Exploring the Potential Energy Surface of Trimetallic Deltahedral Zintl

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Exploring the Potential Energy Surface of Trimetallic Deltahedral Zintl Ions: Lowest-Energy [Sn6Ge2Bi]3− and [(Sn6Ge2Bi)2]4− Structures Rodrigo Baé z-Grez,† Jorge Garza,‡ Alejandro Vaś quez-Espinal,† Edison Osorio,§ Walter A. Rabanal-Leoń ,∥ Osvaldo Yañez,*,† and William Tiznado*,†

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Computational and Theoretical Chemistry Group, Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, República 498, Santiago, Chile ‡ Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340 Mexico City, Mexico § Facultad de Ciencias Naturales y Matemáticas, Universidad de Ibagué, Carrera 22 calle 67, Ibagué, Colombia ∥ Laboratorio de Química Inorgánica y Organometálica, Departamento de Química Analítica e Inorgánica, Facultad de Ciencias Químicas, Universidad de Concepción, Edmundo Larenas 129, Casilla 160-C, Concepción, Chile S Supporting Information *

ABSTRACT: The synthesis and structural characterization of the dimer [(Sn6Ge2Bi)2]4− raise the possibility of obtaining a broad variety of analogous compounds with different Sn/Ge/Bi proportions. Several combinations of nine atoms have been detected by electrospray mass spectrometry as potential assembly units. However, [(Sn6Ge2Bi)2]4− remains as the unique experimentally characterized species in this series. This fact has motivated us to explore its potential energy surface, as well as its monomers’ [Sn6Ge2Bi]3−/2−, in an effort to gain insight into the factors that might be privileging the experimental viability of this species. Our results show that the lowest-energy [Sn6Ge2Bi]3− structure remains in its oxidized product [Sn6Ge2Bi]2−, which corresponds to that identified in the dimer [(Sn6Ge2Bi)2]4−. Additionally, local minima, very close in energy to the lowest-energy monomer, are chiral mixtures that dimerize into diverse structures with a probable energetic cost, making them noncompetitive isomers. Finally, the global minimum of the dimer [(Sn6Ge2Bi)2]4− presents the most stable monomers as assembly units. These results show the importance of considering the simultaneity of all of these conditions for the viability of these types of compounds.

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INTRODUCTION The fascinating chemistry of deltahedral Zintl ions,1 initially based on nine-atom deltahedral clusters of group 14,2,3 has recently been enriched by the discovery of isoelectronic and structurally analogous heteroatomic species.4 Besides, modern experimental approximations provide endless possibilities to alter the stoichiometry of these systems.5−10 More strikingly, the proclivity of some of these clusters to be functionalized on their surfaces using different ligands and to form oligomers, or even stable polymers, has aroused great interest among scientific communities because of their potential use as precursors toward heteroatomic bulk materials, thin films, and zero- and one-dimensional nanostructure formations.11−16 The synthesis and characterization of the first deltahedral trimetallic Zintl ion of the formula [Sn6Ge2Bi]3−, which was structurally characterized in the dimer [(Sn6Ge2Bi)2 ]4− (monomers joined via Ge−Ge bonds),9,10 was undoubtedly a milestone for heteroatomic deltahedral cluster chemistry. This cluster was synthesized either by reacting bimetallic clusters [Sn9−xGex]4− with BiPh3 or by directly extracting precursors with nominal composition “K4Ge4Sn4Bi”.9 © XXXX American Chemical Society

Interestingly, all possible nine-atom clusters with one bismuth atom, i.e., [Sn8−nGenBi]3− for n = 0−8, and a couple of combinations with two bismuth atoms were detected by electrospray mass spectrometry.9 Subsequent work by Sevov et al.10 computationally allowed them to characterize the lowestenergy structures for the 30 [Sn9−m−nGemBin](4−n)− [n = 1−4 and m = 0 − (9 − n)] possible combinations, which include the 14 structures mentioned above. Notably, these authors found that the global minimum (GM) structure predicted for [Sn6Ge2Bi]3− precisely matches the corresponding fragments in the experimentally characterized [(Sn6Ge2Bi)2]4− cluster. In addition, because [Sn9−m−nGemBin](4−n)− Zintl clusters are isoelectronic with the well-studied deltahedral [Sn9]4− and [Pb9]4− clusters, they should adopt the monocapped squareantiprism (CSA) structure according to the Wade−Mingos rules (see Scheme 1).17−19 However, it is known that [Sn9]4− and [Pb9]4− anions also prefer the closo-deltahedral structure of the tricapped trigonal prism (TTP), depending on the Received: April 24, 2019

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DOI: 10.1021/acs.inorgchem.9b01206 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

GM search of clusters and molecules.21 Our study has identified the two best candidates for the GM (for [Sn5GeBi3]− and [Sn3Ge5Bi]3− combinations) and a plethora of new lowestenergy isomers. These theoretical studies have revealed a great variety of isomers, energetically competitive with the GM, for these types of clusters. The above-mentioned structural characterization of the dimer [(Sn6Ge2Bi)2]4− has prompted chemists to explore a broad variety of analogous compounds with different Sn/Ge/ Bi proportions; considering several combinations of nine atoms, potential assembly units have already been detected by electrospray mass spectrometry.9 However, the dimer [(Sn6Ge2Bi)2]4− remains as the sole experimentally characterized species in this series. This has motivated us to perform a computational study, focused on exploring the PESs of both [(Sn6Ge2Bi)2]4− and its monomer [Sn6Ge2Bi]3−/2−, in an effort to gain insight into the factors that might be privileging the experimental viability of this species. Our results show that no structural changes are present in the lowest-energy isomers when [Sn6Ge2Bi]3− is oxidized to [Sn6Ge2Bi]2−. The former cluster is found in the precursor “K4Sn4Ge4Bi”,9 which is subsequently oxidized to the latter and then dimerizes as [(Sn6Ge2Bi)2]4−. This behavior is not observed in all cases where oxidation occurs. For example, our calculations show that the most oxidized [Sn6Ge2Bi]−, which is the identified species in electrospray mass spectrometry, prefers a different structure as the GM. In addition, for the monomer [Sn6Ge2Bi]3− and its oxidized species [Sn6Ge2Bi]2−, we have identified a mixture of enantiomers as local minima, very close in energy to the GM, precluding the formation of a single dimeric structure.

Scheme 1. Polyhedra Corresponding to Closo- and NidoType Structures for 9- and 10-Atom Clusters with 4n + 2 and 4n + 4 Electrons, According to the Wade−Mingos Rules

surrounding counterion.1,20 Taking this into consideration, M u ñ o z - C a s t r o a n d S e v o v 1 0 c l a s s i fi e d t h e [Sn9−m−nGemBin](4−n)− GM candidates in TTP, CSA, or intermediate structures, according to well-defined structural parameters. We have recently revisited the potential energy surfaces (PESs) of the [Sn9−m−nGemBin](4−n)− Zintl clusters with a novel hybrid methodology (AUTOMATON), which combines a probabilistic cellular automaton and a genetic algorithm for the

Figure 1. GM and low-lying isomers of [Sn6Ge2Bi]3− identified by an AUTOMATON search (Sn, yellow; Ge, turquoise; Bi, purple). The relative energies (kcal·mol−1) are shown from single-point calculations at CCSD(T)/Def2-TZVP//PBE0/Def2-TZVP (in bold) and PBE0/Def2-TZVP, as well as from PCM/PBE0/Def2-TZVP (in parentheses). The structures were optimized at the PBE0/Def2-TZVP level. B


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Figure 2. GM and low-lying isomers of [Sn6Ge2Bi]− identified by an AUTOMATON search (Sn, yellow; Ge, turquoise; Bi, purple). The relative energies (kcal·mol−1) are shown for the optimized structures at the PBE0/Def2-TZVP level. Structures similar to those of [Sn6Ge2Bi]3− are identified with an asterisk, where the one corresponding to its GM (1*) is enclosed in a rounded green square. smallest to largest) interatomic distance and average bond length between the atoms of system α (β), respectively. In the AUTOMATON and KICK processes, geometry optimizations and vibrational frequency calculations were carried out using the Gaussian 09 program,28 using the PBE0 hybrid functional29 and the Stuttgart/Dresden effective core potential (ECP), with its corresponding double-ξ basis set.30−34 The lowest-energy isomers delivered by the searches (in a range of 10 kcal·mol−1) were reoptimized at the PBE0/Def2-TZVP35 level, and after verification of the absence of imaginary frequencies, the best minimum was identified as the GM. Note that the relative energies of these kinds of clusters (between different isomers), at the PBE0/Def2-TZVP level, are similar to those obtained by using two-component relativistic Hamiltonians, including spin−orbit coupling and scalar relativistic effects.21 This is because the Def2-TZVP basis set uses quasi-relativistic ECPs for the heavier atoms (Sn and Bi). The dynamic behavior was simulated using Born−Oppenheimer molecular-dynamics (BOMD)36 computations at 600 K for 20 ps (ps) with a time step of 1 fs (the corresponding movies are included in the Supporting Information). To ensure that the temperature remained constant, it was verified that the nuclear kinetic energy stayed consistent throughout the simulation. To accomplish this, all velocities were rescaled at each step. Because this program only includes a velocity rescaling type of thermostat in the atom-centered density matrix propagation (ADMP)37 dynamics, the ADMP dynamics was run with the FULLSCF option, equivalent to BOMD. These calculations were performed at the PBE0-D338/Def2-SVP level, including implicit solvent (water) effects with the polarizable continuum model (PCM),39 using the Gaussian 09 program.28

Another significant result is that the lowest-energy [(Sn6Ge2Bi)2]4− structure presents the most stable monomers as assembly units. These results show the importance of considering the simultaneity of all of these events for the viability of these types of compounds.

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COMPUTATIONAL DETAILS

The PESs of the title clusters were explored using the AUTOMATON21 and KICK methods. The lowest-energy structures for the [Sn6Ge2Bi]3− combination were identified using the AUTOMATON program, a hybrid method that combines a probabilistic cellular automaton to generate new individuals for the initial population at different cycles of the algorithm.21 Then, the initial and subsequent generations were evolved through genetic operations. For further details, see ref 21. Two methods were used to search for the lowest-energy [(Sn6Ge2Bi)2]4− structure: AUTOMATON and a stochastic method, which is our implementation22 of the KICK method of Addicoat and Metha,23 referred to as the KICK method from now on. The KICK searches were restricted to those forms obtained from two combinations: (i) the [Sn6Ge2Bi]3− GM (1) and (ii) the second-lowest-energy isomer (2′). As shown in the Results and Discussion section, isomers 1 and 2′ were identified by the AUTOMATON procedure. Regarding the KICK search, it is important to emphasize that, although a portion of the PES was explored, this strategy adequately identified the GM structure of another kind of cluster aggregate previously studied in our research group, i.e., [Si5Li6]n.22 Both search procedures involved a similarity test to identify and eliminate the duplicate structures. The similarity check algorithm used for this purpose was the one introduced by Rogan et al.,24 which, in turn, is a modification of Grigoryan and Springborg’s algorithm,25−27 based on a distance comparison (eq 1) ÄÅ ÉÑ1/2 ÅÅ N (N − 1)/2 i α β y2 Ñ ÑÑ Å d d j z 2 Å jjj nα − n zzz ÑÑÑÑ d 5 (α , β) = ÅÅÅ ∑ β jD ÅÅ N (N − 1) Dave z{ ÑÑÑÑ ÅÅÇ n=1 k ave (1) Ö

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RESULTS AND DISCUSSION Figure 1 shows the 10 lowest-energy structures, and their corresponding enantiomers, for the combination [Sn6Ge2Bi]3− found by AUTOMATON and optimized at the PBE0/Def2TZVP level. The structures, Cartesian coordinates, and relative energies of the 10 isomers, optimized in the vacuum and using an implicit solvent model (PCM, water, etc.), are shown in

where d 5 (α,β) is a nondimensional quantity, N is the number of the atoms in the system, dαn (dβn) and Dαave (Dβave) are the ordered (from C


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probably with an energetic compromise, which could explain why the [(Sn6Ge2Bi)2]4− dimer is presented as a single structure formed by two cages that correspond to the [Sn6Ge2Bi]3− GM, as discussed below. It is worth mentioning that all [Sn6Ge2Bi]3− isomers prefer a singlet state. The nearest triplet state structure lies at 32.2 kcal·mol−1 from the singlet GM at the PBE0/Def2-TZVP level. To further understand the dynamic behavior of the [Sn6Ge2Bi]3− GM (1), BOMD simulations36 were performed at the PBE0-D3/Def2-SVP level, including implicit solvent (water) effects with the PCM.39 As discussed below, the PCM is the simplest model to stabilize negative charges, providing relative energies of the dimer isomers similar to those obtained by using K+ counterions. In the movie extracted from the BOMD simulations at 600 K and presented in the Supporting Information, it can be seen that, within 1 ps, structure 1 transforms into structure 7, quickly recovering its initial shape after 4 ps. This transformation involves the simultaneous lengthening and shortening of one Ge−Ge bond and one Sn− Sn bond in a Ge2Sn2 rhomboid fragment, respectively. Remarkably, the GM avoids transformation into the secondlowest-energy isomer (or its chiral isomer), in agreement with its persistence in the experimentally characterized dimer [(Sn6Ge2Bi)2]4−. Given that [(Sn6Ge2Bi)2]4− is obtained by the combination of two [Sn6Ge2Bi]2− radicals and that [Sn6Ge2Bi]− is the identified species in electrospray mass spectrometry, the lowest-energy structures for both oxidized species were also sought using AUTOMATON and are reported in Figures 2 and 3 (the structures, Cartesian coordinates, and relative energies of the low-lying isomers of [Sn6Ge2Bi]− and [Sn6Ge2Bi]2− are shown in Tables S3 and S4, respectively). [Sn6Ge2Bi]2− and [Sn6Ge2Bi]3− have structurally similar GMs, which agrees with

Figure 3. GM and low-lying isomers of [Sn6Ge2Bi]2− identified by an AUTOMATON search (Sn, yellow; Ge, turquoise; Bi, purple). The relative energies (kcal·mol−1) are shown for the optimized structures at the PBE0/Def2-TZVP level. Structures similar to those of [Sn6Ge2Bi]3− are identified with a double asterisk, where the one corresponding to its GM (1**) is enclosed in a rounded green square.

Tables S1 and S2, respectively. The GM and next three lowlying isomers coincide with those previously reported in the literature:9,10,21 structures 1−4, respectively. However, seven local minima present nonsuperimposable mirror structures (2′−5′ and 8′−10′), previously unnoted. This last finding is particularly interesting because three of these chiral isomers are very close in energy to the GM (less than 2 kcal·mol−1 at the CCSD(T)/Def2-TZVP//PBE0/Def2-TZVP level). Consequently, taking only energy into account, one would expect the possible formation of nearly degenerate dimers. However, racemic mixtures would lead to a mixture of dimeric structures,

Figure 4. GM and low-lying isomers of [(Sn6Ge2Bi)2]4− identified by AUTOMATON and KICK searches (Sn, yellow; Ge, turquoise; Bi, purple). The relative energies (kcal·mol−1) are shown for the optimized structures at the PBE0/Def2-TZVP level. The GM is enclosed in a rounded green square (identified by AUTOMATON and KICK), isomers identified by AUTOMATON are enclosed in a rounded red square, and isomers identified by KICK combining two isomers 1 and two isomers 2′ are enclosed in rounded blue and gray squares, respectively. D


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Figure 5. GM and low-lying isomers of Li4(Sn6Ge2Bi)2, as well as of their products after geometry optimization (at the PBE0/Def2-TZVP level): by removing Li (vacuum, PCM) and by replacing Li with Na and K (Sn, yellow; Ge, turquoise; Bi, purple; Li, green; Na, orange; K, blue). The relative energies are shown in kcal·mol−1.

the presence of these structures in the [(Sn6Ge2Bi)2]4− dimer. However, the [Sn6Ge2Bi]− GM does not correspond to the [Sn6Ge2Bi]3− GM structure, which is found at 4.9 kcal·mol−1 at the PBE0/def2-TZVP level (see Figure 2). Therefore, it is important to highlight that changes in the charge could have a drastic effect on the relative energy of the oxidized (or reduced) isomers in these kinds of cage-shaped compounds. For the dimer, the following issue appeared during PES exploration: to relieve the strong Coulombic repulsion, the negatively charged [(Sn6Ge2Bi)2]4− species prefer structures

with separated small fragments (see Table S5). Consequently, AUTOMATON failed to identify the expected structures made by connecting two nine-atom cages. Thus, an obvious alternative was to neutralize the negative charges using a simple counterion, i.e., Li+, in the Li4(Sn6Ge2Bi)2 combination. For this cluster, AUTOMATON identified 21 lowest-energy isomers (within 5.0 kcal·mol−1 above the putative GM at the PBE0/Def2TZVP level), consisting of two Sn6Ge2Bi distorted monocapped square antiprisms, or distorted tricapped trigonal prisms, joined by a Ge−Ge bond. Additionally, in all of these E


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with the PCM. As can be seen, throughout the 20 ps of the simulation, the dimer carries out some rotations along the Ge− Ge bond. However, as a whole, the structure remains unaltered, indicating that the isomerization barrier of this structure is high enough to guarantee the kinetic stability of this isomer.

isomers, the four Li atoms are arranged surrounding the Ge− Ge exobond (isomers within 10 kcal·mol−1 from the GM are shown in Table S6). AUTOMATON identifies two competitive Li4(Sn6Ge2Bi)2 GMs, with one of them being structurally analogous to the one characterized in the experiments.9,10 An alternative strategy for predicting the lowest-energy structure of [(Sn6Ge2Bi)2]4− is through analysis of the local reactivity of the paramagnetic monomer [Sn6Ge2Bi]2−. The appropriate descriptor in this case is the spin density. As shown in Figure S1, the spin density of the [Sn6Ge2Bi]2− GM is delocalized through the cluster cage, avoiding a clear prediction of the regioselectivity. Interestingly, when we calculated the same descriptor for the monomeric fragments in the distorted structure as they have in the dimer, the spin density is localized in the Ge atom, in agreement with the Ge− Ge exobond of the dimer. However, to achieve this distorted structure, there is an energetic demand (around 4.4 kcal· mol−1). In addition, the [(Sn6Ge2Bi)2]4− PES was explored by employing the KICK method through two searches. In the first one, the monomer’s GM (1) was used as the fragment to be stochastically permuted, while in the second one, one enantiomer of the first lowest-energy isomer (2′) was used. Most unexpectedly, the first search identified the dimer structurally similar to the experimentally characterized [(Sn6Ge2Bi)2]4− one as the lowest-energy isomer. Besides, all of the collected lowest-energy isomers consist of two Sn6Ge2Bi cages connected to each other by an exobond, with the second isomer at 5.4 kcal·mol−1 above the GM (see Figure 4 and Tables S7 and S8). The differences between the AUTOMATON and KICK searches, regarding both the number and relative energy of the lowest-energy isomers, raise the following question: what is the effect of using different approaches to stabilize the negative charges on the relative energies of the best isomers? To answer this question, the lowest-energy Li4(Sn6Ge2Bi)2 isomers (within 2 kcal·mol−1 above the GM at the PBE0/def2-TZVP level) were modified and optimized as follows: first, by removing the four Li+ ions (in a vacuum and including implicit solvent, i.e., water, effects with the PCM); second, by replacing Li+ with Na+ and K+ as counterions (see Tables S9−S12). As shown in Figure 5, some significant outcomes stand out: (a) the lowest-energy isomer in all cases is similar to the experimentally observed [(Sn6Ge2Bi)2]4− dimer, with the only exception of the system where Na+ is used as the counterion. As mentioned above, the Li4(Sn6Ge2Bi)2 combination presents two candidates to the GM. When using K+ as the counterion, the identified lowest-energy structure corresponds to the experimentally identified dimer, which, in turn, is 3 kcal·mol−1 below the nearest local minimum. This is an important result because K+ is the counterion present in both the quaternary precursor (K4Sn4Ge4Bi) and the [K(2,2,2crypt)]4[(Sn6Ge2Bi)2]·1.5en crystals (see ref 9 for details on the experimental synthesis) that contain the dimer [(Sn6Ge2Bi)2]4−. Finally, we evaluated the use of solvent effects (water) through the PCM in the relative energies of [(Sn6Ge2Bi)2]4− isomers. Surprisingly, the use of this simple model arranges the isomers as expected, meaning that dimers formed by two Sn6Ge2Bi cages are the energetically preferred ones (see Table S13). What is the kinetic behavior of this dimer like? To answer this question, we performed BOMD simulations at the PBE0D3/Def2-SVP level, including implicit solvent (water) effects

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CONCLUSIONS The PESs of the [Sn6Ge2Bi]3−/2− cluster, as well as of its dimer [(Sn6Ge2Bi)2]4−, were explored using two different methods: evolutionary (AUTOMATON) and stochastic (KICK). In the case of the [Sn6Ge2Bi]3− and [Sn6Ge2Bi]2− species, they have structurally similar GMs. Other lowest-energy isomers, very close in energy to the GM (within 1.5 kcal·mol−1), are identified as chiral structures. This finding is reported in the literature for the first time. In the case of the dimer, counterions (i.e., Li+) must be used for the evolutionary search; otherwise, the structure prefers to be fragmented to avoid high Coulombic repulsion among the four negative charges in this species. KICK shows to be a reliable and computationally efficient alternative method to search for the dimer GM. In this work, two isomers of [Sn6Ge2Bi]3− were used for the KICK search: the GM (structure 1) and the first lowest-energy structure (structure 2′). This allowed us to identify a structure similar to the one experimentally characterized as the lowest-energy structure, which, in turn, corresponds to the search that uses two GM structures as fragments. The second combination provides higher-energy isomers. Finally, an economic alternative to stabilizing negative charges in the structural search of these kinds of compounds is by including solvent effects (using a polar solvent such as water) through the PCM.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b01206. Cartesian coordinates and relative energies for all optimized structures computed at the PBE0/def2TZVP level (PDF) BOMD movie (AVI) BOMD movie (AVI)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (O.Y.). *E-mail: [email protected] (W.T.). ORCID

Rodrigo Báez-Grez: 0000-0001-9303-1559 Jorge Garza: 0000-0003-4249-6078 Alejandro Vásquez-Espinal: 0000-0003-3501-7905 Edison Osorio: 0000-0001-7636-8168 Osvaldo Yañez: 0000-0001-8993-9353 William Tiznado: 0000-0002-6061-8879 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest. F


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ACKNOWLEDGMENTS The authors are grateful for financial support from Fondecyt Grant 1181165. The authors are thankful for the facilities provided by the Laboratorio de Supercómputo y Visualización en Paralelo at Universidad Autónoma Metropolitana-Iztapalapa.

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Exploring the Potential Energy Surface of Trimetallic Deltahedral Zintl

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