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# Au19M (M=Cr, Mn, and Fe) as magnetic copies of the golden pyramid

## Abstract

An investigation on structure, stability, and magnetic properties of singly doped Au19M (M=Cr, Mn, and Fe) clusters is carried out by means of density functional theory calculations. The studied clusters prefer forming magnetic versions of the unique tetrahedral Au20. Stable sextet Au19Cr is identified as the least reactive species and can be qualified as a magnetic superatom. Analysis on cluster electronic structures shows that the competition between localized and delocalized electronic states governs the stability and magnetic properties of Au19M clusters.

## Introduction

Last decades have witnessed an increasing interest in gold nano-clusters thanks to their precious catalytic, electronic, and optical properties1,2,3. In this respect, geometric and electronic structures of gold clusters with different sizes and charge states have been studied intensively through both theoretical simulations4,5,6,7,8 and experiments, for instance, infrared vibrational spectroscopy9,10,11, photoelectron spectroscopy12,13,14, photoionization spectroscopy15,16, photodissociation17,18,19, and ion mobility measurements20,21. The cluster form of gold containing low-coordinated edge atoms22 can adopt binding geometries and lead to a strong reactivity that differs from the bulk23. Enhanced stabilities were observed when the number of gold atoms corresponds to the following “magic” values: 2, 8, 18, 20, 34, 58, and 92, where the electronic supershells of clusters are supposed to be closed24,25,26,27,28,29. A rich structural diversity compared to other coinage metals has been reported for gold clusters due to their strong relativistic effects. It has been revealed that small Au n clusters prefer planar structures till the cluster size of 8–13 atoms depending on charge states20,30,31,32,33,34. Larger species evolve via hollow cage structures at n = 14–189,35,36,37, tube-like structure at n = 24–2638,39, fullerene type at Au32 40,41, and a possibly chiral structure at n = 348. Among the wide range of studied gold nanoclusters, the discovery of the tetrahedral Au20, as an outstanding landmark in cluster science, has attracted an exceptional attention than any others9,12,42,43. It was reported that Au20 possesses a perfect pyramidal structure (T d ) with a considerably large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy gap of 1.77 eV, suggesting its remarkably high stability and offering a potential platform for optical and catalytic nanostructured materials. The underlying physics behind its magic stability has been attributed to the formation of the 20-electron supershell closure in which each Au atom contributes one itinerant 6s electron42. Au20 can also be considered as either a group of ten 2-electron superatoms in superatom-network model or a superatomic molecule Au16 bonded with four vertex Au atoms44.

Interests in synthesizing novel elementary units for advanced nano-structured materials led to extensive search for stable cluster species with desired properties. A presence of impurity (i.e. alkali, coinage, and transition metal) atoms can provide a key to tune the properties of Au20 clusters with minor effects on its magic stability. In this regard, the structures, binding energies, ionization potentials, electron affinities, and energy gaps of Au19X (X = Li, Na, K, Rb, Cs, Cu, and Ag) were systematically examined45. Au19Li, Au19Cu, Au19Ag, and Au19Pt are found to retain the pyramidal geometry of Au20 46,47,48,49,50,51. Increasing the Ag concentration induces the energy gap and optical transition of Au19−n Ag n 48,49. Au19Cu and Au19Pd clusters are potential for adsorption of trivalent arsenic50. Substitutional doping of Pt in Au20 leads to significant enhancement of the cluster binding energy and reactivity while the geometry remains the same as that of Au20 51. The 20-electron supershell closure in Au20 can be reproduced in a stable icosahedral E@$${{\rm{Au}}}_{12}^{q}$$ system, where E is a p-block element, through bonding-antibonding interactions between structural shells52. The adsorption energies of CO and O2 on Au19H are similar to those on the Au20 cluster53. More recently, selective doping with Hf and Ge atoms has been applied to modify the catalytic activity of Au20 through transforming the cluster structure54.

Although there have been some progress on the structural features and catalytic behavior of doped 20-atom gold clusters, the role of impurities in tailoring the magnetic properties of Au20 has been far less understood. Considering the fact that Cr, Mn, and Fe are interesting magnetic elements due to their unpaired 4s 13d 5, 4s 23d 5, and 4s 23d 6 valence electrons, respectively, the interaction between these impurities and host electrons is expected to trigger essential changes in the magnetism of 20-atom gold clusters. In this study, we report results on searching for lowest-lying structures of gold clusters doped with a transition metal impurity Au19M (M=Cr, Mn, and Fe) and discussing the origin of their magnetic and stability properties. The finding results unravel the possibility of producing new magnetic superatoms in the golden pyramid’s family.

## Computational setup

The structural optimization of Au19M clusters have been carried out by density functional theory (DFT) calculations implemented in the Gaussian 09 software55,56. We used the BP86 functional in conjunction with basis sets cc-pvDZ-pp for Au and cc-pvDZ for Cr, Mn, and Fe. Possible structures of Au19M clusters were generated using a stochastic algorithm57. In addition, the local minima of previously-reported doped Au n clusters also served as reference input. All guessing structures were initially optimized using the BP86 functional in jointing with cc-pvDZ-pp for Au atoms and cc-pvDZ for Cr, Mn and Fe dopants. Isomers having relative energies within 2.0 eV were selected for recalculating single point energies at the same functional but combining with larger basis set, cc-pvTZ-pp for Au and cc-pvTZ for Cr, Mn, and Fe. In the following, we discuss the structural, stability, and magnetic aspects of the doped Au19M clusters.

The selection of the BP86/cc-pvDZ-pp and cc-pvDZ functional resulted from test calculations for Au2, AuCr, AuMn, AuFe, Au2Cr+, and Au2Mn. The calculated results are presented in Table 1, along with available computational and experimental data for comparison. It can be seen that the used level provide reliable results for all of the examined properties. For example, the calculated spin states of all dimers and molecules are in excellent agreement with the other theoretical and experimental values58,59,60,61,62,63. The computed D e of Au2, AuCr, and AuFe are 2.27, 2.27, and 2.20 eV, which are well consistent with the experimental ones, 2.29 ± 0.30, 2.28 ± 0.30, and 2.29 ± 0.30 eV, respectively. Although the predicted D e of AuMn obtained in this work likely overestimates the experimental one, it is apparently in closer agreement with experiment than that of other calculations. It is worth to mention that the BP86 functional has been proved to yield the most reliable results for yttrium and vanadium doped gold species64,65,66. Therefore we are confident that the used computational approach is suitable to describe the structures and properties of Au19M clusters.

## Results and Discussions

The geometries of low-lying Au19M isomers with M=Au, Cr, Mn, and Fe are shown in Fig. 1. Although a large number of different structures and spin configurations are considered for each cluster, only the lowest-energy isomers are discussed. As expected, singlet Au20 is found to be very stable in form of a tetrahedral with a calculated HOMO-LUMO energy gap of 1.80 eV, in an excellent agreement with the measured value (1.77 eV)12. It is noteworthy that the ground-state geometry of all investigated clusters favor a slightly distorted tetrahedral form caused by the displacement of the impurity, where the dopant substitutes for a gold atom on the surface center. The second lower-lying isomers of Au19Cr, Au19Mn, and Au19Fe have the same motif of an endohedrally-doped truncated pyramid, lying at 0.33, 0.08, and 0.23 eV above their corresponding ground states, respectively. A tetrahedron with a substituted dopant atom on the edge serves as the next isomers of Au19Cr and Au19Fe with relative energies of 0.48 and 0.29 eV, respectively. On the other side, that of Au19Mn is a spin isomer (septet) of the corresponding ground state, locating at 0.14 eV higher in energy.

The most interesting feature of Au19M clusters is their magnetic behavior. Unlike the non-magnetic Au20, the ground state spin multiplicities of Au19Cr, Au19Mn, and Au19Fe clusters are sextet, quintet, and quartet, corresponding to total magnetic moments of 5, 4, and 3 μ B , respectively. The decreasing trend of the total magnetic moments with the increasing number of dopant’s valence electrons is noticeable. Other low-lying spin isomers are examined and listed in Fig. 1. It is found that the ground states of Cr and Fe doped Au19 clusters have relatively robust spin configurations. In particular, the next spin excitations of Au19Cr are quartet and doublet at 0.82 and 1.54 eV, respectively. For Au19Fe, at least 0.89 eV is needed to excite it from quartet to sextet states and 1.31 eV is required for the quartet-to-doublet transition. The spin stability of Au19Cr and Au19Fe is again reflected by the fact that their second and third lowest-energy isomers also favor the same spin states as the ground state ones. Whereas, the spin ground state of Au19Mn is less stable since an energy amount of 0.14 eV is sufficient to trigger a spin excitation.

To gain insight into the magnetic behavior of Au19M clusters, the total/partial density of states (DOS), the molecular orbitals (MO) diagram, and the spin distribution of Au19M clusters are calculated and plotted in Fig. 2. Typically, when a metallic cluster is doped with a magnetic atom, the outermost orbitals of the magnetic impurity can hybridize with delocalized orbitals of the host to form supershells. Cr, Mn, and Fe atoms have electronic configurations of [Ar]4s 13d 5, [Ar]4s 23d 5, and [Ar]4s 23d 6 corresponding to 6, 7, and 8 valence electrons, respectively. Assuming the each gold atom delocalizes one 6s electron, adding a Cr atom to the cluster of nineteenth gold atoms can create a pool of 25 itinerant electrons. Ordinarily, this forms an open shell of 2P 5 and does not lead to the observed spin state. However, there is another possibility in which valence orbitals of the Cr atom and delocalized MOs of the host hybridize and form a localized and a delocalized MO sets67. Once the delocalized MO set occupies states of itinerant electrons, the localized MO set has enough exchange splitting to cause a magnetic moment. With this picture in mind, the first 20 delocalized electrons of a Au19Cr cluster might be used to fill the molecular shell of 1S 21P 62S 21D 10, which leads to the stable species. Its five remaining localized electrons are taken to partially fill the d-Cr atomic shell, which results in a total magnetic moment of 5 μ B . Similar argument can be applied for Au19Mn and Au19Fe, in which their delocalized electrons fulfill a shell configuration of 1S 21P 62S 21D 10 and magnetic moments oscillates between 4 and 3 μ B , depending on the number of valence electrons in dopant atoms.

The results presented in Fig. 2 confirm the latter picture. The total/partial DOS [Fig. 2(a)] in combination with the MO diagram [Fig. 2(b)] indicate that the s orbitals from Au atoms play an essential role to the cluster shell orbitals while the half-filled sd orbitals of transition metal dopants become a key factor for the magnetic moment of studied species. In particular, the hybridized sd-M and s-Au electrons in Au19M clusters form both localized and delocalized electronic states. Similar to Au20, the delocalized states can be expressed in the full occupied electron shell sequence of 1S 21P 62S 21D 10. Two low-energy DOS peaks at −11.9 and −11.0 eV response for the molecular shell orbitals 1S and 1P (navy and dark yellow levels), respectively. The molecular shell orbitals 2S and 1D (blue and red levels) that overlap with atomic orbitals d of Au atoms (light blue levels) are observed at −6.5 and 6.0 eV, respectively. Meanwhile, the localized states (magenta levels) are used to fill the atomic five d orbitals from the dopant atom with five, six, and seven electrons from Au19Cr, Au19Mn, and Au19Fe clusters, respectively. Since the delocalized states account for the 20-electron supershell closure, the unpaired electrons in the localized d orbitals cause the magnetic moments of clusters. It can be approximately considered that the chromium atom provides one electron to the cluster supershells and five others to the majority spin channel of d atomic subshell orbitals. Similarly, the manganese (iron) atom donates one electron to the cluster supershell orbitals, five electrons to the majority spin channel, and one (two) other(s) to the minority spin channel, respectively. According to the energy levels in MO diagrams, the electronic configurations of Au19Cr, Au19Mn, and Au19Fe clusters can be written as 1S 21P 62S 23$${d}_{\uparrow }^{5}$$1D 10, 1S 21P 62S 23$${d}_{\uparrow }^{5}$$1D 103$${d}_{\downarrow }^{1}$$, and 1S 21P 62S 23$${d}_{\uparrow }^{5}$$1D 103$${d}_{\downarrow }^{2}$$, respectively. This picture can be further examined by mapping the spin distribution of studied Au19M clusters. As shown in Fig. 2(c), the total spin of the clusters is largely localized at the dopant atom, provided by the 3d state electrons as described in their aforementioned electronic configurations. A small amount of ferrimagnetic spin alignment adding to the total magnetic moments is found in Au atoms. Calculated local magnetic moments of Au19M clusters (not shown here) supports our argument that the total magnetic moments in Au19M clusters essentially result from the localized 3d-M orbitals.

Inheriting the major 20-electron supershell closing 1S 21P 62S 21D 10 and highly symmetric geometry from the tetrahedral Au20, Au19Cr, Au19Mn, and Au19Fe are potentially stable species. Their dopant-dependent stability can be reflected through the comparison between corresponding binding energies per atom E b with that of Au20. The calculated average binding energy of Au20 is found as 2.25 eV, which is in good agreement with the previously reported values58. Whereas, E b of alloy species are slightly higher, that are 2.29, 2.30, and 2.31 eV for Au19Cr, Au19Mn, and Au19Fe clusters, respectively. Since the Au19M and Au20 systems have nearly identical geometries and similar E b values, it could be suggested that the incorporation of transition metal dopants tends to stabilize the gold host and the stability of Au19M system can be relatively comparable to that of the robust Au20. We further examine the bonding nature between the dopant and Au host by analyzing the electron localizability indicator (ELI-D)68. The ELI-D isosurface of Au19M clusters produced at the bifurcation value of 1.0 are presented in Fig. S1 in the Supplementary Information file (Supplementary Information: The electron localizability of ground-state Au19M clusters). No localization domain is observed in the region between the dopant and Au19 host, implying that the dopant likely connects with Au moiety via ionic and/or highly polarized covalent bonds. A similar picture was also reported for Re@Au11Pt and Ta@Au11Hg superatomic systems, in which the energy decomposition analysis (ETS-NOCV) is used to emphasizes the importance of electrostatic and covalent interaction between metal dopant and host in stabilizing clusters69. To measure the chemical stability of the clusters, we examine the energy gaps between the LUMO of the minority (beta) spin and the HOMO of the majority (alpha) spin $$[{\delta }_{1}=-({\varepsilon }_{HOMO}^{alpha}-{\varepsilon }_{LUMO}^{beta})]$$ and between the LUMO of the majority (alpha) spin and the HOMO of the minority (beta) spin $$[{\delta }_{2}=-({\varepsilon }_{HOMO}^{beta}-{\varepsilon }_{LUMO}^{alpha})]$$. These values suggest the required amount of energy for an electron to jump from the HOMO of majority (minority) spin channel to the LUMO of minority (majority) one. The larger gap means the less reactive and more stable clusters70,71,72. Table 2 lists the HOMO and LUMO energies for the majority and minority spin channels and the values of δ 1 and δ 2 calculated for the ground states. Both energy gaps δ 1 and δ 2 take positive values, again confirming the inertness of all studied clusters. Notably, Au19Cr has the largest gaps of δ 1 and δ 2, which means that it is the most stable and least reactive species compared to the others and can be assigned as a magnetic superatom. Among clusters with higher doping concentration, Au16M4 would be a promising system due to its potential as a giant magnetic and highly symmetric superatom. Although the dopant atom apparently prefers substituting one Au atom in the surface center of singly doped species, the situation for Au16M4 clusters could be more puzzling. It is worth to mention that the unique stability of the golden pyramid Au20 can be understood in term of a superatomic molecule Au16Au4, where its superatomic core Au16 binds with four vertex Au atoms42. This approach has been supported by the recent findings of the golden pyramid’s smaller sisters, the tetrahedral $${{\rm{Au}}}_{17}^{+}$$ and $${{\rm{Au}}}_{10}^{2+}$$. These two systems were found highly stable in form of Au13 and Au6 octahedral cores, respectively, and the other four gold atoms are above four their triangular faces37,73,74. In this scenario, Au16M4 and its smaller magnetic counterparts, $${{\rm{Au}}}_{13}{{\rm{M}}}_{4}^{+}$$ and $${{\rm{Au}}}_{6}{{\rm{M}}}_{4}^{2+}$$, might be considered as a core in −4 charge state and four vertex M atoms. A careful examination of this interesting issue is perhaps warranted for future research.

## Conclusions

In summary, we have investigated structure, stability, and magnetic properties of singly doped Au19M (M=Cr, Mn, and Fe) clusters using DFT calculations. The most interesting point of our results is that all studied Au19M clusters favorably form magnetic copies of the golden pyramid Au20. The dopant atom is found to substitute for a gold atom on the surface center. The coexistence of both delocalized and localized electronic states in these clusters allows to fill the supershell orbitals and to simultaneously promote local magnetic moments, leading to stable magnetic systems. Au19Cr is the most stable species that can be assigned as a magnetic sister of the golden pyramid Au20.

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## Acknowledgements

N.T.T. acknowledges support by the National Key Laboratory of Electronic Materials and Devices and the Institute of Materials Science, Vietnam Academy of Science and Technology under grant number CSCL05.2017. N.T.C. thanks the Ministry of Education and Training of Vietnam for financial support under grant number B2015-17-68.

## Author information

### Affiliations

1. #### Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

• Nguyen Minh Tam
2. #### Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

• Nguyen Minh Tam
3. #### Faculty of Chemistry and Center for Computational Science, Hanoi National University of Education, Hanoi, Vietnam

• Ngo Tuan Cuong
4. #### Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001, Leuven, Belgium

• Hung Tan Pham
5. #### Institute of Materials Science and Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi, Vietnam

• Nguyen Thanh Tung

### Contributions

N.M.T. and N.T.T. conceived the calculations, N.M.T. and H.P.T. conducted the calculations, N.T.C. and N.T.T. analysed the results. All authors prepared and reviewed the manuscript.

### Competing Interests

The authors declare that they have no competing interests.

### Corresponding authors

Correspondence to Nguyen Minh Tam or Nguyen Thanh Tung.