Structural and Electronic Properties of Ruthenium-Doped Germanium

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Structural and Electronic Properties of Ruthenium Doped Germanium Clusters Yuan-Yuan Jin, Yonghong Tian, Xiaoyu Kuang, Cheng Lu, Jose Luis Cabellos, Sukanta Mondal, and Gabriel Merino J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02225 • Publication Date (Web): 01 Apr 2016 Downloaded from http://pubs.acs.org on April 4, 2016

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The Journal of Physical Chemistry

Structural and Electronic Properties of Ruthenium Doped Germanium Clusters Yuanyuan Jin,†,‡ Yonghong Tian,¶ Xiaoyu Kuang,∗,† Cheng Lu,∗,‡,§ José Luis Cabellos,∥ Sukanta Mondal,∥ and Gabriel Merino∗,∥ †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China Department of Physics, Nanyang Normal University, Nanyang 473061, China ¶ Department of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China § Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, USA ∥ Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados, Unidad Mérida, Km 6 Antigua Carretera a Progreso, Apdo. Postal 73, Cordemex, 97310, Mérida, Yuc., Mexico ‡

Supporting Information ABSTRACT: We have performed a global minimum search for the multicharged ruthenium doped germanium clusters with the formula RuGen q (n = 2–12, q = –2, –3) using particle swarm optimization metaheuristic coupled with density functional theory computations. Leading candidates for the lowest-energy forms have been identified. Among the global minimum geometries, going from the size of n = 2 to n = 12, it is perceived that the cluster growth directs towards the formation of endohedral aggregate. Particularly, the half-encapsulated structures of RuGe7 q and RuGe8 q made the bridge between small open-shell (n = 2–6) geometries with the endohedral (n = 9–12) geometries. The endohedral constructions contain the Ru atoms at their interstitial positions. Particularly, the 10-vertex endohedral cluster RuGe10 2− has an unprecedented 3-connected C3v polyhedral geometry. The positive values of highest occupied molecular orbital energies of global minimum anions depict the electronic instability. Countercation effect is discussed to show the compensation of Coulomb repulsion among excess negative charges. RuGe12 2− as well as RuGe12 3− have S4 - and D2d -symmetric endohedral shapes, respectively, which match with the previous experimental results. Natural population analysis charge is also examined to understand the associated charge transfers.

∎ INTRODUCTION During the past decade, there has been tremendous interest in germanium-based clusters because they are the building blocks of self-assembling semiconductors and are useful in synthesizing new novel materials. 1–4 A large number of experimental and theoretical investigations have been performed on pure germanium clusters. 5–14 According to these studies, such clusters cannot form stable fullerene-like cages. However, some theoretical and experimental studies suggest that the doping by a transition metal (TM) atom could stabilize germanium cages. 15–28 For instance, the pentagonal prism [Co@Ge10 ]3− and Zintl ion cage [Fe@Ge10 ]3− were synthesized by Wang et al. and Zhou et al. respectively. 16,17 Jing et al. showed that in the ground states of Gen Co (n ≥ 9) clusters, the Co atom stays at the center of the cages. Additionally, the Co atom enhances the stability of the host Gen frameworks. 15 Trivedi et al. stated that the most stable isomer of Mo@Ge12 − is a hexagonal prism. 18 Subsequently, Deng et al. reported distorted hexagonal prisms (D3d ) of V@Ge12 −/0 using anion photoelectron spectroscopy in combination with density functional theory (DFT) computations. 4 On the basis of hybrid DFT and CCSD(T) study, Tai and Nguyen pointed out that the addition of Au and Cu into the empty Ge10 cages forms highly symmetric endohedral structures. 19 Wang and Han reported the growth-pattern, stabilities, charge transfer, and polarities of the NiGen (n = 1–13) clusters. 20 They also suggested that among W@Gen (n = 1–17), the endohedral ge-

ometries show up for n > 8 and the fullerene-like W@Gen systems appear at n ≥ 14. 21 The same authors reported that among the CuGen and Gen (n = 2–13) clusters, respectively, CuGe10 and Ge10 are relatively more stable. 22 Kumar and Kawazoe found the Frank-Kasper polyhedral M@Ge16 structures for M = Ti, Zr, Hf, as well as capped decahedral or cubic M@Ge14 and M@Ge15 for several M atoms. 23,24 Via DFT study King et al. shown that with the group 10 metals (M = Ni, Pd, and Pt) Ge can form endohedral M@Ge10 z (z = 0, –2, –4) clusters, where signigicant structural differences noted among the M@Ge10 z isomers depending on the central metal atom. 25 The same group reported the metal-centered 10-vertex group 15 clusters M@E10 4+ (M = Ni, Pd, Pt; E = As, Sb, Bi) and shown that out of the possible nine M/E combinations, only Pd@Bi10 4+ and Pt@Bi10 4+ possesses the D5d pentagonal antiprism as the lowest energy structure, which in some aspects tally with experimental observation. 26 Later, King and co-workers unveiled the D5h pentagonal prismatic global minimum against the deltahedral structure predicted by the Wade-Mingos rules for the trianionic Co@Ge10 in accordence with the experimental result as well as for the Fe@Ge10 system in all nine charged state ranging from –3 to +5. 27,28 Among the second row transition metals, ruthenium has extensive use in alloy industries and as a catalyst. It is located at the center of the periodic table with an unfilled 4d shell, causing rich physical and chemical properties. Recently, Espinoza-Quintero et al.

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identified the 12-vertex endohedral cluster [Ru@Ge12 ]3− with an unprecedented D2d -symmetric 3-connected polyhedral skeleton. 29 This contrasts dramatically with the known deltahedral or approximately deltahedral geometries of [M@Pb12 ]2− (M = Ni, Pd, Pt) and [Mn@Pb12 ]3− due to a large electron transfer from the transitionmetal center onto the cage. 29 Afterwards, Goicoechea et al. theoretically confirmed the stability of the bicapped pentagonal prism [Ru@Ge12 ]3− . 30 In line with the aforementioned studies on germanium clusters as well as a few negatively charged ruthenium doped germenium clusters, herein we describe in detail the structure and energetics of ruthenium doped and encapsulated RuGen q (n = 2–12, q = – 2, –3) systems. The lowest energy isomers of different dianionic and trianionic systems of RuGen (n = 2–12) are envisaged by DFT computations. The stabilities of the obtained global minima are evaluated by analyzing the average binding energies. In light of the electronic instability due to the Coulomb repulsion among the excess negative charge in the global minimum clusters, the effect of counterion is ascertained. In addition, the natural population analysis (NPA) is carried out to trace the negative charge dense regions in the dianionic and trianionic forms.

∎ COMPUTATIONAL DETAILS The exploration of the potential energy surfaces (PESs) of the ruthenium doped germanium clusters was performed using a generalized version of a particle swarm optimization algorithm as is implemented in the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) code. 31–35 Using this methodology one can explore the PES of any given chemical composition. It has been successful in predicting the ground state geometries of several systems. 33,34,36 The details of the CALYPSO software have been described elsewhere. 31–33 The underlying energy computations and local geometry optimizations for the thousands of the sampled coordinates are performed using the PBE0 approach 37 in conjunction with the LANL2DZ basis set. These settings are enough for the preliminary evaluation of relative energies of the sampled structures. Lowest lying isomers are further optimized using the PW91 functional 38 with a def2-TZVP basis set. Different spin multiplicities are taken for the considered systems. Harmonic vibrational frequency computations are conducted to assure that the clusters are local minima. All computations are done using Gaussian 09 suite of programs. 39

∎ RESULTS AND DISCUSSION Structures. The global minimum isomers of dianionic and trianionic Ru doped Gen (n = 2–12) clusters are displayed in Figures 1 and 2, respectively, along with their other two low-lying forms for discussion. Each isomer is denoted by the label nx.y, where n stands for the number of Ge atoms, x indicates the charge of the cluster (d for dianion and t for trianion), and y represents the y-th low-lying isomer of the cluster (1 for the lowest-energy isomer). Their electronic states, point groups, relative energies, energy gaps between the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO) and charge on Ru atoms are given in Table S1 in the Supporting Information (SI). The ground state of RuGen 2− (n = 2–4) are triplets (Table S1), whereas the larger clusters are singlet in ground state. The most stable isomer of RuGe2 2− (2d.1) is of C2v -symmetry with a vertex angle 69.6 ○ . 2d.2 is also C2v -symmetric but it is 6.33 kcal/mol higher in energy than 2d.1. The vertex angle of 2d.2 is 98.7 ○ . For comparison, we add the linear 2d.3; it has two imaginary frequencies and is higher in energy by 33.77 kcal/mol respect to 2d.1. 3d.1 forms a quadrilateral structure having two adjacent sides equal, whereas

Figure 1. Low-lying isomers of RuGen 2− (n = 2–12), along with the point group symmetry and relative energy (kcal/mol). Relative energies are given at PW91/def2-TZVP level.

3d.2 and 3d.3 are distorted trigonal pyramidal and angular geometries, having energy 9.56 and 30.82 kcal/mol higher, respectively. Three low-lying forms of RuGe4 2− have a similar shape, their constitution represents that Ru in 3d.1 has captured one Ge atom and they are formed. Three distinctive geometries are found for RuGe5 2− , 5d.1 is an irregular pentahedron, 5d.2 (at 2.19 kcal/mol) is a square pyramid, and 5d.3 (at 53.46 kcal/mol) is triangular. Contrastingly, the energy difference between the pentagonal bipyramid 6d.1 and 6d.2 is highest (21.97 kcal/mol) among the studied dianions. 7d.1 and 8d.1 reveal that the cluster growth directs towards the formation of endohedral geometries. Among the higher analogues, 9d.1 displays an endohedral structure with the Ru atom at the center. Notice that the cluster 10d.1 has an unprecedented C3v symmetric 3-connected endohedral geometry, which is a new member of the endohedral Zintl ion family, whereas 10d.2 and 10d.3 are irregular pentagonal prism. 11d.1 appears like a Ge atom capping the triangular face of 10d.1. Interestingly, 12d.1 is S4 -symmetric with 3-connected endohedral geometry which is alike to the experimentally achieved RuGe12 3− . 29 Isomer 12d.2 can be viewed as a Ge atom capping the side face of 11d.1 and is higher in energy than 12d.1 by 9.68 kcal/mol. Another endohedral cluster at 19.84 kcal/mol (12d.3) is noted for RuGe12 2− , which can be perceived as two Ge atoms capping the top and below faces of pentagonal prismatic RuGe10 2− . In the case of trianions, except for RuGe5 3− , RuGe7 3− and RuGe9 3− , all the ground state geometries are close to those of the corresponding dianionic species. The energy difference between 10t.1 and 10t.2 is only 0.97 kcal/mol, which indicates that both of them could be detected in the gas phase but Coulomb repul-


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Figure 3. Size dependences of average binding energies (Eb ) and second order difference (∆2 E) for the global minimum RuGen q (n = 2–12, q = –2, –3) clusters.

RuGen q (n = 2–12, q = –2, –3) anions, Eb can be calculated by Eb (RuGen q ) = [E(Ru) + ∣q∣E(Ge− ) + (n − ∣q∣)(E(Ge))

Figure 2. Low-lying isomers of RuGen 3− (n = 2–12), along with the point group symmetry and relative energy (kcal/mol). Relative energies are given at PW91/def2-TZVP level.

sion among the excess charge is also expected (vide infra). Isomer 10t.1 has similar shape like 10d.1, but it is less symmetric, whereas most surprisingly 10t.2 is a perfect D5h 3-connected pentagonal prismatic cage encapsulating an interstitial Ru atom. In addition, the ground state isomer 12t.1 has an unusual D2d -symmetric 3-connected endohedral geometry, which is in excellent agreement with the experimentally reported structure of Espinoza-Quintero et al. 29 The computed bond lengths and bond angles of 12t.1 are listed in Table S2 in the SI, along with the experimental data for comparison. 29 In a nutshell, the Ru-Ge bond lengths and the GeGe distances lie in the range 2.74-2.80 Å and 2.49-2.64 Å, respectively, are very close to the experimental values (Ru-Ge: 2.65-2.77 Å, Ge-Ge: 2.44-2.60 Å). 29 The majority of multicharged ground state Ru-doped germanium clusters are of lowest spin multiplicity with the exceptions of RuGe2 2− , RuGe3 2− , RuGe4 2− , they are triplet as well as RuGe2 3− is a quartet. Going from the smaller sized cluster to the larger one, the later prefer to be of lowest spin. Particularly, the C3v -symmetric structure of RuGe10 2− , as well as the D5h pentagonal prismatic cage of RuGe10 3− supplement the 10-vertex, 3-connected Zintl ion endohedral cluster family. The D2d -symmetric 3-connected endohedral RuGe12 3− is in excellent agreement with the experimental report, 29 and the similar S4 -symmetric structure of RuGe12 2− replenishes the 12-vertex Zintl ion family. Binding energies and stability. The inherent stability of a cluster can be evaluated by its binding energy (Eb ). For multicharged

− E(RuGen q )]/(n + 1)

where E(Ru), E(Ge− ), and E(Ge) are the energy of neutral Ru atom, anionic Ge− , and neutral Ge atom, respectively, whereas E(RuGen q ) is the energy of RuGen q . The binding energies for multicharged RuGen q anions are summerized in Figure 3 (a). Larger Eb value indicates a higher stability. For both dianions and trianions, the binding energy gradually increases with the increasing number of Ge atoms, suggesting that the formation of a larger cluster is easier. The Eb values of dianions are always higher than that of their corresponding trianions, implying that the dianions are thermodynamically more stable. Note that RuGe2 3− has negative Eb value, indicating its inherent instability, which is a consequence of strong Coulomb repulsion by the excess of charge (vide infra). 40 To elucidate the relative stability, the second order energy differences (∆2 E) of multicharged Ru-doped germanium clusters were calculated in their ground state geometries by the following formula: ∆2 E(RuGen q ) = E(RuGen−1 q ) + E(RuGen+1 q ) − 2E(RuGen q ) (2) It is apparent from Figure 3 (b) that the anions with larger positive values of ∆2 E are more stable than their nearest neighbors. Oscillations with asymmetric crest and trough in the multicharged clusters are perceived. The ∆2 E values suggest that RuGe6 2− , RuGe8 2− , RuGe10 2− as well as RuGe5 3− , RuGe7 3− and RuGe10 3− are more stable than their corresponding neighbors. One can assess the electronic stability of multiply charged anions using the simplest direct approach (employing Koopmans’ theorem) 41,42 in which the ionization energy is equal to the negative of the HOMO energy (E HOMO ). At the choosen level, positive values of HOMO (in Figure 4 (a)) for RuGen q clearly indicate the electronic instability of the studied dianionic and trianionic globally geometrically stable species. 43 But going from the small Ru-Ge


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Figure 5. Natural charge populations of Ru atom for the global minimum structures of RuGen q (n = 2–12, q = –2, –3) clusters.

Gen framework to the Ru atom decreases with the increasing ionization. Figure 4. Computed HOMO energies (eV) of RuGen q , LiRuGen − , and Li2 RuGen − (n = 2–12, q = –2, –3) clusters at PW91/def2-TZVP level.

system (n = 2) to the larger cluster (n = 12), the HOMO value decreases, which indicates the increment in stability relative to the preceding anion. In turn, the counterion environment could stabilize such multiply charged anions. One and two Li+ are chosen as the counterions for dianionic and trianionic RuGen q , respectively. The local minima structures of LiRuGen − and Li2 RuGen − indicate that the dianionic and trianionic RuGen q clusters retain their geometry (excluding 7d.1) in the presence of one or two countercations, respectively. From the positive E HOMO values of LiRuGe2 − , LiRuGe3 − , Li2 RuGe2 − , Li2 RuGe3 − , Li2 RuGe4 − , and LiRuGe5 − anions (Figure 4 (b)) it is clear that they need more countercations to hold their electrons. Whereas the same set of counterions fetch electronic stability up to reasonable extent for the other anions as it reflects from the E HOMO values (Figure 4 (b)). The overall decreasing E HOMO values for both the LiRuGen − and Li2 RuGen − systems with increasing cluster size mark the experimental achievements as well as the plausibility of obtaining other RuGen analogs. 29 Charge Transfer. As the electronegativity value of Ru (2.2 in Pauling scale) is higher than that of Ge (2.0) atom, it is obvious that Ru should hold more negative charge in comparison to the individual Ge atom. As the cluster size increases, the charge on the Ru atom in dianions does not follow any order up to n = 4, but increases steadily from n = 5 to n = 11 (see Figure 5). On the other hand, for trianions the charge on the Ru atom decreases firmly up to n = 5 with subsequent increment up to the cluster size of n = 11. It is clear that up to the size of n = 6, Ru atom in the title anions hold more negative charge when it is trianion, but for n > 6, Ru in dianions bears more negative charge. The transfer of electron from the Ge skeleton to Ru is related to the formation of endohedral structure, because the formation of endohedral arrangement is also ascertained when n ≥ 7. Even another fact is perceived, the negative charge in the title anions are located at the Ru atom with greater extent (respect to their total charges) for dianions in comparison with the trianions. Consistently, for the trianions the charge is more spread over the Gen framework in comparison to the dianions. Thus we can say, that the transfer of negative charges from

∎ CONCLUSIONS In summary, three categories of the ground state structures of RuGen q are noticed, according to the cluster size. It is realized that going from the smaller sized Ru-Ge system to the larger one there is an inherent tendency of formation of endohedral cage with the increasing stability. The unprecedented C3v -symmetric geometry of RuGe10 2− , the D5h pentagonal prismatic cage of RuGe10 3− as well as S4 , 3-connected endohedral construction of RuGe12 2− supplement the 10-vertex and 12-vertex Zintl ion endohedral cluster families. The ground state figure of trianionic RuGe12 3− is in good agreement with the experimental observation. 29 Countercations can yield electronic stability up to reasonable extent by counterbalancing the Coulomb repulsion among excess negative charges for the studied dianionic and trianionic RuGen systems. The transfer of negative charge from Gen framework to the Ru atom decreases with the increasing ionization.

∎ ASSOCIATED CONTENT Supporting Information

The electronic states, point groups, relative energies, HOMO– LUMO gaps and charge on Ru atoms of RuGen q isomers listed in Table S1. The bond lengths and bond angles of ground state RuGe12 3− summarized in Table S2. The labelled structure of RuGe12 3− plotted in Figure S1. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.xxxxxxx.

∎ AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. Telephone: +86-28-85403803. *E-mail: [email protected]. Telephone: +86-377-63513721. *E-mail: [email protected]. Telephone: +52-999-94294-00-Ext-2591. Notes

The authors declare no competing financial interest.

∎ ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 11274235 and 11304167), 973 Program


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of China (2014CB660804), Program for Science&Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020), and Open Project of State Key Laboratory of Superhard Materials (No. 201405). The work in Mexico was supported by Red Temática de Fisicoquímica Teórica and CGSTIC (Xiuhcoatl).

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Structural and Electronic Properties of Ruthenium-Doped Germanium

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