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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Ultimate Manipulation of Magnetic Moments in the Golden Tetrahedron Au with a Substitutional 3d Impurity 20

Nguyen Minh Tam, Nguyen Thi Mai, Hung Tan Pham, Ngo Tuan Cuong, and Nguyen Thanh Tung J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03378 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 20, 2018

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The Journal of Physical Chemistry

Ultimate Manipulation of Magnetic Moments in the Golden Tetrahedron Au20 with a Substitutional 3d Impurity Nguyen Minh Tam,∗,†,‡ Nguyen Thi Mai,¶ Hung Tan Pham,§ Ngo Tuan Cuong,k and Nguyen Thanh Tung∗,¶ †Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam ‡Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam ¶Institute of Materials Science and Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Vietnam §Department of Chemistry, KU Leuven, Leuven B-3001, Belgium kCenter for Computational Science, Hanoi National University of Education, Vietnam E-mail: [email protected]; [email protected]

Abstract Nano-cluster systems that are electronically stable and highly magnetic have been of intense research interest due to their potential as magnetic superatoms. In this study, we consider a more intriguing case of the unique golden pyramid with a substitutional 3d impurity. In particular, we investigate the geometry, stability, and magnetic properties of Au19 M clusters (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) by means of density functional theory calculations. It is found that the structural patterns of doped species evolve from endohedrally-doped cages to exohedrally-doped tetrahedrons when M goes

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from Sc to Cu. The robustness of the Au20 unit tends to be retained in its tetrahedral doped counterparts. Remarkably, the quenched magnetic moment of Au20 increases in a systematic manner with the appearance of 3d impurities. It is demonstrated that not only the interaction between the magnetic impurity and valence electrons of the Au host but also the itinerant behavior of the impurity valence states have been taken into account to understand the magnetism of Au19 M clusters.

Introduction Last decades have witnessed an increasing interest in superatomic nanoclusters because of their significant promises as novel elementary building blocks for advanced nanostructured materials. 1 The most fascinating aspect of these tiny systems is the ability to mimic the physical and chemical behavior of various elements while retaining their stable structures in assemblies. The basic idea of the superatomic concept relies on the fact that the valence structure and associated physical/chemcial features of clusters with selected size and composition can be designed to be analogous to those of elementary atoms. 2 Pioneering experiments of Knight and coworkers revealed the mysterious size-dependent mass-spectrum of simple metal species, demonstrating the existence of electronic shell structure, as seen in atoms, formed by delocalized valence electrons in clusters. 3 Cluster sizes corresponding to filled electronic shells with enhanced abundance and higher stability were found potential as superatoms. Meanwhile, investigations on transition metal clusters have shown a different size-dependent picture. 4 The partially occupied d electrons in transition metal atoms are quite localized, prevailing the formation of a valence electronic structure. In this case, the cluster stability often obeys a geometric shell of atoms and species with completed shells forming close-packed high-symmetry geometries will be remarkably stable and can be as5 signed as superatoms. Al− 13 is an inspiring example of the superatomic cluster. It has

an almost perfect icosahedral structure with 40 valence electrons corresponding to the completely filled electronic configuration 1S2 1P6 1D10 1F14 2S2 2P6 . This coincident closure of both 2


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geometric and electronic shells makes the cluster magic with a pronounced stability as an inert gas atom. Al13 and Al12 B clusters have 39 valence electrons, which can be achieved by 6,7 removing one single electron from the closed-shell Al− As a consequence, these clusters 13 .

show a high electron affinity, imitating the chemical behavior of halogen atoms. In a similar 8 approach, Al14 I− 3 was found highly stable. If considering Al14 in a +2 state, the behavior

of a Al14 cluster in compounds with iodine is therefore analogous to alkaline earth atoms. 9 Another member of the aluminum superatom family, which should not be excluded, is Al− 7.

Unlike Al14 with a state of +2, this superatom exhibits multiple valence states and has the ability to form stable complex clusters with diverse species. For instance, the valence of +2 would resemble C atom and the stability of Al7 O− could be similar to that of CO. On the other hand, the valence of +4 would make it analogous to Si atom and the stability of Al7 C− could be correlated with that of SiC.

It should be mentioned that the existing idea of superatoms does not restrict to nonmagnetic species. Reveles and coworkers have proposed that magnetic superatoms could be realized in a cluster if its electronic structure contained both localized and delocalized states. 10 Such system would obtain a high stability through the filled electronic shells of diffused valence electrons while orbitals that are still localized at atomic sites have enough exchange splitting to cause a magnetic moment. The most interesting feature offered by magnetic superatoms lies in the coupling between their localized spin moments and shells of free valence electrons. Since this interaction is weak and can be easily modulated, it opens up the possibility to switch the magnetic ordering of cluster assembled materials through the application of small fields. A potential candidate that can fulfill this condition is the binary system of transition metal, for providing localized orbitals, and metal elements, for supplying free valence electrons. Within this framework, several clusters, including V@Cs8 , V@Na8 , Fe@Mg8 , Fe@Ca8 , Cr@Sr9 , Mn@Sr10 , and Cr@Zn17 , have been identified as potential magnetic superatoms since they posses a considerable magnetic moment while preserving

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their stability. 11–16 In particular, V@Cs8 and V@Na8 present a highly stable square prism structure even though they have 13 electrons each in the molecular shell. 10,11 The coexistence of diffused and localized valence electrons in these clusters results in an energy gain larger than any other cluster size and a total moment of 5 µB . Similarly, Cr@Sr9 and Mn@Sr10 are found stable in the form of capped and bi-capped square anti-prisms with a relatively large HOMO-LUMO gap of ∼0.45 eV and corresponding magnetic moments of 4 and 5 µB , respectively. 14 On the other hand, it has been demonstrated that the superatomic behavior of Zn17 units that has the simultaneous closing of geometric and electronic shells can be used for stabilizing the magnetic moment of a Cr dopant. 15,16

The Au20 tetrahedron has been known as an outstanding landmark in cluster science because of its exceptional stability and particular 20-electron superatomic shell structure. 17,18 The peculiar behavior of Td Au20 has been rationalized by considering the cluster either as ten interacting Au4 sections with corresponding 4c-2e bonds 19 or as a central 16c-16e Au16 superatomic core capped by four vertex Au atoms. 20 The magic number of 20 valence electrons in Au20 can also be explained by the spherical concentric bonding shell model in terms of a multilayered architecture [(Au4 @Au12 )Au4 ]. 21 Most recently, a remarkable magnetic moment has been reported for robust tetrahedral Au19 M (M = Cr, Mn, and Fe) clusters. 22 It has been found that due to the strong tetrahedral field the transition metal dopant shares its valence electrons with those of the Au host to keep possession of the 20electron shell closure, regardless the difference in outermost electronic shells of the dopants. The charming stability of these doped species inherits from both their closed electronic supershell and perfect pyramidal geometry. The remaining unshared electrons localized mainly on the transition metal impurity response for unquenched magnetic moments. Doping with other transition metal impurities might influence, in an unpredictable manner, not only the structure but also the stability and magnetic properties of Au20 clusters. This work is to explore all these exciting possibilities by presenting a comprehensive study on the structural

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evolution, relative stability, and magnetism of the Au20 system with a substitutional 3d atom. The electronic interaction between valence electrons of the Au host and specific localized orbitals of the magnetic impurity M is investigated. The itinerant behavior of outermost valence electrons is examined for each transition metal dopant. This finding might allow us to identify novel superatoms with an ultimate control of their magnetic moments.

Computational method The structural optimization of Au19 M clusters (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) has been performed by density functional theory (DFT) calculations implemented in the Gaussian 09 software. 23,24 We used the BP86 functional in conjunction with basis sets cc-pvTZ-pp for Au atoms and cc-pvTZ for transition metal ones. The selection of functionals is based on our previous test calculations 22 and reliable results reported for yttrium and vanadium doped gold species. 25–27 All possible structures and spin configurations of Au19 M clusters, assuming that Au19 has one alone electron and all 4s3d electrons of M atom can be unpaired, were generated using a modified stochastic algorithm. 28 Within this process, an additional module physically checking input structures is added to the original stochastic algorithm proposed by Saunders. 29 This module examines all generated candidates and eliminates unmeaning structures, which are fragmented or superpositioned before geometrically optimizing. In addition, the local minima for pure and doped Aun clusters published elsewhere 18,25–27,30,31 were also used as potential references. To achieve the computational accuracy without the additional increase in computing time, guessing structures were first optimized using the BP86 functional in jointing with cc-pvDZ-pp for Au atoms and cc-pvDZ for M ones. Isomers with relative energies less than 2.0 eV were selected for recalculating single point energies at the same functional but combining with larger basis sets, cc-pvTZpp for gold and cc-pvTZ for transition metal atoms. The natural bonding orbital (NBO) analysis was performed by NBO 3.0 program, which was implemented in Gaussian package.

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The total and local magnetic moments (TMMs and LMMs) were defined as the difference between the numbers of spin-up and spin-down electrons occupying the molecular/atomic orbitals of the cluster/atom. The convergence criterion was set to 10−6 a.u. for energy in the structural optimization.

Results and discussions Geometric structures According to the aforementioned computational procedure, more than 200 candidates with different geometries and spin configurations have been considered to determine the global minima of each Au19 M cluster. The low-lying isomers obtained from the optimization process are displayed in Fig. 1 with their corresponding spin states and relative energies. The followings are to discuss the geometrical structure of Au19 M clusters and the dopant-dependent progression of the cluster geometry as M goes from Sc to Cu. The isomers are labeled with additional A, B, C, and D letters to indicate their increasing order of energy.

For the lightest dopants (M = Sc and Ti), their ground states prefer a singlet and doublet cage-like structure with a dopant atom occupied at the center site, respectively. The growth of Au19 Sc and Au19 Ti can be established by differently incorporating five Au atoms to a distorted bicapped hexagonal antiprism Au14 @Sc/Ti core. The cage-like hexagonal antiprism-based structures are also found for other low-lying isomers, confirming the stability of this structural pattern. Because of the structural similarity between these isomers, the difference in their relative energies is expectedly small, about the order of 0.2 eV for Au19 Sc and 0.1 eV for Au19 Ti. Attention should be paid for the case of Au19 V, which has four possible ground-state structures. A distorted truncated pyramid with a central V atom is determined as the ground-state structure (Au19 V-A, 0.00 eV) with quintet state. The next structural isomer Au19 V-B again has an endohedrally-doped cage-like geometry, which 6


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is analogous to those of Au19 Sc and Au19 Ti ground states, with a relative energy of 0.03 eV. The third isomer (Au19 V-C, +0.07 eV) is a spin isomer with triplet state. Noticeably, the fourth isomer lying at +0.09 eV higher in energy (Au19 V-D) is found in form of a highsymmetry golden tetrahedron with a surface-central V atom. It is worth to mention that the same structural motif has been reported for Au19 Cr, Au19 Mn, and Au19 Fe clusters. In particular, these systems also favor the tetrahedral packing unit as the ground-state structures, in which the dopant atom isomorphously substitutes for a gold atom on the surface center. For heavier 3d impurities, it is surprising that gold atoms still adopt a nearly-perfect tetrahedral structure while the transition metal dopant keeps occupying the surface central site. Their next isomers are generally less stable in form of an endohedrally-doped truncated pyramid and a tetrahedron with a substituted dopant atom on the edge. It should be noted that the Mn doped Au19 cluster has a degenerate structural (truncated pyramid) isomer lying +0.08 eV above its corresponding ground state (quintet) and a spin isomer (septet) with a relative energy of +0.14 eV.

From the geometrical characteristics described above, the structural evolution of Au19 M when M moving from the begin to the end of the first-row transition metals can be revealed. It is obvious that for M = Sc and Ti the most stable form of Au19 M clusters is an endohedrally-doped cage-like structure. The aggregation of gold atoms and heavier dopants (Cr, Mn, Fe, Co, Ni, and Cu) shows a preference on building-up the tetrahedral structure with the dopant locating at a surface center. Similar features were observed earlier for Aun M+ cations, in which clusters with heavy dopants shows the magic number 20 while those with light dopants manifest the magic number 18. 32 This can be understood in relation to a modification of the effective mean field potential by changing from the tetrahedral to cage-like (or spherical) geometry. A structural competition appears at Au19 V, where the truncated pyramid seems to be the lowest-energy structure but the endohedral cage and the tetrahedron with a substituted dopant atom on the surface center are also found very stable

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at +0.03 and +0.09 eV, respectively. With this picture in mind, the Au19 V cluster can be considered as a transition point, where the structure of Au19 M clusters starts turning from the cage-like to the tetrahedral geometry due to the overwhelming stability of the pyramid Au20 . This observation can be understood in term of their dimer binding energies, which reflect the relative strength of Au-Au and Au-M bonds. The binding energy per atom (BE) of the doped clusters is defined as the average difference between the total energy of the cluster and the energy sum of all the free atoms constituting the cluster as follows:

BE =

nEAu + EM − Ec BE = , n+1 n+1

(1)

in which BE is the binding energy of the cluster. EAu , EM , and Ec are the total energy of the Au atom, the dopant, and the doped cluster, respectively, while n is defined as the number of gold atoms (for AuM dimers, n = 1). Figures 2(a) plots binding energy (in eV) of AuM dimers normalized with their pure counterpart. The exact values of binding energies and corresponding spin states of AuM dimers are presented in Table S1 in the Supplementary Information. 33 Our calculations show that the Au-Sc and Au-Ti interactions (BE = 3.04 and 2.98 eV, respectively) are considerably stronger than that of Au-Au one (BE = 2.27 eV). Thereby, substituting one Au atom by one Sc/Ti atom is expected to trigger a structural transformation in the pyramidal Au20 . The endohedrally-doped cage-like structure with the central dopant becomes most favored for the Au19 Sc and Au19 Ti clusters since it can maximize the number of strong AuM bonds and enhance the cluster stability. This argument is in line with literature where the same structural motif has been reported for several doped gold clusters with strong Au-dopant bonds. For instance, the ground state of Al- and Hfdoped Au19 clusters also prefers a cage-like structure in which the doping atoms is surrounded by the surface gold atoms. 34 Like the AuSc/AuTi bond strength, the experimental value of BE for AuAl dimers is about 3.37 eV, considerably larger than that of Au2 . 35 For M = Cr, Mn, Fe, Co, Ni, and Cu, the AuM interaction strength draws an opposite picture, in

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which their dimer binding energies are comparable to that of Au2 (with a difference of less than ±0.2 eV). As a matter of fact, doping these atoms results in a negligible effect on the tetrahedral structure of the gold cluster. Earlier studies of the Au19 doped with Na, Pt, Rb, and Cs showed a similar story, 36,37 where the pyramidal structure is energetically preferred with a surface-center dopant atom. In these species, the cage-like structure with endohedral doping is found to be significantly less stable. As expected, the binding energies of AuNa, AuPt, AuRb, and AuCs are 2.22, 2.66, 2.51, and 2.62 eV, respectively, which are comparable (Na) and slightly higher (Pt, Rb, and Cs) than that of the Au2 one. 35–37 Our structural analysis shows that for the V dopant, the exhohedrally-doped tetrahedral structure of Au19 V is almost as stable as the endohedrally-doped cage-like structures. The coexistence of Au19 V tetrahedral structure with exohedral doping and cage-like structure with endohedral doping is in line with the binding-energy picture of AuM dimers. The BE value of the AuV dimer is 2.70 eV, which is larger than that of AuCr, AuMn, AuFe, AuCo, AuNi, and AuCu but is smaller than that of AuSc and AuTi ones. This value, which is sufficient for the Au19 M cluster to provoke a structural distortion from the tetrahedral to cage-like geometry, can be considered as a critical point for predicting structures of doped gold species in future studies.

Relative stability and dissociation behavior The binding energy can also reflect the thermodynamic stability of a cluster. Figure 2(b) plots the binding energy per atom of Au19 M as a function of dopant M. It is pointed out that the binding energy per atom BE of Au19 M clusters can be divided into two different regimes. For M = Cr, Mn, Fe, Co, Ni, and Cu, the BE values are similar to the pure counterpart, while those of Au19 V, Au19 Ti, and especially Au19 Sc are obviously larger. This observation suggests stronger interactions between the atoms in V, Ti, and Sc doped Au19 clusters than in Cr, Mn, Fe, Co, Ni, and Cu doped Au19 clusters, which can be explained by the enhanced binding strength between V/Ti/Sc and Au as well as the increased number 9



of V/Ti/Sc-Au bonds in the cage-like structure. It is also confirmed that the structural transition point occurs at M = V, from that either the cage-like structure or the tetrahedral structure becomes more energetically competitive than the other. In the other words, the stability of a cluster doped with lighter dopants (Sc and Ti) is enhanced for the cage-like structure while a cluster doped with heavier dopants (Cr, Mn, Fe, Co, Ni, and Cu) is most stable with the tetrahedral form.

The binding energy per atom, which is an average sum of all binding energies, nevertheless may not tell us about the intrinsic stability of a cluster. For example, a cluster with a large average binding energy might contain a weak bond and becomes less stable than a cluster with a lower average binding energy. In this regard, the dissociation energy (DE) a minimum amount of energy required to break a cluster into smaller pieces is often used to identify stability patterns. 39–42 The clusters associated with larger DE are usually more stable and can be identified as higher-intensity species in photofragmented spectra. In addition, since the dissociation process has the tendency to terminate at sizes and stoichiometries with enhanced stability, the energetic competition between possible dissociation pathways of an excited cluster system also gives valuable information on the stability of the formed daughters. To examine the dopant-dependent stability of Au19 M clusters, their DEs corresponding to plausible dissociation channels, 43 (i) Au19 M → Au19 + M and (ii) Au19 M → Au18 M + Au, are computed. The results are listed in Table 1. In our calculations, these energies are obtained using the lowest-energy structures and spin states for parents and daughters. The optimized structures of Au19 and Au18 M clusters are given in the Supplementary Information. 33 The energy required to fragment Au20 into Au19 and an Au atom, which is the most plausible dissociation channel of pyramid Au20 , 44 is determined as about 3.12 eV for comparison. It can be seen that for all doped Au19 M clusters, the evaporation of one Au atom to form Au18 M is the most energetically preferred dissociation channel. Except for Au19 Mn, the lowest dissociation energies of clusters with heavier dopants (M = Cr, Fe,

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Co, Ni, and Cu) are greater than or equal to those with lighter dopants (M = Sc, Ti, and V). This feature could be related to the unique stability of the tetrahedral structure over the cage-like one rather than their specific electronic structures. The energy required for Au19 M clusters to decay into Au19 and one M atom is considerably higher, especially for Sc, Ti, and V doped species. This could be understood by the larger number of M-Au bonds in their corresponding cage-like ground-state structures with the central dopant (Sc, Ti, and V) as well as their strong dimer (ScAu, TiAu, and VAu) binding energies. Among studied clusters, Au19 Cr, Au19 Co, Au19 Ni, and Au19 Cu are more stable by demanding no less than 2.70, 2.76, 3.01, and 3.11 eV to release a Au atom, respectively. The least stable species is Au19 Mn since the minimum energy to trigger its fragmentation process is 2.18 eV only. This particular behavior of Au19 Mn can be explained by the reduction of the tetrahedral stability as a consequence of the stronger displacement of Mn atom from the center surface of the cluster compared to others. 22

It is worth to mention that the relative stability of Au19 M+ was observed in the mass 32 Mass abundance spectra of photofragmented transition metal doped Au+ n cationic clusters.

spectra recorded after photofragmentation reflect a size distribution with higher abundance for more stable species. Distinct intensity peaks were seen at Au19 Cr+ and Au19 Co+ , suggesting that they are highly stable. Since these clusters have an open-shell electronic structure, one might expect a negligible influence of electronic structures on their dissociation behavior. From this perspective, the enhanced abundance of Au19 Cr+ and Au19 Co+ is in a very good agreement with our calculated dissociation energies and above-discussed stability picture for their neutral counterparts. On the other hand, although Au19 Mn and Au19 Fe are less stable than other tetrahedral Au19 M species in terms of dissociation energies, the small drops appearing after Au19 Mn+ and Au19 Fe+ in photofragmented mass spectra imply that they are relatively stable compared to their neighboring-size species. A similar explanation can be applied for the clear intensity step recorded at Au18 Ni+ instead of Au19 Ni+ , implying that

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Au19 Ni+ might be less stable than its neighboring-size ones.

The reactivity potential and chemical stability of Au19 M clusters can be measured by the energy gaps between the LUMO of the minority spin and the HOMO of the majority spin

minor δ1 = −(major HOM O − LU M O )

(2)

and between the LUMO of the majority spin and the HOMO of the minority spin

major δ2 = −(minor HOM O − LU M O ).

(3)

They are the required amounts of energy for an electron to jump from the HOMO of majority (minority) spin channel to the LUMO of minority (majority) one. The larger value means the less reactive or more chemically stable clusters, and vice versa. 45–47 For closed-shell systems, δ1 and δ2 are identical and equal to the HOMO-LUMO gap. The calculated HOMO and LUMO energies for the majority and minority spin channels and the corresponding values of δ1 and δ2 are presented in Table 1. For comparison, the HOMO-LUMO gap of Au20 tetrahedron (1.80 eV) is calculated, which is in an excellent agreement with the experimental value (1.77 eV). 17 With a very large HOMO-LUMO gap of 1.76 eV and a high dissociation energy of 3.11 eV, it can be concluded that the non-magnetic tetrahedral Au19 Cu is extremely stable and it chemical stability can be comparable to that of the unique Au20 pyramid. These might be a hint about the possibility of consecutively substituting one Au atom by one Cu atom in Au20 with negligible effects expected on its chemical and physical properties. The closed-shell Au19 Sc system has a smaller HOMO-LUMO gap, 1.26 eV, but this value is still remarkable, suggesting that Au19 Sc is stable and less reactive. For opened-shell systems, all energy gaps δ1 and δ2 take positive values, suggesting that they are, in general, chemically stable. The energy gaps of Au19 Mn and Au19 V are smallest (0.26 and 0.30 eV, respectively), implying that they are more reactive than other clusters while Au19 Cr is least 12


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reactive with a highest energy gap (0.78 eV). In addition, the NBO atomic charges are calculated and included in Table 1 to illustrate the electron distribution in the dopants and their bonding nature. The dopant atomic charge takes negative values in all studied clusters, meaning that there are charge transfers from the Au host to the dopants and the interactions between the dopants and the Au atoms are essentially ionic-like bonding. Notably, the charge transfers in endohedrally-doped species (from -4.61 to -3.53) are much significant than those in exohedrally-doped ones (from -0.87 to -0.28), suggesting a considerable enhancement of interactions between lighter dopants (Sc, Ti, and V) and Au atoms. This finding supports the above discussion, in which these dopants favor the central position and the required energy to dissociate them is much higher than that of heavier ones.

Magnetic moments The magnetic behavior of Au19 M clusters is the most intriguing finding. It is worth to mention that the magnetism of localized electronic states in a finite electron cloud has been a subject of significant research because of its potential in unveiling the smallest-size structures from that exciting phenomena as the Friedel oscillation, the Kondo effect, or the magnetic superatoms may show up. 10,48 To approach this picture, Hirsch and coworkers have considered a system of Cr doped Au+ n clusters (n = 2-9), in which a typical magnetic impurity is incorporated into a well-controlled pool of valence electrons. 48 While 3d electrons of the Cr atom carry a local magnetic moment, the number of gold atoms in the cluster defines the number of free electrons interacting with the impurity. Tuning the cluster size would allow them to see how the impurity magnetic moment interacts with different numbers of free electrons.

Here, nevertheless, by investigating dopant effects on the unique golden pyramid Au19 M we deal with an alternative picture, where the interaction of a fixed valence electron cloud with various localized states of a single magnetic impurity can be examined in a uniquely 13



stable host. Figure 3 displays TMMs of the ground-state Au19 M clusters and corresponding LMMs on the dopant. Except for Au19 V, all lowest-lying isomers of Au19 M clusters favor the same spin states as their ground-state ones. While other clusters exhibit their uniqueness of the spin configuration, the magnetic ground-state of Au19 V (quintet) is degenerate with an energy of only 0.03 eV to attain the nearest magnetic state (triplet). Interestingly, the magnetism evolution of Au19 M clusters shows a systematic dopant-dependent behavior. In particular, the TMM of Au19 M clusters increases when M going from Sc to Cr but gradually declines as M going from Cr to Cu. The TMM of Au19 Sc and Au19 Cu are completely quenched while Au19 Cr has the largest TMM of 5 µB . For all studied Au19 M clusters, the magnetic moment is mainly found on 3d state electrons of the dopant. A small amount of magnetic moments is contributed by the 6s states of the Au host. The 4s and 4p states of the dopant has almost no contribution to the corresponding TMMs. This picture can be visualized by plotting the spin distribution of the obtained energy minima structures. As illustrated in Fig. 3, the total spin gradually increases and then decreases when M goes from Sc to Cu with a maxima at M = Cr. Except for non-magnetic Au19 Sc and Au19 Cu clusters, the total spins of other species mainly locate at the dopant position (endohedral site for M = Ti and V, and surface site for M = Cr, Mn, Fe, Co, and Ni). A minor amount of ferrimagnetic spin alignments is found in Au atoms in cases of Au19 V and Au19 Cr, which is in good agreement with their TMM and LMM values.

A detailed analysis of the magnetic evolution allows to understand the interplay between the electronic structure and the observed magnetic features of Au19 M clusters. Their total and local magnetic moments are disclosed in Table 2, together with the atomic electron configuration of the dopant M. At this point we restrict ourselves to a qualitative interpretation based essentially on the phenomenological shell model. In fact, the existence of closed electronic shells in compliance with the 20-electron rule has been observed for Au19 M (M = Cr, Mn, and Fe). 22 A closer study on molecular orbitals of these clusters shows that shared

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valence electrons from both the Au19 host and the dopant form two sets of bonding and nonbonding electronic states. The first set composed of delocalized electrons fills the 20-electron supershell. The second set consisting of localized electrons cause the cluster magnetic moments. The contribution of the Au host and the dopant on the LMMs can be used to extract their itinerant behavior. In particular, the numbers of delocalized nd and localized electrons nl stemming from the dopant are estimated and listed in Table 2, respectively. The total number of dopant valence electrons nv that includes both delocalized and localized electrons (nv = nd + nl ) is also presented. For example, if each gold atom supplied one 6s electron, the vanadium atom has to donate at least two electrons to the bonding set (nd = [2]) and three others localize at the majority spin channel of its d atomic orbitals (nl = [3]) to match the magic number 20 and a LMM of 2.76 µB . It means that the vanadium atom contributes all five valence electrons (nv = 5) from its outermost electronic shells 3d3 4s2 . The degenerate triplet state of Au19 V is therefore established by the contribution of three electrons from V atom, corresponding to the 3d3 valence states. Pursing this argumentation, the Cr atom in Au19 Cr would contribute all six valence 3d5 4s1 electrons (nv = 6) to exhibit the magnetic moment of 5 µB . The valency behavior of other dopants is somewhat different: only their unpaired d valence electrons are used together with valence electrons from the gold host to yield the filled cluster shells and to produce their magnetic moment. For instance, the magnetic feature of Au19 Mn (4 µB ) can be linked with the 20-electron shell closure if only five d valence electrons of the manganese atom were considered (nv = 5). A rather unexpected feature is the observation of 20-electron rule for endohedral spherical-like Au19 Sc and Au19 Ti clusters. Although 18 is often known as a magic number for spherical doped Au systems, 32,49 the application of 20-electron shell closure to these clusters is still valid with a suitable adjustment. The central dopant in this case may stimulate a modification from the center of the cluster potential, leading to a further upward shift of the 2S molecular orbitals relative to the corresponding 1D and decreasing the gap between 2S and 1F . The smaller HOMO-LUMO gap of Au19 Sc compared to that of Au19 Cu confirms this argument.

15



As an important point of predictive efforts is to find plausible structures for experimental realization, it is interesting to comment on how these finding superatoms can be linked to readily produced related systems. Attempts to chemically synthesize and stabilize Au20 superatoms have shown that Au16 Ni24 (CO)40 ]4− can be considered as the solution version of this 20-electron system. 50,51 Both [Au16 Ni24 (CO)40 ]4− and Au20 share a common tetrahedral [Au16 ]4− central core with an electronic configuration of 1S 2 1P 6 2S 2 1D10 . In Au20 , the [Au16 ]4− core is capped by four Au+ cations, whereas it is capped by four Ni6 (CO)10 units in [Au16 Ni24 (CO)40 ]4− . The bonding nature between the [Au16 ]4− core and the Ni6 (CO)10 fragments has been found similar to that of the [Au16 ]4− core and the Au+ ions in Au20 , which is mainly associated with a delocalization of the 20 valence electrons. 51 Since the Au19 M species can be generally viewed as a superatomic core composed of 20 valence electrons with a localized magnetic shell, it should be possible to experimentally obtain them in a similar way to their bare gold counterparts. The solution version of Au19 M clusters thus can be imagined as made of the [Au15 M]4− core embedded in the outer shell Ni24 (CO)40 . It is also worth to mention that systems with higher doping concentrations, i.e. Au18 M2 , Au17 M3 , and Au16 M4 , would be promising for future studies owing to their potential as giant magnetic and highly symmetric superatoms. Nevertheless, the potential position of the next transition metal dopants would be a puzzling question, especially for those with M = Sc, Ti, and V. For systems with M = Cr, Mn, Fe, Co, Ni, and Cu, even the dopant atom apparently prefers substituting one Au atom in the surface center of singly doped species, the situation is not straightforward when increasing the doping concentration. It should be noted that the unique stability of the golden pyramid Au20 can be explained in terms of a superatomic core Au16 binding with four vertex Au atoms. 20 This core-shell motif has also been reported 2+ in the tetrahedral Au+ 17 and Au10 . These two systems are highly stable in form of Au13

and Au6 octahedral cores, respectively, capped by four Au atoms above four their triangular faces. 52,53 Therefore, the structural prediction of Au20−X MX as well as their smaller sisters,

16


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2+ Au17−X M+ X and Au10−X MX (X = 2-4) is a challenging task and a careful examination of

this issue is perhaps interesting for future research.

Conclusions The structure, stability, and magnetic properties of the gold cluster doped with transition metal atoms, Au19 M (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu), have been investigated within the framework of the density functional theory. Species with lighter dopants (M = Sc and Ti) prefer the endohedrally-doped cage-like structure while those with heavier ones (M = Cr, Mn, Fe, Co, Ni, and Cu) tend to retain the tetrahedral structure from the pure Au20 with the surface-center dopant. The structural preference of Au19 M depends on the AuM dimer bond strength, in which the value of AuV can be considered as a critical point. All studied clusters are found relatively stable in terms of average binding energies and lowest dissociation energies. Exceptional stabilities are determined for Au19 Cr, Au19 Co, Au19 Ni, and Au19 Cu. A comprehensive picture of the magnetic behavior is shown for Au19 M clusters, in which the observed dopant-dependent magnetic moment can be understood by not only the co-existence of the 20-electron shell closure and the localized magnetic states but also the itinerant behavior of impurity valence electrons. We hope that this work will be useful for understanding physics of magnetic impurities in nonmagnetic metal clusters and could lead to rational designs of novel superatoms with a desired magnetic shell.

Supporting Information Spin states and dissociation energies (eV) of AuM (M = Au, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) systems; Optimized geometries and spin states of ground-state Au19 and Au18 M clusters.

17



Acknowledgement This research is funded by Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), website: http://fostect.tdtu.edu.vn, under Grant FOSTECT.2017.BR.03.

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23



CAPTIONS

Figure 1. The structures, spin multiplicities (superscript), and relative energies (in eV) of low-lying isomers for Au19 M (M = Sc-Cu). The isomers are labeled with additional A, B, C, and D letters to indicate their increasing order of relative energies.

Figure 2. The binding energy BE (in eV) of (a) AuM dimers and (b) binding energy per atom BE of Au19 M clusters normalized with those of Au20 and Au2 , respectively.

Figure 3. The evolution of total magnetic moments (TMM, in µB ) of ground-state Au19 M clusters and corresponding local magnetic moments (LMM, in µB ) of the dopant. The insets illustrate the total spin distribution of the obtained energy minima structures plotted at a density of 0.004. The navy basins stand for alpha-spin while the green ones represent beta-spin.

Table I. DE (in eV) to evaporate a Au (or M) atom from Au19 M clusters, calculated HOMO and LUMO energies (in eV) of the majority and minority spin channels, corresponding values (in eV) of δ1 and δ2 , and natural bonding orbital atomic charges (qN BO in e) on M atom.

Table II. Atomic electron configuration of the dopant M, total magnetic moment (TMM, in µB ) of the Au19 M clusters, local magnetic moment (LMM, in µB ) on the dopant M and on the Au host, and the estimated numbers of delocalized nd , localized nl , and valence electrons nv stemming from the dopant. The brackets stand for rounding-off values.

24


Page 24 of 35

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Au19Sc-A 0.001

Au19Sc-B 0.151

Au19Sc-C 0.161

Au19Sc-D 0.171

Au19Ti-A 0.002

Au19Ti-B 0.042

Au19Ti-C 0.052

Au19Ti-D 0.072

Au19V-A 0.005

Au19V-B 0.033

Au19V-C 0.073

Au19V-D 0.095

Au19Cr-A 0.006

Au19Cr-B 0.336

Figure 1

25


Au19Cr-C 0.486


Page 26 of 35

Au19Mn-A 0.005

Au19Mn-B 0.085

Au19Mn-C 0.147

Au19Fe-A 0.004

Au19Fe-B 0.234

Au19Fe-C 0.294

Au19Co-A 0.003

Au19Co-B 0.163

Au19Co-C 0.403

Au19Ni-A 0.002

Au19Ni-B 0.262

Au19Ni-C 0.322

Au19Cu-A 0.001

Au19Cu-B 0.291

Au19Cu-C 0.521

Figure 1: (Cont’)

26


BE(Au19M) - BE(Au20) (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


BE(Au-M) - BE(Au2) (eV)

Page 27 of 35

1.0 tetrahedral structure

(a)

0.5 cage-like structure

0.0

transition point Sc

Ti

V

Cr

Mn

Fe

Co

Ni

transition point

0.2

tetrahedral structure

Cu

(b)


0.0

Sc

Ti

V

Cr

Mn

Fe

Figure 2

27


Co

Ni

Cu


8

Total magnetic moment Local magnetic moment on M atom

7 Magnetic moment ( B)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 35

6 5.0

5

4.19

4.0

4 3

4.0

3.77 3.0

2.76

2.78 2.0

2 1.0

1 0

1.88 1.0 0.83

0.78

0.0 0.0

0.0 0.0

Sc

Ti

V

Cr

Mn

Fe

Figure 3

28


Co

Ni

Cu

Page 29 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1 Clusters Au20 Au19 Sc Au19 Ti Au19 V Au19 Cr Au19 Mn Au19 Fe Au19 Co Au19 Ni Au19 Cu

DE Au-atom loss M-atom loss 3.12 2.59 2.32 2.25 2.70 2.18 2.59 2.76 3.01 3.11

7.34 6.37 4.88 3.89 4.03 4.21 4.08 4.09 3.81

alpha HOM O

beta HOM O

-5.86 -5.57 -5.41 -4.99 -5.62 -4.86 -5.79 -4.83 -4.44 -5.86 -4.66 -5.84 -4.84 -5.60 -5.05 -5.60 -5.81

29

alpha LU M O

beta LU M O

-4.05 -4.31 -4.49 -4.58 -4.22 -4.56 -4.06 -4.05 -4.18 -4.31 -4.08 -4.10 -4.10 -4.22 -4.06 -4.89 -4.05


δ1

δ2

1.80 1.26 0.41 0.92 0.30 1.40 0.78 1.73 1.55 0.26 1.74 0.58 1.38 0.74 0.71 0.99 1.76

qN BO -4.61 -4.32 -3.53 -0.87 -0.72 -0.63 -0.43 -0.44 -0.28


Page 30 of 35

Table 2

M Sc Ti V Cr Mn Fe Co Ni Cu

Valence 3d1 4s2 3d2 4s2 3d3 4s2 3d5 4s1 3d5 4s2 3d6 4s2 3d7 4s2 3d8 4s2 3d10 4s1

TMM 0 1 4 5 4 3 2 1 0

nd

nl

nv

4s-M

LMM 4p-M 3d-M 6s-Au

0 0 -0.01 0.02 0.01 0.01 0 0 0

0 0.01 0 0.06 0.01 0.01 0 0 0

1 [1] [2] [2] [1] [1] [1] [1] 1

0 [1] [3] [4] [4] [3] [2] [1] 0

1 2 5 6 5 4 3 2 1

30

0 0.78 2.76 4.19 3.77 2.78 1.88 0.83 0


0 0.26 1.24 0.81 0.23 0.22 0.12 0.17 0

Page 31 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Au19Sc-A 0.001

Au19Sc-B 0.151

Au19Sc-C 0.161

Au19Sc-D 0.171

Au19Ti-A 0.002

Au19Ti-B 0.042

Au19Ti-C 0.052

Au19Ti-D 0.072

Au19V-A 0.005

Au19V-B 0.033

Au19V-C 0.073

Au19V-D 0.095

Au19Cr-A 0.006

Au19Cr-B 0.336


Au19Cr-C 0.486


Page 32 of 35

Au19Mn-A 0.005

Au19Mn-B 0.085

Au19Mn-C 0.147

Au19Fe-A 0.004

Au19Fe-B 0.234

Au19Fe-C 0.294

Au19Co-A 0.003

Au19Co-B 0.163

Au19Co-C 0.403

Au19Ni-A 0.002

Au19Ni-B 0.262

Au19Ni-C 0.322

Au19Cu-A 0.001

Au19Cu-B 0.291

Au19Cu-C 0.521


BE(Au19M) - BE(Au20) (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

BE(Au-M) - BE(Au2) (eV)

Page 33 of 35


1.0 tetrahedral structure

(a)


0.0

transition point Sc

Ti

V

Cr

Mn

Fe

Co

Ni

transition point

0.2

tetrahedral structure

Cu

(b)


0.0

Sc

Ti

V ACS Paragon CrPlus Environment Mn

Fe

Co

Ni

Cu


Magnetic moment ( B)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Page 34 of 35

8

Total magnetic moment Local magnetic moment on M atom

7 6 5.0

5

4.19

4.0

4 3

4.0

3.77 3.0

2.76

2.78 2.0

2 1.0

1 0

1.88 1.0 0.83

0.78

0.0 0.0

0.0 0.0

Sc

Ti

V

Cr

Mn


Fe

Co

Ni

Cu

Page 35 of 35

Magnetic moment (B)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


7

Total spin moment Local spin moment on M atom

6 5 4 3 2 1 0

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

The evolution of geometric structures and total/local spin moments (µB) of Au19M clusters (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and Cu)


Ultimate Manipulation of Magnetic Moments in the ... - ACS Publications

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