thermodynamic stability of the 10-atom clusters is evaluated by the average binding energies (E b ).In this work, the average binding energies (E b ) of all lowest-lying structures of Au x Pt y 2+ can conventionally be dened using the following formula (eqn ( 1)-( 3)): where E(Au), E(Au + ), E(Pt), E(Pt + ), and E(Au x Pt y

2+
) represent the total energies of the Au-atom, the cationic Au + , the Pt atom, the cationic Pt + , and the dicationic Au x Pt y 2+ , respectively.Given that the ionization energy of the Au atom (13.03 eV) signicantly exceeds that of the Pt atom (9.18 eV), we opt to utilize only the total energies of the Pt + cation E(Pt + ) for calculating the average binding energy instead of the total energies of the Au + cation E(Au + ).This replacement is grounded in the assumption that the loss of two electrons takes place on Pt atoms, rather than one Au atom and one Pt atom, elucidating the inclusion of the 2E(Pt + ) term in formula (1).The plots of E b illustrating their evolution are depicted in Fig. 3.The mixed clusters exhibit varying levels of stability, with the Au 8 Pt 2 2+ cluster being the least stable due to energetic degeneracy between singlet and triplet states.Mixed clusters with a limited number of Pt atoms (y = 1-6) exhibit lower stability as compared to the original Au 10

2+
. This could be attributed to the insufficiency of Pt-Pt bonds due to the limited number of Pt atoms and the deciency of multi-center bonds formed between atomic orbitals (AOs) of Pt and Au atoms.In these cases, some distortion in the overall bonds (10c-1e) occurs because of the contamination in S and P-MOs within the mixed clusters in comparison to the pure Au 10 2+ clusters (cf.section "chemical bonding" hereaer).However, as the number of Pt atoms increases beyond y = 2, the mixed clusters exhibit a linear stabilization (see Fig. 3).Notably, starting at y = 7, where it resembles a doped Pt cluster, the stability of the mixed clusters surpasses that of the Au 10 2+ cluster.At y = 10, which corresponds to a pure Pt cluster, Pt 10 2+ emerges as the most stable conguration.This suggests that a Pt cluster, even with the same number of atoms as its Au counterpart, is inherently more stable.
The underlying reason for this enhanced stability lies in the intrinsic strength of the Pt-Pt bond, boasting a bond energy of 2.91 eV, as compared to the Au-Au (2.03 eV) and Au-Pt (2.04 eV) bond energy.As the number of Pt atoms increases, this strength is amplied, resulting in the formation of more robust Pt-Pt bonds.Consequently, these stronger bonds contribute to greater stability within the mixed clusters.
It's worth noting that the prevalence of stronger Pt-Pt bonds leads Pt atoms to congregate together, forming small Pt blocks within the clusters.This arrangement facilitates the movement of d-electrons between the Pt atoms, resulting in a creation of smaller aromatic regions characterized by free d-electrons in the Pt blocks.These exists alongside the primary aromaticity arising from in S and P-MOs throughout the entire Au x Pt y 2+ clusters (cf.section "chemical bonding" hereaer).

Magnetic moments
In terms of spin state, the total and local magnetic moments (TMMs and LMMs, respectively) are determined by calculating the difference between the number of spin-up and spin-down electrons occupying the molecular or atomic orbitals.When using the B3PW91 and TPSSh functionals, an increase in the number of Pt atoms in the mixed clusters, due to the intrinsic triplet ground state of Pt atom, invariably leads to a higher multiplicity of their most stable isomers.In other words, as the size of Pt increases from 0 to 10, the corresponding total magnetic moment of the Au x Pt y 2+ steadily increases from 0 to 10 m B (cf. Fig. 4).The electronic conguration of pure Au 10 2+ , as mentioned earlier, is a closed-shell singlet state with four bonds formed by the SP 3 -Au 6 2+ core bonded with four 6s electrons of four external Au atoms using the eight shared valence electrons, 38 leading to a completely quenched total magnetic moment.When Pt atoms replace Au in Au 10 2+ , the closed-shell electronic conguration becomes defective due to the deciency of one electron on each Pt 5d-AO.NBO results conrm that the magnetic moment mainly localizes on Pt atoms (as shown in Table 1) with a spin density range of 0.7-1.2electron for each Pt atom and the unpaired d-electron is xed on each Pt atom.As each Pt atom donates one single electron, an increase in the number of Pt atoms results in an increasing number of unpaired electrons in the cluster, and thereby leads to a signicant increase in magnetic moments.However, when utilizing the BP86 and revTPSS methods, the magnetic moments reach their peak at y = 8 (eight Pt atoms) with a value of 8 mB, and then gradually decrease to 6 mB when y = 10 (ten Pt atoms) (cf.Fig. 4).
Both the Pt 10 2+ clusters with septet and 11-et spin states and the AuPt 9 2+ clusters with octet and dectet spin states, the relative energy gaps among all four DFT methods considered, as listed in Fig. S2, † are very small (<0.1 eV).This indicates that these spin states can be considered to be energetically degenerate, arising from the closely spaced energy levels of the d-orbitals within these clusters.
The high spin states exhibited by these clusters pose a challenge for the coupled-cluster method calculations as well, primarily due to an increasing spin contamination, resulting from its unrestricted Hartree-Fock (UHF) wavefunctions, whose spin contamination tends to lead to a slow and deceptive convergence of the coupled-cluster expansions, and thereby incorrect total energies.Consequently, determination of a reliable method for these systems becomes a complex task, in particular for system having multi-reference character.

Chemical bonding
For a rationalization of the chemical bonding of these Au-Pt mixed clusters, the electronic conguration of each lowest-lying isomer Au x Pt y 2+ .A displayed in Fig. 2 is analyzed using NBO at the B3PW91/cc-pVTZ-PP theory level and related adaptive natural density partitioning (AdNDP) analysis. 70Conventionally, the (nc-me) label species the number n of atomic centers and the number m of electrons moving within those centers.For instance, (10c-1e) indicates one electron moving over ten atomic centers in the cluster.
The binary Au x Pt y 2+ clusters, with y varying from 0 to 10, prominently exhibit a spherical aromaticity.This aromaticity arises from the presence of (10c-2e) bonds in case of the Au 10 This discrepancy in behaviour between Au and Pt atoms can be attributed to the differences in their electronic structures and bonding capabilities.The localized nature of Au's d-electrons restricts their involvement in multi-center bonding, while the more exible d-electrons of Pt enable them to engage in such bonding interactions.This distinction inuences the preferred placement of Pt atoms in the core of the binary clusters, where they can effectively form multi-center bonds and establish connections with neighbouring Pt atoms.
In addition, Fig. S15 † illustrates that the density of states (DOS) maps of the Au x Pt y 2+ exhibit two distinct trends, which  As the number of Au atoms in the cluster decreases from x = 10 to x = 0, there is a signicant reduction in the DOS of Au x Pt y 2+ , especially from the critical point at y = 5 onward.
Furthermore, the downward shi of the SOMO-LUMO gap on the beta side results in a reduced gap size (almost half) compared to the alpha side (see Table 2).This shi facilitates electron movement between the frontier orbital levels, ultimately causing an energetic degeneracy among the spin states within the clusters considered.

Concluding remarks
In the present theoretical study, the binary gold-platinum clusters Au x Pt y 2+ containing ten atoms with x + y = 10 were systematically studied using DFT calculations with the B3PW91, TPSSh, revTPSS and BP86 functionals in conjunction with the aug-cc-pVTZ-PP basis set.The main results demonstrated that all the most stable structures of the Au x Pt y 2+ clusters follow the tetrahedral pyramid pattern.In their dicationic state, a mixture of ten Au and Pt atoms consistently holds the pyramidal shape of both pure clusters.A critical point at y = 5 marks the onset of two distinct tendencies in the structural growth that characterize their chemical bonding.cluster (in terms of dissociation energy) but from y = 7 onwards, the system becomes Pt clusters, and they can be more stabilized by the formation of the stronger Pt-Pt bonds.In fact, the pure platinum Pt 10 2+ , corresponding to y = 10, exhibits the highest thermodynamic stability.Furthermore, the substitution of Pt atoms into the pure Au 10 2+ cluster increases signicantly the magnetic property.The spin density of the Au x Pt y 2+ clusters is mainly located on Pt atoms and the total magnetic moment increase steadily from 0 to 10 m B , corresponding to the number y of Pt atoms increased from 0 to 10 with calculations using B3PW91 and TPSSh functionals.Overall, admixture of both Au and Pt atoms within a small size emerges as an elegant way of keeping the small pyramidal structure but bringing in a high and controllable magnetic moment.
relative energy.Hence, the notation Au x Pt y 2+ .A invariably stands for the most stable isomer A of the Au x Pt y 2+ dication.
-doped Pt clusters, and Pt atoms assemble forming the cores of the pyramid.The lowestlying structures at sizes y = 6-9, namely Au 4 Pt 6 2+ .A, Au 3 Pt 7 2+ .A, Au 2 Pt 8 2+ .A and AuPt 9 2+ .A follow a similar pattern that can be traced back to the shape of the Au 5 Pt 5 2+ .B isomer and are achieved by sequentially replacing the remaining Au atoms in

For y = 2 , 3 , 4 ,
and 5 where the Au x Pt y 2+ are basically Au clusters, the Pt atoms gather together into symmetric Pt y blocks as a line, a triangle, a quadrangle, and a tetragonal pyramid, respectively, located at the inner octahedral core of the cluster.At these sizes, some d-electrons of Pt atoms tend to form (2c-1e) bonds.Meanwhile, larger y = 6-10 leading to the doped Pt clusters, Pt atoms substitute Au atoms in the structure of the Au 5 Pt 5 2+ .B isomer and form larger multi-center d-electron bonds.All ten-atom binary Au x Pt y 2+ clusters are characterized by bonds whose electrons are delocalized on S-MO and P-MOs for each alpha and beta stream.The S-MO and P-MOs are more distorted when the number of Pt atoms rise due to contaminations with d-AOs of Pt atoms.For the number of Pt atoms y = 1-6, the mixed clusters Au x Pt y 2+ are less stable than the pure gold Au 10 2+ Au 5 Pt 5 2+ .B, the Au 4 Pt 6 2+ .A isomer which has more Pt atom than Au, is formed by replacing one of the two Au atoms at the core of the Au 5 Pt 5 2+ .B with a Pt atom.Consequently, Au 4 Pt 6 2+ .A is now composed of ve Pt atoms in the internal core and one Pt atom locating at an external vertex and with Au atoms serving as dopants (cf.Fig.2).This substitution leads to a relaxation towards C s symmetry.A similar phenomenon is witnessed in the Au 3 Pt 7 2+ .A, where the substitution of Au atoms with Pt atoms takes place at an external vertex of Au 4 Pt 6 2+.A, resulting in the attainment of C 1 symmetry.Continuing this trend, replacing the last Au atom at the internal core of the Au 3 Pt 72+.A with a Pt atom, we obtain the 2+.A with Pt atom(s), we eventually arrive at the AuPt 9 2+

Table 1
Local and total spin magnetic moment of the binary Au x Pt y 2+ (x + y = 10) obtained at B3PW91/aug-cc-pVTZ-PP theory level

Table 2
Frontier orbital energy gap (eV) of the binary Au x Pt y 2+ (x + y = 10, B3PW91/aug-cc-pVTZ-PP) Pt y 2+ is primarily contributed by the d-electrons of Au and Pt atoms, with Au making a more signicant contribution.