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Theoretical Investigation on Metallic Hetero-fullerenes of Silicon and Germanium Mixed with Phosphorus and Arsenic Atoms M-A8E6, A = Si, Ge, E = P, As and M = Cr, Mo, W Hung Tan Pham, and Minh Tho Nguyen J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 08 Jun 2017 Downloaded from http://pubs.acs.org on June 9, 2017

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The Journal of Physical Chemistry

Theoretical Investigation on Metallic Hetero-fullerenes of Silicon and Germanium Mixed with Phosphorus and Arsenic Atoms M-A8E6, A = Si, Ge, E = P, As and M = Cr, Mo, W

Hung Tan Phama,b and Minh Tho Nguyena,b,c,* a)

Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam b)

Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

c)

Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium

(Abstract) Recently, metallic hetero-fullerenes were experimentally prepared from mixed Ge-As clusters and heavier elements of groups 14 and 15. We found that shape of these hetero-fullerenes doped by transition metal appears to be a general structural motif for both silicon and germanium clusters when mixing with phosphorus and arsenic atoms. Structural identifications for MSi8P6, MSi8As6, MGe8P6 and MGe8As6 clusters, with M being a transition metal of group 6 (Cr, Mo and W), showed that most MA8E6 clusters, except for Cr-doped derivatives CrSi8As6, CrGe8P6 and CrGe8As6, exhibit a high symmetry fullerene shape in which metal dopant is centered in D3h A8E6 hetero-cage consisting of six A3E2 pentagonal faces and three A2E2 rhombus faces. The stability of MA8E6 metallic hetero-fullerene is significantly enhanced by formation an electron

*

Emails: [email protected]; [email protected]; [email protected]

ACS Paragon Plus Environment

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configuration of [1S2 1P6 1D10 1F14 1G18 2S2 2P6 2D10] enclosing 68 electrons. The A8E6 heterocages give a great charge transfer (~4 electrons) to centered dopant, establishing subsequently a d10 configuration for metal, and as a consequence it induces an additional stabilization of the resulting ME8P6 fullerene in a high symmetry D3h shape, and completely quenches the high spin of the metal atom finally yielding a singlet spin ground state. 1. Introduction Both silicon and germanium elements are essential for semiconductors and optoelectronic industries.1,2,3,4 Development of new and tiny electronic devices has attracted much interest in the basic studies of the geometric, electronic, thermodynamic and spectroscopic properties of small Si5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 and Ge23,24,25,26,27,28,29,30,31,32,33,34,35,36,37 clusters and their doped varieties. The main objective of such investigation is a search for appropriate cluster units that can be used as building blocks for different materials whose properties can effectively be controlled by changing the cluster size as well as the nature of the elements and dopants. In this context, incorporation of dopants encapsulated in a cage-like Si and Ge cluster has extensively been studied to generate doped clusters with properties completely different from those of pure clusters.38,39,40 In view of the low stability of the bare Si and Ge clusters, metals (M) tend to stabilize the resulting doped clusters in a variety of special sizes and shapes, and thus they can serve as building block for assembly materials. With magnesium as dopants, [MgSin] units can connect each other using Mg atoms as linkers to make nanowires.41 Other examples such as the MSi16 clusters (M = Sc, Ti and V), that are of high symmetry and stability, were theoretically predicted to form the ScSi16-VSi16 hetero-dimer and ScSi16-TiSi16-VSi16 hetero-trimer.42 A metal– silicon tubular structure was synthetized on the basis of BeSi12 hexagonal prismatic structure.43 Introduction of transition metal also provides a magnetic moment for doped silicon clusters.44,45,46


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The stability of various singly transition metal doped Si clusters has frequently been explained by the 18-electron rule where the d levels of M atom are fulfilled. WSi12,47,48 CrSi14,49 and FeSi1450 having high symmetry structure and singlet spin state can be viewed as examples where the 18electron rule is satisfied. Indeed, this electron count successfully rationalizes the interplay between the electronic ground state and shape of many singly doped MSi12 clusters.51,52 However, many exceptions of this count have also been found, that include among others CrSi12 (16 electrons) 49 MSi16 (20 electrons)53 or USi206- (32 electron).54 The high thermodynamic stability of M-doped Si clusters has been rationalized in terms of strong overlap of d-AOs(M) and sp-AOs (Si atoms), whose resulting electron shells are fully occupied. For instance, the high spin of the Mn+ cation in MnSi14+ is completely quenched,55 and the delocalized electrons of the cation fully occupy the [2S, 2P, 2D] shells. On the contrary, while cobalt dopants also stabilize Si clusters yielding different high symmetry forms, their high spin states are in part kept, and lead to some interesting magnetic properties of the resulting Co-doped Si clusters.56,57 A Mn2 unit is vertically attached within a Si15 tube and enjoys stabilizing orbital interaction with this host giving rise to a stable triple ring Mn2Si15 in which the high spin of metal atom is also quenched.58 Stability of M2Si12 prism and anti-prism shapes (M2=Nb2, Ta2, Mo2, W2, NbMo and TaW) is majorly contributed by strong overlap of d-AOs(M) and sp-AOs (Si atoms) where the orbital interaction of M2 with Si12 host reveals a bimetallic configuration.59 With respect to the pure germanium clusters,60 geometries of doped Ge clusters are also greatly modified where many high symmetry structures have been observed. Despite their richness in physical and chemical properties, systematic exploration on Ge clusters doped by 4d and 5d transition metals is more limited than their Si counterparts. As indicated by previous investigations, the formation of (5/5) MGe10q prismatic shape, a structural motif where M is located at the central


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position of (5/5) Ge10 prism, is significantly influenced by the nature of metallic dopant. Of the Mdoped germanium clusters, CoGe103- and FeGe103- exhibit in a remarkable form in which the M atom is centered in D5h (5/5) Ge10 prism.61,62 The same shape was observed for RuGe102-, and AuGe10-, but they are significantly unstable.71,73 A prism shape is actually degenerate with an incomplete icosahedral form for the ground state of MoGe10 cluster.70 It is clear that the nature of M plays an essential role in the formation of D5h MGe10q prismatic shape. Dependence of growth pattern of transition metal doped Ge clusters has abundantly been found with respect to the nature of metal dopants. For instance, the Co dopant prefers to be located inside a Gen cage from the size n = 9, whereas an endohedral shape has been observed at the size of NiGe8.63,64,65 The VGe9- is again identified as a transition between exohedral and endohedral forms, whereas VGe12 is stable in a distorted hexagonal prism.66 Geometry and stability, and topology of chemical bonding of small sizes CrGen,36 and LinGem67 and enhanced stability of some clusters in this series can be understood by formation of a closed electron shell configuration.68 Regarding to WGen clusters, the endohedral form is dominated in the size of n = 8-17.69 A hexagonal prism structure was found for MoGe1270 whereas Ru and Zr dopants turn out the incomplete cage for RuGe12 and ZrGe12 clusters.71,72 Also with size containing 12 Ge atoms, AuGe12- presents interestingly an icosahedral Ih structure.73 Other doped Ge clusters have also been characterized including the lithium,74,75 and titatium76 derivatives. Recently, the mixed [VGe8As4]3- and [NbGe8As6]3- clusters were experimentally prepared in the laboratory.77 Structural identifications showed that both V and Nb dopants are situated in the central region of Ge8As4 and Ge8As6 hetero-cages, respectively. This structural motif is also observed for heavy elements of groups 14 and 15. For instance, the structural characterizations for [LnPbxBi14-x]q and [LnPbyBi13-y]q clusters with x/q = 7/4, 6/3 and y/q = 4/4, 3/3 indicate that


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PbxBi14-x and PbyBi13-y turn out to be hetero-fullerenes in which each Ln atom occupies the central site.78 These results suggest that a multiple doping of group 15 elements appears to be an efficient way of producing a stable fullerene structure for group 14 elements. The brief literature survey given above emphasizes that a combined effect between transition metal atoms and group 15 elements can lead to a stabilized hetero-fullerenes for Ge-based clusters. However, study on mixed Ge-P systems is rather rare, and no comparative investigation on the effect of metals from the same group of the Periodic Table has been reported. Particularly, the simplest mixed Si-P and Si-As clusters doped by M atoms are not considered yet, even though some new structural motifs were found for both doped Si and Ge clusters. With the aim to search for novel prototypes of Si and Ge clusters, we set out to carry out, and report in this paper, a theoretical investigation on the geometric and electronic structure of a series of MA8E6 clusters in which A is Si or Ge atom, and the mixture between P and As atoms is in a proportion of 8A/6E. Such a proportion is based on experimental observation of stable NbGe8As6 hetero-cages. As for a more systematic exploration, transition metal atoms M of group 6 including Cr, Mo and W are used as dopants. Obtained results demonstrate that the metallic hetero-fullerene, having high symmetry and low spin state, constitutes a general structural motif for stable mixed Si/Ge and P/As clusters.

2. Computational Methods To explore the potential energy surface (PES) of MA8E6 doped derivatives, we use a stochastic genetic algorithm to generate all probable initial structures.79 This approach is highly efficient in the search for structures including different compositions. Additionally, the guess structures of MSi8E6 and MGe8E6 are also manually built up by replacing six A (Si or Ge) sites of the A14 framework by P or As atoms. Combination of both search approaches leads to a good convergence


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for the ground state structure, as well as for the lower-lying structures of a specific cluster. All electronic structure computations and geometry optimizations are carried out with the aid of the Gaussian 09 suite of programs.80 Equilibrium structures are first optimized from initial guess structures using low-level computations (using the DFT/B3P86 functional81 and the LANL2DZ basis set). Lower-lying equilibrium structures obtained are subsequently reoptimized using the same functional but with the larger aug-cc-pVTZ-PP basis set for the metals82,83 (with PP for effective core potential), and the 6-311+G(d) basis set for the Si, Ge, P and As atoms.84,85 Although a systematic exploration is carried for the low-spin states, namely both singlet and triplet states, the higher spin states are also calculated for the lower-lying isomers to identify the most stable electronic state of each cluster considered. It turns out that the higher spin states are lying much higher in energy, and they are therefore not examined further. For an analysis of the electronic distribution, we use the conventional canonical MOs, and the electron localizability indicator (ELI_D) 86 and atom in molecule (AIM) approaches.87

3. Results and Discussion 3.1 Geometries Results of extensive searches for the lowest-lying structures of the clusters considered in the low spin state are presented in Figure 1 and Figures S1-S12 of the Supporting Information (ESI) file. Structures are labelled as M.X.Y.i where M denotes a transition metal being Cr, Mo and W, X stands for Si and Ge, and Y for P and As of the Si8P6, Si8As6, Ge8P6 and Ge8As6 cages, respectively, and i = A, B, C,… indicates the isomers with increasing relative energy. Although the Cr, Mo and W atoms intrinsically exhibit high spin electronic ground state, their appearance as a dopant within a XY cage gives rise to a singlet ground state in a high symmetry hetero-fullerene for the doped MSi8P6 clusters. According to the convention for M.X.Y.i, a


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structure noted by A, such as Cr.Si.P.A (D3h 1A’1) in CrSi8P6, consistently corresponds to the global energy minimum isomer. Structurally, the Cr dopant in Cr.Si.P.A is encapsulated by a Si8P6 hetero-fullerene consisting of six Si3P2 pentagonal faces and three Si2P2 rhombus faces. Some lower-lying isomers of CrSi8P6 are displayed in Figure S1 of ESI. Many hetero-cages containing one, two or three P-P connections are found to be significantly less stable than Cr.Si.P.A. The same form is equally observed for the doped MoSi8P6 and WSi8P6 clusters. Geometries of some lower-lying isomers of both series are shown in Figure S2 and S3 of ESI file. Accordingly, these clusters tend to prefer encapsulated structures where the Mo or W dopant is centered in a D3h Si8P6 hetero-fullerene (cf. Figures S2 and S3). Of these isomers, the lowest-energy Mo.Si.P.A and W.Si.P.A have the same shape as their homologous Cr.Si.P.A (Figure 1). In both MoSi8P6 and WSi8P6 series, the structures containing direct P-P bonds are significantly less stable. Overall, the most interesting finding here is that the hetero-fullerene singlet structure M.Si.P.A is beyond any doubt the most stable isomer of the MSi8P6, and such a general tendency for M elements of group 6 thus presents a typical structural motif of the metallic hetero-fullerene family. The results of the search for MSi8As6 clusters are displayed in Figure 1, and S4, S5, S6 of the ESI file. Metallic hetero-fullerene structures are again found for MoSi8As6 and WSi8As6 derivatives. Structural determinations for MoSi8As6 and WSi8As6 clusters (Figures 1 and S5, S6) show that metal atoms are encapsulated in hetero-cage formed by combining six Si3As2 pentagonal faces and three Si2As2 faces. In comparison to their phosphorus homologous MoSi8P6 and WSi8P6 series, the arsenic atom in both MoSi8As6 and WSi8As6 clusters locates at the same position as P atom. The MoSi8As6, WSi8As6, MoSi8P6 and WSi8P6 have also the same structural motif. DFT calculations point out that CrSi8As6 is not stable in a singlet D3h cage as its homologous CrSi8P6


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structure (Figure 1). CrSi8As6 is favored in a low symmetry and triplet state cage Cr.Si.As.A, whereas the singlet D3h structure, similar to Cr.Si.P.A, is ~10 kcal/mol higher than ground state. Regarding the heavier Ge derivatives, there are some similarities and differences with respect to the Si. Although a metallic hetero-fullerene can be expected for the Ge8P6 doped by transition metals, DFT calculations point out that CrGe8P6 exhibits a low symmetry triplet ground state, rather than a D3h symmetry singlet state as in the Si homologue CrSi8P6 (Figure 1). In the lowest energy isomer Cr.Ge.P.A (C1 3A), the Cr element is surrounded by a Ge8P6 cage containing now some P-P connections. Several fullerene-like structures are located for CrGe8P6, as given in Figure S7 (ESI file), but all of them are significantly less stable than Cr.Ge.P.A. A similar behavior is found for CrGe8As6 where the triplet cage Cr.Ge.As.A having no special shape (Figure 1) is identified as the global minimum isomer. Some high symmetry structures are identified for CrGe8As6, as displayed in Figure S7, but they are less stable than Cr.Ge.As.A. These results point out that the Cr atom does not prefer to form D3h singlet hetero-cage with the Si8As6, Ge8P6 and Ge8As6 moieties. On the contrary, DFT calculations confirm that a high symmetry and singlet is the lowest energy structure of WGe8P6. The W dopant in W.Ge.P.A (D3h 1A’1) is effectively covered by a hetero-fullerene established by combination of six Ge3P2 pentagonal faces and three Ge2P2 rhombus faces giving rise to a D3h point group. The shapes of some lower-lying isomers of WGe8P6 are given in Figure S9 (ESI file), and structures possessing P-P connections are again less stable. Similarly, in the isovalence WGe8As6, the singlet hetero-cage is confirmed as its global minimum structure W.Ge.As.A (D3h 1A’1).


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Concern to the Mo doped derivatives, an extensive search for MoGe8P6 clusters, as given in Figure S8, leads to the lowest-lying structure Mo.Ge.P.A (C2v 1A1) which is however 0.7 kcal/mol more stable than Mo.Ge.P.B (D3h 1A1’). Thus, both Mo.Ge.P.A and Mo.Ge.P.B are competing for the ground state of MoGe8P6. For MoGe8As6 clusters, the high symmetry Mo.Ge.As.A (D3h 1

A’1) is found again as the ground state (Figure 1). The structural identifications given above clearly emphasize that the singlet MA8E6 clusters,

in which the metal dopant M occupies a central position of a symmetrical A8E6 hetero-cage, appears to be a preferred structural motif for both heavier metals Mo and W when interacting with Si8P6, Si8As6, Ge8P6 and Ge8As6 moieties. The lighter Cr metal adopts such a shape only with the Si8P6 moiety. With the mixed clusters Si8As6, Ge8P6 and Ge8As6, the Cr doping leads to a lower symmetry and higher spin structure. 3.2 Bond indices in D3h hetero-fullerenes. In view of the new structural motif, it is necessary to probe the chemical bond distribution induced when metal dopant interacts with the main elements of the A8E6 cage, as well as the connections of the P, As atoms with the Si or Ge sites. For this purpose, the Wiberg bond indices (WBI) are calculated for all D3h hetero-fullerenes examined. For a comparison, the bond lengths and WBI of free diatomic species are also given in Table 1. The Si2 and Ge2 dimers have bond lengths of 2.3 and 2.4 Å, respectively, and WBI values of 2.0 and 2.5 associating with typical double bond are found for these diatomic molecules. However, when participating to a MA8E6 hetero-fullerene, as listed in Table 2, the Si-Si and Ge-Ge can better be characterized as single bond suggested by the WBI values ~1.0. A similar bond character is equally found for the P-Si, PGe, As-Si and As-Ge connections. While the P-Si, P-Ge, As-Si and As-Ge diatomic molecules are of triple bond character with WBI of ~3 (Table 1), these connections in the ME8P6 hetero-cages


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have WBI of ~1.0 (Table 2), suggesting a weak single bond. Overall, the D3h A8E6 cage of a MA8E6 hetero-fullerene is constructed upon formation of Si-Si, Ge-Ge, P-Si, P-Ge, As-Si and As-Ge single bonds. Let us now consider the nature of connections involving metal atoms from the viewpoint of Wiberg bond index (WBI). For M-P and M-As diatomic molecules, their equilibrium distances amount to ~2.2 Å, and the associated WBI’s of 2.4 is found for Cr-P, and of ~3.5 for Mo-P, W-P, Mo-As and W-As dimeric species. These connections become significantly longer upon formation of MA8E6 hetero-fullerenes, with bond lengths of ~2.6 Å and WBI values lying in a range of 1.1 ~ 1.5. The metal dopants connect with P, As hetero-atoms through multiple bonds, and are weaker than those of corresponding free diatomic molecules. The M-Si and M-Ge distances of metallic hetero-fullerenes amount to ~3.0 Å, and are longer than the corresponding diatomic species. A single bond character is found for the M-Si and M-Ge bonds of hetero-fullerenes as indicated by WBI’s of ~1.0, whereas WBI’s of the M-Si and M-Ge diatomic molecules are in the range of 2.0 ~ 2.8. As a result, the connections of metal atoms become longer and weaker when ME8P6 heterofullerenes are generated. 3.3 Characteristics of bonding using electron shell model On the basis of the free-electron gas model, the electron shell model, or Jellium model, has been introduced, and it has successfully rationalized the thermodynamic stability of a wide range of elemental clusters.88 This qualitative approach assumes that valence electrons move freely under a mean field formed by nuclei and core electrons. The valence electrons occupy the S, P, D, F,… shells (or orbitals) according to the angular momentum number L = 0, 1, 2, 3… and with a given quantum number L, the lowest-lying level has a principle number N = 1. Within such a shell model,


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the successive occupation of a level, giving a corresponding magic number such as 2, 8, 20, (34), 40, … leads to a thermodynamically stable cluster. The electron shell model thus gives a consistent interplay between electronic structure and thermodynamic stability for several types of transition metal doped clusters.89,90,91,92,93,94 In order to determine the electron shells of the compounds considered here, their DOS and pDOS maps are performed, and on basis of irreducible representation of molecular orbitals, the shell configuration is established. Figures 2 and 3 display the partial (pDOS) and total (DOS) density of states of Mo-containing clusters including MoSi8P6 and MoGe8P6, as typical examples, while those of other metallic hetero-fullerenes are shown in Figures S13-S18 of ESI file. The pDOS of each doped hetero-fullerene is mainly determined by contributions of the atomic orbitals sd-AOs of metal and sp-AOs of P, As, Si or Ge, whereas the total DOS include all AOs. The pDOS curves given in Figures 2 and 3 indicate that the AO’s of Mo, Si, P and Ge are in strong overlap with each other. A similar result is found for Cr and W containing clusters. As a result, sd-AOs of metal strongly interact with sp-AOs of P, As, Si or Ge inducing stability for MA8E6 clusters. It should be noted that the doped silicon and germanium clusters do not have a spherical symmetry as in the ideal model, therefore the energetically degenerate levels will be split into separate energy levels. The shell configurations of both MoSi8P6 and MoGe8P6 clusters are presented in Figures 2 and 3, respectively. The valence electrons of MoSi8P6 fully occupy the shell configuration of [1S2 1P6 1D10 1F14 1G18 2S2 2P6 2D10] implying 68 electrons, as shown in Figure 2. The same configuration is also found for the valence electrons of MoGe8P6 (Figure 3), and as a result, formation of a closed shell induces stability and high symmetry for Mo-doped hetero-fullerenes. A shell configuration of [1S2 1P6 1D10 1F14 1G18 2S2 2P6 2D10], as shown in Figures S13-S18 of ESI, is again identified for


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CrSi8P6, MoSi8As6, WSi8As6, WSi8P6, WGe8P6, MoGe8As6 and WGe8As6. This result emphasizes clearly that whole 68 valence electrons† of MA8E6 hetero-fullerenes occupy fully in a closed configuration of [1S2 1P6 1D10 1F14 1G18 2S2 2P6 2D10]. The establishment of a closed electron shell enhances stability for D3h MA8E6 hetero-fullerene. 3.4 Electron distribution analysis To probe further the chemical bonding of MA8E6 hetero-cage, in particular the bonding of metal dopant with other atoms, their electron distribution is examined using the electron localizability indicator (ELI_D) approach and atom-in-molecule (AIM) analysis. Within the ELI_D approach, the whole electron density of a chemical system is partitioned into local basins where electrons are concentrated.49 The AIM analysis shows the Laplacian (−𝟏/𝟒𝛁 𝟐 𝒑) value of the electron density at critical points involving bond critical points (BCP, green ball) and ring critical points (RCP, red ball). The positive and negative values of Laplacian of electron density emphasize the accumulation and depletion of electrons. Figure 4 displays the ELI_D iso-surfaces generated using a bifurcation value of 1.3, whereas Figure 5 shows the bond critical points and ring critical point of a MA8E6 hetero-cage. The Laplacian values of electron density at BCP and RCP of MA8E6 hetero-cage are listed in Table 3. A localization domain is observed at the central region of Si-Si, as well as Ge-Ge connections in all clusters considered (Figure 5). This result emphasizes the covalent bond character for both Si-Si and Ge-Ge connections. Similarly, a localization domain is found for P-P,

†

Actually each Si or Ge atom contributes 4 valence electrons, each P or As gives 5 valence electrons, thus each A8E6

has 62 valence electrons. As Cr, Mo or W uses each 6 valence electrons from their valence shell (ns1 (n-1)d5), a MA8E6 has therefore the same number of valence electrons of 68.


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As-As, Si-P, Si-As, Ge-P and Ge-As connections, and thus they are also covalent in nature of bonding. This result is supported by AIM analysis where there is between an A-A or A-E connection a bond critical point (Figure 6). Regarding the connections involving a metal atom, a corresponding localization domain is found at a lower bifurcation value, and an ionic bond character is subsequently emerging. The atomic charges, as computed using the NBO method, show a significant charge transfer from the A8E6 host to the metallic center. The metal atom in each cluster is in fact highly negative charge, bearing up to ~ -3.5 electrons. The M-A and M-E bonds are thus quite polarized, and this result is internally consistent with the ELI_D analysis in which electrons are mainly concentrated around the metallic centers, as reflected in the lower bifurcation values on the V(M,A) and V(M,E) basins. The AIM analysis illustrates the covalence and delocalization feature of connections involving metal dopants. As shown in Table 3, the Laplacian’s at the BCP of M-Si, M-Ge, M-P and M-As of MA8E6 hetero-cage have positive values and this result again illustrates the existence of covalence bond between a metal dopant and the Si, Ge, P and As atoms of the host. Particularly, the ring critical points between M with A-A and A-E connections (A=Si, Ge; E=P, As), as shown in Table 3, exhibit positive Laplacian values. Electrons are accumulated at the region located between the metal center and A8E6 hetero-cage, giving rise to a great delocalization of M electrons toward the A8E6 hetero-cage. 3.5 The 18 electron count For

transition

metal

doped

clusters,

as

demonstrated

by

several

previous

investigations,47,48,49,50,51,52 the d level of the dopant is responsible for their stability and high magnetic moment. When the d level of a metal dopant is completely occupied, the 18 electron


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count can be recovered, and the corresponding doped cluster emerges in a high symmetry shape. As for a typical example, the 5d level of the W atom accepts electrons to become a closed 5d10 configuration, and as a consequence, the WAu1295 and WSi1247,48 clusters are found to be highly stable in an Oh point group. When the dopant is an f-element, a 34 electron count has been suggested in which both d and f levels are fully occupied. Additionally, within both 18 and 34 electron counts, the S and P-like MOs are contributed mainly by ligands or hosts.54 An incompletely occupied d level of the dopant induces a spin moment for the doped cluster. For instance, following doping of a transition metal possessing a multiply open configuration such as Fe and Cr, magnetic clusters can be found for metal doped clusters MLi n and MNan.96,97,98 Recently, the role of d level of Cr is identified for the CrCun series (n = 9-16), and a magnetic moment of CrCun is generated mainly by these electron levels.99 In this context, the electronic structure of metallic hetero-fullerenes considered in the present study is explored using the 18 electron count. Each of Cr, Mo and W atoms has a general configuration as [ns1 (n-1)d5] ,which thus needs four additional electrons in order to fulfill the (n1)d10 shell. An NBO analysis of the electron density suggests that each of the Si8P6, Si8As6, Ge8P6 and Ge8As6 cages makes a transfer of ~3.5 electrons to the metal center, and it establishes a closed (n-1)d10 levels for the atomic metal. Therefore, high symmetry D3h geometry with singlet spin state of MA8E6 hetero-fullerene can be rationalized by the 18 electron count where (n-1)d levels of metal are fulfilled by 10 valence electrons. To further rationalize the stability of MA8E6 clusters from the viewpoint of the 18 electron count, Figure 6 presents a qualitative diagram of orbital interactions of the MOs of A8E6 cage with the d-levels of TM giving rise to an 18 electron configuration. Accordingly, the set of five d-AOs of TM enjoys a stabilizing interaction with sp-AOs of A8E6, and thereby it releases five fulfilled


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2D levels as denoted by electron shell model. On the other hand, these orbital interactions invariably lead to formation of a completed d10 configuration for TM atom upon a large electron transfer, and it stabilizes subsequently the MA8E6 cluster. Similarly, the overlap of s-AOs including those of metal and A8E6 produces the S level of the 18 electron configuration. Finally, three P levels are mainly made from contributions of sp-AOs of A8E6 moieties. As an outcome, the 18 electron count is recovered for MA8E6 hetero-fullerenes where each A8E6 cage supplies three P levels, and d levels of each TM are now fully occupied. Overall, the d10 metal configuration, whose ~4 electrons are gained from a cage-metal transfer is the basic event and constitute a key factor stabilizing the MA8E6 fullerene as discussed above.

4. Concluding Remarks We presented a theoretical investigation on the geometry, stability and chemical bonding of the transition metal doped MA8E6 clusters in which M is a transition metal of group VI including Cr, Mo and W, and A is Si and Ge atoms, and E is P and As. CrSi8P6, MoA8E6 and WA8E6 clusters present a novel structural motif for both silicon and germanium based clusters where the metal dopant is centered in a D3h A8E6 hetero-cage consisting of six A3E2 pentagonal faces and three A2E2 rhombus faces, so called as metallic hetero-fullerene. The main group elements such as Si, Ge and P, As atoms connect each other through single bonds and thereby turning out the D3h A8E6 hetero-cage. The metal atom binds to the P and As atoms inducing multiple bonds, whereas they form single bonds with Si or Ge. The stability of MA8E6 hetero-fullerene is significant enhanced by formation an electron configuration of [1S2 1P6 1D10 1F14 1G18 2S2 2P6 2D10] enclosing 68 electrons. Under the viewpoint of the 18 electron rule, the metal dopant attains a d10 configuration upon receipt of ~4 additional electrons transferred from the A8E6 cage, and as a consequence it


15


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Page 16 of 34

induces an additional stabilization of the resulting ME8P6 fullerene in a high symmetry D3h shape, and completely quenches the high spin of the metal atom finally yielding a singlet spin state. Acknowledgements: The authors are indebted to Ton Duc Thang University (TDTU-Demasted) and the KU Leuven Research Council (GOA program) for continuing support.

Supporting Information. Figures S1-S12 display the lower-lying isomers of M-A8E6 clusters, and Figures S13-S18 show the DOS maps. This material is available free of charge via the Internet at http://pubs.acs.org. Authors Information: Emails: [email protected]; [email protected]; [email protected]


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FIGURES:

CrSi8P6

MoSi8P6

WSi8P6

D3h 1A’1

D3h 1A’1

D3h 1A’1

MoSi8As6

MoSi8As6

WSi8As6

C1 3A

D3h 1A’1

D3h 1A’1


17


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Page 18 of 34

CrGe8P6

MoGe8P6

WGe8P6

C1 3A

D3h 1A’1

D3h 1A’1

CrGe8As6

MoGe8As6

WGe8As6

C1 3A

D3h 1A’1

D3h 1A’1

Figure 1. The shape of the lowest-energy isomer of MA8E6 clusters with A = Si, Ge; E=P, As and M=Cr, Mo and W. Geometries were optimized using B3P86 functional 6-311+G(d) basis set for Si, Ge, P, As and aug-cc-pVTZ for Cr and aug-cc-pVTZ-PP for Mo and W.


18

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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


2P6 1G10

sp-AOs(Si)

6

2D10

sp-AOs(P) sd-AOs(Mo) 5

1F14

Total

1G8

4

2S2 3

2

1

0 -13

-12

-11

-10

-9

-8

-7

-6

Figure 2. Partial (pDOS) and total (DOS) density of state maps of MoSi8P6 hetero-fullerene.


19


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8

Page 20 of 34

sp-AOs(Ge) sp-AOs(P)

7

2P6

sd-AOs(Mo)

1G10

2D6

Total 6

5

4

3

1F

1D10

2S2

8

1F6

1G8

2D4

2

1

0 -16

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

Figure 3. Partial (pDOS) and total (DOS) density of state mas of MoGe8P6 hetero-fullerene.


20

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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


CrSi8P6

MoSi8P6

MoSi8As6

WSi8As6

WSi8P6

MoGe8P6

MoGe8As6

WGe8As6

Figure 4. The ELI_D isosurface generated at the bifurcation value of 1.3 for some ME8P6 heterofullerenes.


21


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MoSi8P8

MoSi8As8

WSi8P8

WSi8As6

MoGe8P6

Ge8As6

WGe8P6

WGe8As6

Page 22 of 34


22

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Figure 5. The bond crital point (BCP, green ball) and ring crital point (RCP, red ball) of MA8E6 hetero-cage.

Figure 6. A representative orbital interaction diagram of the M atom with a A8E6 cage producing MO’s containing 18 electrons.


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Page 24 of 34

TABLES. Table 1. Bond lengths and WBI’s for diatomic molecules. d

WBI

d

WBI

d

WBI

Cr-P

2.2

2.4

Mo-P

2.1

3.6

W-P

2.1

2.7

Cr-Si

2.4

2.0

Mo-As

2.3

3.5

W-As

2.2

3.5

Cr-Ge

2.5

2.0

Mo-Si

2.3

2.7

W-Si

2.3

2.7

Ge-Ge

2.4

2.5

Mo-Ge

2.4

2.8

W-Ge

2.4

2.8

P-P

1.9

3.6

Ge-P

2.2

2.7

Si-P

2.4

3.1

Ge-As

2.3

2.7

Si-Si

2.3

2.0

Si-As

2.2

2.6


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Table 2. NBO charges, bond length (Å) and WBI of different connections within the D3h heterofullerenes.

CrSi8P6

MoSi8P6

WSi8P6

MoSi8As6

WSi8As6

qNBO(M)

A-A

-3.8

2.3/0.82

-3.6

-3.4

-3.5

-3.3

A-E

M-A

2.3/0.83

2.7/0.9 2.6/1.10

2.3/0.83

2.9/0.7

2.4/0.75

2.7/1.2

2.3/0.75

2.6/1.4 2.3/0.79

2.9/0.90

2.3/0.74

2.7/1.21

2.3/0.73

2.6/1.50 2.4/0.71

2.9/1.03

2.4/0.79

2.8/1.1

2.3/0.81

2.8/1.3 2.4/0.80

3.0/0.9

2.4/0.78

2.8/1.2

2.3/0.78

2.8/1.5 2.4/0.76

2.6/0.74 MoGe8P6

-3.3

2.4/0.80

MoGe8As6

WGe8As6

-3.3

-3.1

2.6/1.3 2.9/1.1

2.4/0.77 -3.1

3.0/0.95 2.8/1.1

2.6/0.85

WGe8P6

M-E

2.9/1.20

2.5/0.80

2.7/1.4 2.4/0.78

3.0/1.20

2.5/0.84

2.9/1.1

2.4/0.87

2.8/1.2 2.5/0.84

3.1/0.87

2.5/0.80

2.9/1.2

2.4/8.5

2.8/1.3 2.5/0.80

3.1/0.96


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Page 26 of 34

Table 3. The Laplacian of electron density (∇2 𝑝(𝑟𝐵𝐶𝑃 ) at ring critical point and bond critical point.

Bond critical point

MoGe8P6

A-M

E-M

0.042

0.059

0.033

0.043

Ring critical point A-A-M

A-E-M

0.32 0.031 0.027

0.035

0.019

0.028

0.033 0.041

WGe8P6 0.028 0.033 MoSi8P6

0.022

0.053

0.022

0.022

0.035 0.048

0.022 0.033 WSi8P6

0.015

0.044

0.017

0.015

0.031 0.043

0.015 0.029 MoSi8As6

0.019

0.042

0.021

0.019

0.031 0.043

0.019 0.029 MoGe8As6

0.028

0.035

0.022

0.039


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0.028

0.031

0.028 0.030 WGe8As6

0.022

0.028

0.018

0.022

0.036 0.029

0.022 0.028


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Page 28 of 34

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TOC Graphic

D3h 1A1’

[1F14 2D101G18]


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