A remarkable mixture of germanium with phosphorus and arsenic atoms making stable pentagonal hetero-prisms [M@Ge5E5]+, E = P, As and M = Fe, Ru, Os

A pentagonal hetero-prismatic structural motif was found for singly transition metal doped M@Ge5E5+ clusters, where the transition metal atom is located at the centre of a (5/5) Ge5E5 prism in which Ge is mixed with either P or As atoms. Structural characterization indicates that each (5/5) Ge5E5 prism is established by joining of two Ge3E2 and Ge2E3 strings in a prismatic fashion rather than two Ge5 and E5 strings. Each string results from a remarkable mixture of Ge and E atoms and contains only one E–E connection due to the fact that Ge–E bonds are much stronger than E–E connections. From the donor–acceptor perspective, the Ge5E5 tube donates electrons to the M center, which behaves as an acceptor. NBO atomic charge and ELI_D analyses demonstrate such electrostatic interactions of the M dopant with a Ge5E5+ tube which likely induce thermodynamic stability for the resulting M@Ge5E5+ cluster. CMO analysis illustrates that the conventional 18 electron count is recovered in the M@Ge5E5+ cations.


Introduction
Due to a potentially important role of germanium based compounds in semiconductors and optoelectronic industries, 1-4 the geometric, electronic, thermodynamic and spectroscopic properties of small Ge clusters and their doped varieties have carefully been investigated by both theoretical and experimental methods alike. [5][6][7][8][9][10][11][12][13][14][15] According to numerous previous studies on doped germanium clusters, singly transition metal doped germanium clusters provide us with a wide range of geometrical features. It is known that the M@Ge 16 clusters with M ¼ Ti, Zr, and Hf establish Frank-Kasper polyhedrons in which each metal dopant is encapsulated by a T d Ge 16 cage. 16 Similar to silicon clusters, a hexagonal prism shape has been identied for the V@Ge 12 À , Mo@Ge 12 and W@Ge 12 clusters. [17][18][19][20] Of the transition metal doped MGe 12 À/0 clusters, the gold doped AuGe 12 À anion presents a high symmetry structure whose Au dopant is encapsulated by an I h Ge 12 host. 21 Some previous theoretical studies found that the threedimensional star-like structure can be constructed by the ionic interactions of seven satellite alkali cations with a at E 5 6pentagonal ring in which E is one of elements of group 14. [22][23][24] Moreover, by using DFT calculations including van der Waals effects, Li et al. has point out the small Ge 6 , Ge 9 , and Ge 10 clusters can play as the block units which can be connect together in order to form assembly materials and the van der Waals force impressively strengthens the covalent bond between different units, but plays less important role on the bonds in unit. 25 Remarkably, it is highly particular that the pentagonal prism shape was experimentally observed for the CoGe 10 3À and FeGe 10 3À clusters in which either the Co or the Fe atom is centered in a D 5h (5/5) Ge 10 pentagonal prism. 26,27 A large number of systematic investigations were carried out to elucidate the structural evolution of singly metal doped germanium clusters at various charged states. [18][19][20][28][29][30][31][32][33][34][35] Accordingly, an interplay between the metal dopant and the Ge-host gives rise to the richness on geometries varying from incomplete cage through encapsulated tube to Frank-Kasper polyhedron.
Within a great effort in the search for novel geometrical motifs of germanium-based cluster, multiple doping of P and As hetero-atoms to germanium hosts produced some symmetric hetero-fullerene structures. Following introduction of As atoms the mixed [V@Ge 8 10 ] enclosing 68 electrons. The existence of Ge-cages with mixed P and As elements suggests that a doping of P or As into a germanium host emerges as a good approach to generate high symmetry hetero-structures.
Although the MGe 10 q prismatic structures have gained so much attentions, their hetero-derivatives with P and As have been not considered yet. Indeed, while the FeGe 10 q was identi-ed as a pentagonal prism in nine charge states with q being from À5 to +3, the isovalent RuGe 10 q clusters are of polyhedral geometry. 34,38 Additionally, the compounds containing a P 5 or As 5 pentagon were found in the carbon-free as well as mixed M(Cp)E 5 sandwich complexes. Within these coordination compounds, each P 5 or As ring coordinates to a transition metal rather than forms any mixed-ring. [39][40][41][42][43] It is subsequently predicted that M@Ge 5 P 5 + and M@Ge 5 As 5 + could be stable in a sandwich form where the M center is coordinated by both Ge 5 and E 5 rings. In this context, it is of interest to explore the effects of the P and As hetero-atoms to geometry of Fe@Ge 10 q pentagonal prism. With the aim to search for novel clusters possessing a stable tubular structural motif, we set out to carry out a theoretical investigation on geometries and electronic structure of the species Ge 5 E 5 + in mixing the ve germanium atoms with ve P or As counterparts, and then they are singly doped by a transition metal (TM) giving rise to the doped M@Ge 5 E 5 + clusters. The main role of the TM dopant is to stabilize the high symmetry tubular prism motif which is usually not stable in free forms. For a systematic exploration, we consider the elements of group 8 including Fe, Ru and Os as the dopant M. It turns out that such a mixture between Ge with either P or As leads to a set of remarkably stable pentagonal prisms containing an unprecedented combination of these elements.

Computational methods
In order to explore the potential energy surface (PES) of each of the M@Ge 5 E 5 + systems considered, its guess geometries are generated by using a stochastic algorithm previously implemented by us. 44 Our stochastic search method was improved based on the 'random kick' procedure reported by Saunders 45 for exploring the low-lying isomers of compounds. According to this procedure, each atom of an initial structure is kicked to randomly move within a sphere of radius r, then the structures, generated from that, become the inputs for subsequent geometry optimizations using electronic structure calculations, and the "moving radius" r of atoms is the only variable controlled in this procedure. In our modied stochastic searching procedure, three additional variables will be controlled to provide better structures constructed for the following geometry optimizations. We modify this algorithm by adding a permutation subroutine in which each atom exchanges its position with all the others. For each MGe 5 E 5 + system, we generate 1000 initial isomers for geometry optimization. This algorithm has been proven to be highly efficient in the search for the energetically lower-lying isomers of the systems containing various components. [46][47][48] Additionally, on the basis of the well-known MGe 10 q structures that have already been reported in previous studies, we substitute Ge atoms by either P or As atoms, and thereby generate the initial isomers for the mixed M@Ge 5 E 5 + systems.
All guessing structures of each series are geometrically optimized by using B3P86 functional in conjunction with small LANL2DZ basis set. 49 Subsequently, the obtained structures, which have relative energy in range 50 kcal mol À1 , will be selected to re-optimize using the same functional but in conjunction with a larger basis set, including the 6-311+G(d) set 50 for Ge, P and As atoms, and the aug-cc-pVTZ or aug-cc-pVTZ-PP for Fe, Ru and Os 51,52 in which PP stands for pseudopotential. The current study utilizes the hybrid B3P86 functional due to it has previously been tested as suitable for treatment of geometrical and electronic structures of mixed clusters containing transition metals. 53 All geometric optimizations and electronic structure calculations are performed using the Gaussian 09 suite of program. 54 It should be noted that the cationic state is considered in order to probe the closedshell electron conguration with a low spin state.

Geometries
As for a convention, we label the structures considered as A.M.x in which A ¼ P and As stand for Ge 5 P 5 and Ge 5 As 5 hosts, respectively, M ¼ Fe, Ru and Os denotes the TM dopant, and nally, x ¼ 1, 2, ., indicates the isomers with increasing relative energy. For the Ge 5 E 5 + cations, the structures are denoted as A.
x. Relative energies given here under are consistent with respect to the corresponding isomer x ¼ 1.
To probe the effects of the metal dopant on the geometries of Ge 5 P 5 + and Ge 5 As 5 + cations, we rst present in Fig. 1 the lowerlying isomers of both Ge 5 P 5 + and Ge 5 As 5 + cations obtained at the B3P86/6-311+G(d) level. No special shape is observed for both Ge-P and Ge-As mixed systems (Fig. 1). For Ge 5 P 5 + , the lowest energy structure P.1 contains four P-P connections, whereas P.2 turns out to contain a P 5 cycle connected to a Ge 5 counterpart and is only 3 kcal mol À1 higher in energy than P.1. The next isomers including P.3, P.4 and P.5 are signicantly less stable. Regarding the Ge 5 As 5 + cations, As.1 contains only one As-As bond but it emerges as the lowest-energy structure. The geometric characteristic of As.1 is completely different from that of the isovalent P.1. Remarkably, As.3 possesses an As 5 pentagonal string and is 8 kcal mol À1 higher. Other higher energy isomers of the Ge 5 As 5 + cation are also shown in Fig. 1.
Geometry identication for M@Ge 5 P 5 + cations with M ¼ Fe, Ru and Os clearly points out that a metal dopant M stabilizes the Ge 5 P 5 + host into a double ring shape. The lower-lying isomers of M@Ge 5 P 5 + clusters are displayed in Fig. 2, and also in Fig. S1-S3 of the ESI le. † Accordingly, the M@Ge 5 P 5 + cations mainly feature a pentagonal prism, and each metal dopant, involving Fe, Ru and Os, is found to be located in the central region of a mixed (5/5) Ge 5 P 5 double ring, which actually is formed by connecting Ge 4 P, Ge 3 P 2 , Ge 2 P 3 and GeP 4 pentagons together in a prismatic fashion. Of the latter, a combination of both Ge 3 P 2 and Ge 2 P 3 strings establishes the global energy minimum structure for the M@Ge 5 P 5 + cation. No isomer having a (Ge 5 )M(E 5 ) + sandwich complex has been found. The appearance of M@Ge 5 P 5 + double ring prism emphasizes the crucial role of the metal dopant Fe, Ru and Os in stabilizing a Ge 5 P 5 + cation in a high symmetry form.
Similar to the Fe@Ge 10 q cluster, a mixed Fe@Ge 5 P 5 + cluster is thus stabilized in a pentagonal prism. Moreover, such  This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 19781-19789 | 19783 a structural motif is consistently found for both Ru@Ge 5 P 5 + and Os@Ge 5 P 5 + as their ground state, whereas the Ru@Ge 10 q cluster does not exist. This result again demonstrates the important role of P atoms in formation of pentagonal prism, in such a way that a multiple doping of P atoms into a germanium host, or replacing of Ge by P atoms, appears to be an efficient approach to generate double ring structures for germanium-based clusters. It is interesting to note that the formation of P-P direct connections in each cluster series containing Fe, Ru and Os is in relation to the cluster stability. The most stable structure of Fe@Ge 5 P 5 + , Ru@Ge 5 P 5 + and Os@Ge 5 P 5 + cations contains each only one P-P bond, whereas other isomers having two or more P-P bonds are signicantly less stable (Fig. S1-S3 †). The isomers P.Fe.5, P.Fe.6 and P.Fe.7 contain each three P-P direct connections, and they are 10-15 kcal mol À1 higher in energy. Similarly, structures containing Ru and Os exhibit three or more P-P direct bonds are calculated to be highly unstable. Overall, introduction of Fe, Ru and Os dopants into a Ge 5 P 5 + host establishes a (5/5) hetero-prism double ring structure for M@Ge 5 P 5 + cations, but the Ge and P atoms are mixed in such a way that formation of two or more P-P direct bonds tend to destabilize the resulting clusters.
Regarding the M@Ge 5 As 5 + clusters, a similar behavior is again observed. DFT calculations emphasize that a heteroprismatic shape is again dominating as displayed in Fig. S4-S6 of the ESI le. † On the structural aspect, each of the Fe, Ru and Os dopants occupies a place of the central region of a prismatic cage formed by the Ge 4 As, Ge 3 As 2 , Ge 2 As 3 and GeAs 4 pentagons. Similar to M@Ge 5 P 5 + , disposition of both Ge 3 As 2 and Ge 2 As 3 pentagonal strings in an anti-prism form gives rise to the most stable structure for M@Ge 5 As 5 + , as depicted in Fig. 2. The similarity on geometric characteristic of M@Ge 5 As 5 + clusters and their P homologues (M@Ge 5 P 5 + cations) again emphasizes the crucial stabilizing role of Fe, Ru and Os metals in turning an irregular cage to a tubular structure. In case of FeGe 5 As 5 + , there is a competition for the ground state. Actually, the triplet As.Fe.1 and As.Fe.2 isomers, which are structures containing two and three As-As connections, are only $1 kcal mol À1 more stable than the singlet As.Fe.3, an isomer containing only one As-As bond. Additionally, the triplet 3 A 00 (C s ) As.Fe.3 is only $1 kcal mol À1 higher than its single state, so that they are competitive for ground state of the Fe@Ge 5 As 5 + cluster. However, this result emphasizes that the existence of hetero-prism containing one As-As connection is a general tendency in M@Ge 5 As 5 + clusters.
As in the P homologues, the thermodynamic stability of M@Ge 5 As 5 + cations is found again in correlation with the number of direct As-As bonds. In fact, the isomer having one As-As connection is signicantly more stable than those possessing two or more As-As bonds, as shown in Fig. S4-S6 of the ESI le. † In other words, formation of additional As-As bonds tends to destabilize the doped clusters. The above structural identications illustrate the coherent fact that the metal atoms of group 8 involving Fe, Ru and Os induce a great geometrical modication for the Ge 5 E 5 + cations with E being an element in group of 15 (P and As). Both Ge 5 P 5 + P.1 and Ge 5 As 5 + As.1 cations do not exist in a special form, and more importantly, a prismatic shape is not observed at all for their lower-lying isomers. Incorporation of a metal of the group Fe, Ru and Os into such Ge 5 E 5 + cations brings in a (5/5) pentagonal double ring prismatic shape for doped M@Ge 5 E 5 + clusters, in which the strings are formed upon mixture of atoms. This appears to be a general tendency for this class of clusters (Fig. 3). The geometric feature of M@Ge 5 E 5 + clusters clearly shows that they prefer a mixed tubular shape rather than form a carbon-free sandwich complex. In fact, the existence of M@Ge 5 E 5 + shows a different trend in which both P 5 and As 5 rings no longer exist. The sandwich structure (Ge 5 ME 5 ) + is extremely unstable, even it does not appear as a local minimum on the M@Ge 5 E 5 + potential energy surface. It can thus be concluded that in the global minimum isomer of MGe 5 E 5 + , the metal center is coordinated by both Ge 3 E 2 and Ge 2 E 3 rings without any E 5 string.
For a further characterization of the electron distribution, the bond length and Wiberg bond index (WBI) of the Ge-E, Ge-Ge and E-E bonds are tabulated in Table 2. For free M-E molecules, a bond length of $2.1Å is found for M-P connections with M ¼ Fe, Ru and Os, but their WBI values vary from 2.6, 3.2 to 3.5, respectively (Table 1). According to the usual meaning of WBI, P atom forms a triple bond with Fe and Ru while a nearly quadruple bond is identied for OsP dimer. A similar result is observed in M-As and M-Ge diatomic molecules where Os establishes a nearly quadruple bond with As and Ge, and a triple bond character is found for Fe-As, Fe-Ge, Ru-As and Ru-Ge dimeric species. The strength of M-E and M-Ge dimers tends to increase in going from M ¼ Fe to Os. The WBI values of free Ge 2 , GeP and GeAs dimers are calculated to be 2.5, 2.7 and 3.1, respectively. As a consequence, they can be formally classied as a triple bond. Particularly, P 2 and As 2 have bond lengths of 1.9 and 2.2Å, respectively, and the corresponding WBI values amount to 3.6 and 3.5.
Within the M@Ge 5 P 5 + clusters, P-P connections have bond length of $2.2Å and WBI values of $1.0 clearly indicating Fig. 3 Geometric shapes of the lowest-energy structure of a single bond character. A similar single bond character is found for Ge-Ge, which exhibits a WBI value of 0.7 in Fe@Ge 5 P 5 + , and 0.5 in both Ru@Ge 5 P 5 + and Os@Ge 5 P 5 + .
Connections of Ge with P atoms are characterized by WBI values in the range of 0.4-0.9, also implying a Ge-P single bond. Accordingly, Ge and P atoms form Ge-Ge, Ge-P and P-P single bonds in the Ge 5 P 5 prismatic tube. A similar pattern is observed for the Ge 5 As 5 cages in which Ge-As connections have WBI values of 0.5-0.9 for Ge-As bonds, and $1.0 for As-As and Ge-Ge bonds. It is important to explore the bonding between Ge 3 E 2 and Ge 2 E 3 rings. The connectivities associated with the superposition between both Ge 3 E 2 and Ge 2 E 3 strings is identied as single bond according to WBI results. Therefore, it is not possible to consider the pentagonal Ge 3 E 2 and Ge 2 E 3 rings of M@Ge 5 E 5 + as two independent rings. On the other hand, the the WBI analysis indicates that Ge and E atoms either E ¼ P or As, connect together by a single bond whereas a metal atom gives rise to multiple bonds in interacting with the Ge, P and As elements. Although both P 2 and As 2 dimeric molecules are highly stable, as indicated by large values of their dissociation energies and WBI, the appearance of P-P and As-As connections in a M@Ge 5 E 5 + prismatic cluster tends to destabilize it. Within the most stable isomer of a M@Ge 5 E 5 + cluster, both P-P and As-As connections are identied as single bonds, according to WBI results. Therefore, in order to rationalize the rather negative effect of the P-P and As-As connections on the stability of M@Ge 5 E 5 + cluster, the dissociation energies (DE) of the E-E bonds as evaluated from the homolytic breaking H 2 E-EH 2 / 2EH 2 , H 3 Ge-EH 2 / Ge 3 H 3 + EH 2 and H 3 Ge-GeH 3 / 2GeH 3 processes which describe well the dissociation of E-E, Ge-E and Ge-Ge single bonds, are calculated and given in Table 1. Accordingly, the DEs of the H 3 Ge-GeH 3 bond has a value of 66 kcal mol À1 whereas the DE values of H 3 Ge-PH 2 and H 3 Ge-AsH 2 are computed to be $60 kcal mol À1 . The H 2 P-PH 2 and H 2 As-AsH 2 species have DEs of $50 kcal mol À1 which are signicantly smaller than the others. This result points out both P-P and As-As single bonds are consistently weaker than the mixed Ge-P, Ge-As and the pure Ge-Ge counterparts.  Therefore, formation of Ge-P, Ge-As and Ge-Ge bonds is expected to give raise more thermodynamic stability to M@Ge 5 E 5 + prismatic structure than the P-P and As-As connections. As a result, the most stable isomer of each M@Ge 5 E 5 + cluster contains only one P-P or As-As bond whereas eight Ge-E connections are formed (Table 3).

Chemical bonding analysis: donor-acceptor complex
Interaction between a metal dopant M with a Ge 5 E 5 + cage is further probed using the NBO atomic charges ( An analysis of the electron distribution using the electron localization indicator (ELI_D) 55 is carried out to further explore the bonding phenomena of M@Ge 5 E 5 + clusters. As shown in This result is consistent with the NBO analysis given above in which Ge 5 E 5 + is shown to transfer much electron to the M center. Both NBO and ELI_D analyses illustrate that the electrostatic interaction of a negatively charged metal dopant with a Ge 5 E 5 + positively charged tubular moiety contributes to a thermodynamic stabilization of the resulting M@Ge 5 E 5 + hetero-prisms.

The 18 electron count
The stability of the singly metal doped tubes is oen rationalized by using the classical electron count in which the metal atom receives electrons to gain a fullled d 10  pentagonal prismatic clusters, which are iso-valent with Fe@Ge 5 E 5 + , are stabilized by a similar mechanism. They are similar to Ge 5 E 5 + prisms; the Ge 10 prismatic host also supplies electrons to fulll 3d 10 levels of Co and Fe centers, and subsequently establishes a 18 electron conguration. 38,56 This gives an emphasis that hetero-atoms including P and As not only replace Ge position in a prismatic framework but also provide electrons to full 18 electron conguration.

Concluding remarks
In summary, we presented a theoretical investigation on geometry, stability and chemical bonding of the Ge 5 E 5 + and MGe 5 E 5 + cationic clusters with E ¼ P, As; M ¼ Fe, Ru and Os.
Structural identications clearly pointed out that the doping of a transition metal atom greatly inuences to geometry of the Ge 5 E 5 + cage. Structurally, the singly doped M@Ge 5 E 5 + clusters are stabilized in pentagonal hetero-prism shape whereas the Ge 5 E 5 + cation is not in any special form. Each hetero-prismatic structure is formed by superposition of the Ge 4 E, Ge 3 E 2 , Ge 2 E 3 and GeE 4 pentagons together in prismatic fashion, but the combination of Ge 3 E 2 and Ge 2 E 3 strings peculiarly establishes the global minimum structure for M@Ge 5 E 5 + cations. Interestingly, the cluster contains only one E-E connection exhibits the lowest-energy while a structure possesses two or more E-E This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 19781-19789 | 19787 bonds is signicantly less stable. Ge-E bonds are in fact stronger than E-E connections. Within the donor-acceptor perspective, with acceptor being the metal dopant, the GeE cage donates around 4 electrons to the M center and then stabilize M@Ge 5 E 5 + clusters. A CMO analysis illustrates that the conventional 18 electron count is effectively recovered in the stabilized M@Ge 5 E 5 + cations.

Conflicts of interest
The authors declare no competing nancial interest.