Ternary XBe4H5− (X = Si, Ge, Sn, Pb) Clusters: Planar Tetracoordinate Si/Ge/Sn/Pb Species with 18 Valence Electrons

Abstract

As one of the important probes of chemical bonding, planar tetracoordinate carbon (ptC) compounds have been receiving much attention. Compared with ptC clusters, the heavier planar tetracoordinate silicon, germanium, tin, lead (ptSi/Ge/Sn/Pb) systems are scarcer and more exotic. The 18-valence-electron (ve)-counting is one important guide, though not the only rule, for the design of planar tetra-, penta-coordinate carbon and silicon clusters. The 18ve ptSi/Ge system is very scarce and needs to be expanded. Based on the isoelectronic principle and bonding similarity between the Al atom and the BeH unit, inspired by the previously reported ptSi global minimum (GM) SiAl₄²⁻, a series of ternary 18 ve XBe4H5⁻ (X = Si, Ge, Sn, Pb) clusters were predicted with the ptSi/Ge/Sn/Pb centers. Extensive density functional theory (DFT) global minimum searches and high-level CCSD(T) calculations performed herein indicated that these ptSi/Ge/Sn/Pb XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters were all true GMs on their potential energy surfaces. These GMs of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) species possessed the beautiful fan-shaped structures: XBe₄ unit can be stabilized by three peripheries bridging H and two terminal H atoms. It should be noted that XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) were the first ternary 18 ve ptSi/Ge/Sn/Pb species. The natural bond orbital (NBO), canonical molecular orbitals (CMOs) and adaptive natural densitpartitioning (AdNDP) analyses indicated that 18ve are ideal for these ptX clusters: delocalized one π and three σ bonds for the XBe₄ core, three Be-H-Be 3c-2e and two Be-H σ bonds for the periphery. Additionally, 2π plus 6σ double aromaticity was found to be crucial for the stability of the ptX XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters. The simulated photoelectron spectra of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters will provide theoretical basis for further experimental characterization.

1. Introduction

The unique structures, peculiar properties and potential application prospect of planar hypercoordinate carbon clusters aroused great interest of theoretical and experimental chemists in the past fifty years, since Monkhrost firstly put forward a hypothetical transition-state structure containing the planar tetracoordinate carbon (ptC) in 1968 [1]. Based on bonding analysis of hypothetical planar CH₄, Hoffmann, Alder and Wilcox Jr. proposed some effective strategies to stabilize the ptC species in 1970 [2]. In 1976, Schleyer and coworkers predicted the first stable ptC species, 1,1-dilithiocyclopropane [3]. In 1977, the V₂(2,6-dimethoxyphenyl)₄ complex was synthesized and characterized experimentally by Cotton et al., which can be seen as the first ptC compound [4]. Since then, a variety of novel ptC, planar pentacoordinate and hexa-coordinate carbon (ppC and phC) clusters, molecules, complexes even to nanomaterials have been reported [5,6,7,8,9,10,11,12,13]. Among them, the most noteworthy are a series of pentatomic ptC species. In 1999–2000, Wang and Boldyrev observed the ptC CAl₄⁻, NaAl₄C⁻, CAl₃Si⁻ and CAl₃Ge⁻ by using the photoelectron spectroscopy (PES) in gas phase combined with theoretical calculation [14,15,16]. Interestingly, these pentatomic ptC species had 18 valence electrons (ve) (except for CAl₄⁻). It was found that 18ve counting is crucial for these pentatomic ptC clusters [17].

Silicon, germanium, tin and lead are in the row below carbon on the periodic table. According to the atomic radius data provided by Pyykkö [18], the covalent radius of C is only 0.75 Å, while the covalent radius of Si, Ge, Sn, Pb are 1.16, 1.21, 1.40 and 1.44 Å, respectively. Although the radius of the atom is increasing, the bonding properties are still similar. Silicon and germanium are dominated by tetrahedral coordination in their pure crystals and compounds. Heavier Sn and Pb atoms have stronger metallicity properties and weaker conjugation. The chemistry of Si/Ge/Sn/Pb is dominated by their tendency to form tetracoordinate tetrahedral structures, just as the tetrahedral carbon. The thermodynamic characteristics of silicon, lead and other metals were investigated by Kolesnikov and coworkers, which can help us to understand the chemical properties of Si and Pb more deeply [19,20]. Thus, the concepts of ptC, ppC and phC are naturally extended to the corresponding Si/Ge/Sn/Pb species. Using the PES combined with the DFT computations, Wang and coworkers identified the global minima of MAl₄⁻ (M = Si, Ge) anions in 2000, which can be seen as the first ptSi and ptGe species [21]. They also found that the neutral MAl₄ (M = Si, Ge) with 16ve remain planar, unlike T_d CAl₄. The experimental PES characterization of MAl₄⁻ (M = Si, Ge) anions greatly stimulated the interest of theoretical researchers in designing and predicting ptSi species. In 2004, Li et al. proposed a general pattern to incorporate planar tetra-, penta-, hexa-, hepta- and octa-coordinate silicons in C_2v B_nE₂Si series (E = CH, BH, or Si; n = 2–5) and D_8h B₈Si [22]. Stimulated by the proposal of aromatic hydrocopper Cu_nH_n (n = 4–6) [23], Li cleverly designed the ptSi SiM₄Cl₄ (M = Ni, Pd, Pt), ppSi M₅H₅Si (M = Ag, Au, Pd, Pt) and phSi SiCu₆H₆ [24,25,26]. Replacing two carbon units of C₆₀ with one silicon atom, Liu designed the spherical C₅₈Si cluster with a quasi-ptSi in 2008 [27]. It is a pity that most of these designed clusters above were just local minima on the potential energy surfaces, which are difficult to observe or characterize experimentally.

In order to preserve the ptSi/Ge structure in the gas phase for spectral experimental detection, the target system should preferably be the global minimum (GM). Note the abbreviation “GM” refers to a structure that is lowest in energy on the potential energy surface of a specific molecular system, which is routinely used in physical chemistry or cluster literature. DFT investigations identified that the most stable structure of silicon carbonyl complex Si(CO)₄ contained the ptSi center [28]. The square ptSi SiIn₄²⁻ with 18ve was predicted by Alexandrova in 2012, in which aromaticity and covalency achieve a very good balance [29]. Nine pentaatomic ptSi GM clusters including Li₃SiAs²⁻, HSiY₃(Y = Al/Ga), Ca₃SiAl₂, Mg₄Si²⁻, C₂Li₂Si, Si₃Y₂ (Y = Li/Na/K) were predicted theoretically by Xu and Ding in 2015 [30]. It should be noted that they are all 14ve species. Due to the larger atomic radius and weaker π conjugation ability, the heavier main-group elements seem to be much more difficult to have a ptX (X = C, Si, Ge, Sn, Pb) GM than the first-row main-group elements. Our group designed the ptSi/Ge superalkali cations Si₃Li₃⁺, Ge₃Li₃⁺, Si₃Cu₃⁺, Ge₃Cu₃⁺, which built the link between the ptSi/Ge and superalkali [31,32]. In 2016, Ding reported a series of planar tetracoordinate group 14 atom species C₂Si₂X^q (X = C, Si, Ge, Sn, Pb; q = +1, 0, −1) [33]. In 2022, a class of ternary 14ve clusters, ptSi/Ge/Sn/Pb XB₂Be₂ (X = Si, Ge, Sn, Pb), were computationally predicted by Zhai [34]. It should be noted that the global minima of XMg₄Y (X = Si, Ge; Y = In, Tl) and SiMg₃In₂ clusters were predicted by Cui and coworkers, which represent the first series of ppSi/Ge clusters [35]. Very recently, the bare and ligand protected planar hexacoordinate silicon (phSi) SiSb₃M₃⁺ (M = Ca, Sr, Ba) clusters were predicted [36]. In addition, Li and co-workers designed the silagraphene consisting of the ptSis [37]. On the basis of the theoretical design of ptSi clusters and their characterization by PES, the researchers began to try to synthesize ptSi species in condensed phase. Important progress was made in laboratory synthesis and characterization of ptSi compounds. In 2018, calix[4]pyrrole hydridosilicate was experimentally synthesized, which contains the ptSi center [38]. The tetrasilane 1,3-diiodotetra-silabicyclo[1.1.0]butane, containing two ptSi atoms, was successfully isolated in 2020 [39]. In 2021, Greb et al. experimentally achieved the ptSi(IV) compound [40]. Recently, a series of thermally stable ptSi [Tp′(CO)₂MSiC(R₁)C(R₂)M(CO)₂Tp′] (M = Mo, W; R₁ = R₂ = Me or R₁ = H, R₂ = SiMe₃, Ph; Tp′ = κ3-N,N′,N″-hydridotris (3,5-dimethylpyrazolyl) borate) complexes were synthesized and characterized [41]. Very recently, Driess reported the synthesis and reactivity of a peculiar ptSi compound [42].

Currently, the ptSi/Ge/Sn/Pb GMs are still scarce, and we are eager to design more examples. To design the ptSi/Ge/Sn/Pb clusters, the match of geometric size is crucial, as well as the number of electrons in the system. Our series of studies showed that the main group metal beryllium with low electronegativity is clever in bonding. Similar to Al, Be is an excellent ligand to stabilize planar hypercoordinate carbon. Here, we designed the ptSi/Ge/Sn/Pb XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters, using the Be as the ligands and H as the auxiliary atoms. The unbiased isomer search and high-level calculation suggest that the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) are all true GMs on the potential energy surfaces. We performed a DFT investigation on the structures, bonding characters and aromaticity of the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters. To the best of our knowledge, there have been no theoretical or experimental investigations reported to date on the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters. The ternary XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters in this work will further enrich the ptSi/Ge/Sn/Pb family and provide new ideas for researcher to carry out relevant theoretical design.

2. Computational Details

The extensive global minimum (GM) structural searches for XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters were performed at the PBE0/def2-SVP level using the Coalescence Kick (CK) program [43,44]. The current CK program was compiled by our research group. For each of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters, around 4000 initial input structures (2000 singlets and 2000 triplets) were generated. The candidate low-lying structures were then reoptimized at the PBE0-D3(BJ)/def2-TZVPP level [45,46]. Frequency analyses were carried out at the same level to ensure that the reported structures are true minima. To obtain an accurate stability ordering, single point energy calculations were performed for the global minima and three lowest-energy isomers at the CCSD(T)/def2-TZVPP//PBE0-D3(BJ)/def2-TZVPP level [47]. The ultimate relative total energies of isomers were determined by the CCSD(T)/def2-TZVPP energies with the PBE0-D3(BJ)/def2-TZVPP zero-point energy corrections.

Natural bond orbital (NBO) [48] analyses were performed to get the Wiber bond indices (WBIs) and natural population analysis (NPA) charges. Here, we used the NBO 6.0 program, which was developed by Glendening, Badenhoop and coworkers in the University of Wisconsin [49]. To assess the aromatic character, the nucleus independent chemical shifts (NICSs) [50] were calculated for the GMs of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters. Vertical detachment energies (VDEs) were calculated with the time-dependent PBE0 (TD-PBE0) method. All calculations for electric structures in this work were performed using the Gaussian 16 package [51]. Gaussian is a powerful commercial quantum chemistry package from Gaussian Inc. in USA, which was developed by Frisch and coworkers. The compositions of canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP) [52] analyses were performed using the Multiwfn program [53]. Multiwfn program was developed by Lu at the Beijing Kein Research Center for Natural Sciences, which is free, open-source, high-efficient, very user-friendly and flexible. Molecular structures, CMOs and AdNDP bonding patterns were visualized using the CYLview [54], GaussView and Molekel [55] programs, respectively. CYLview was created by Legault in Université de Sherbrooke in 2009, which is a powerful and free graphics software. Molekel is also a free graphic package, which was developed by Varetto in Swiss National Supercomputing Centre.

3. Result and Discussion

3.1. Geometies and Stability

The current study was primarily motivated by the previously reported 18ve ptC CAl₄²⁻ [15] and ptSi SiAl₄²⁻ [29]. Using the isoelectronic BeH units to replace the Al atoms of ptSi SiAl₄²⁻ cluster and replace an electron with one H atom at the same time, the 18ve ptSi SiBe₄H₅⁻ cluster was formed. Previous studies showed that the bridge H has an obvious advantage over the terminal H in the ternary CBe₅H_n^n–4 (n = 2–5) species [56]. The optimized geometries of GM structures 1–4 are depicted in Figure 1, along with their bond distances. The GMs of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters possessed the fan-shaped XBe₄ core, three bridging H and two terminal H atoms. The X center was tetracoordinated in plane by four Be atoms, whereas the H atoms were situated on the periphery and interacted only with Be atoms.

All GM clusters 1–4 assumed perfectly planar geometries with C_2v symmetry. The low-lying isomeric nB–nE structures are presented in Figure 2, along with the relative energies at single-point CCSD(T)//PBE0-D3(BJ)/def2-TZVPP level. Their optimized Cartesian coordinates for GMs 1–4 and the low-lying isomers 1B–4E are provided in Table S1. C_2v XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) (1–4) were the true GMs, being reasonably well separated from alternative structures by at least 4.80/6.13/8.64/8.63 kcal mol⁻¹ at the single-point CCSD(T)/def2-TZVPP//PBE0-D3(BJ)/def2-TZVPP level. Rotating the Be-H at the end of 1/2/3/4 upward towards the plane, the 1B/2B/3B/4C isomers with the C_s symmetry were obtained. In these structures, the X atoms formed the three-dimensional tetracoordination. Moving the terminal Be-H in 1/2/3/4 to the middle of adjacent two Be atoms and bonding with them as a bridging group, the isomers 1C/2C/3C/4B can be obtained. In terms of energies, the 1–4 structures were the true GMs.

Although the X-Be/Be-H bonding in clusters 1–4 was partially polar in nature, owing to different electronegativities of the elements (Si: 1.90; Ge: 2.01; Sn: 1.96; Pb: 2.33; Be: 1.57; H: 2.20), the covalent radii [18] gave the upper bound of single X-Be, Be-H bonds to be 2.18/2.23/2.42/2.46 Å and 1.34 Å, respectively. The Be₄ component in 1–4 had a curved chain shape. The Be–X distance was mainly affected by the bonding situation of Be atom. The Be atoms in 1–4 can be divided into two classes: one was bonding with two bridge H atom and the other was bonding with a bridge H and a terminal H. The Be-Si distances in 1 were in the range of 2.14–2.18 Å. The Si-Be links in 1 showed quite strong bonding, although their bond distances were uneven. The Be-H bond distances were in the range of 1.37–1.60 Å in 1, while the Be–Be bond distances were in the range of 1.90–2.04 Å. As the radius of the X atom increased, the Be–X bond distances increased accordingly. The change in the X atom did not seem to affect the peripheral Be–Be, Be–H bond distances. As shown in Figure 3, the bond distances of Be–X, Be–H and Be–Be bonds seemed to be positively (albeit not strictly) correlated with their WBIs. The WBIs of Si–Be links in 1 were 0.81–0.98, indicating that there were effectively single bonds. As the electronegativity of X atom decreased gradually from Si to Pb, the WBIs of X-Be bonds also decreased to some extent. The Be–Be bonding in 1–4 was close to half bond, with the WBIs 0.31–0.58. The WBIs were 0.84–0.85, indicating that there was a single bond between terminal H and Be atom in 1–4. The WBIs 0.32–0.59 were relatively small, suggesting there was only half bond between the bridging H and Be. These values did not correlate positively or precisely with bond distances, suggesting that the Be element is a flexible ligand for a ptSi/Ge/Sn/Pb configuration.

As shown in Figure 3, the ptSi/Ge/Sn/Pb centers in 1–4 possessed the negative charges −0.53/−0.50/−0.24/−0.20 |e|. The outer H atoms can also affect the charges on Be. The Be atoms bonding to two bridging H were nearly neutral, with only a small negative or positive charge. The Be atoms at both ends had the positive charges +0.37~+0.42 |e| in 1–4. Since H was more electronegative than Be, both the bridging H and the terminal H carried a certain amount of negative charge (−20~−0.38 |e|). In short, the outer H ligands had a rather limited effect on chemical bonding in the XBe₄ core.

The HOMO-LUMO energy gaps were computed at the PBE0-D3(BJ)-def2-TZVPP level to investigate the stability of the ptSi/Ge/Sn/Pb GM species. C_2v XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) (1–4) had sizable HOMO-LUMO gaps (3.89, 3.85, 3.51 and 3.39 eV), suggesting that these ptX species were electronically robust. The large energy gap also indicates that a 18ve is all ideal for such ptSi/Ge/Sn/Pb clusters.

3.2. Chemical Bonding

Why were these ptSi XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters stable? Canonical molecular orbitals (CMOs) analysis is important to help us understand the good stability of these ptSi/Ge/Sn/Pb GM clusters. The CMOs are fundamental in understanding the bonding nature in a molecular system. For the sake of simplicity, we took XBe₄H₅⁻ (1) as an example to reveal the bonding characteristics of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters by molecular orbital analysis (Figure 4), aided with orbital composition analysis (Table S2). As shown in Figure 4, its nine occupied CMOs can be divided into four subsets, according to their compositions. Subset (a) had two CMOs: HOMO-3 and HOMO-4, which were primarily composed of Be 2s/2p and H 1s atomic orbitals (AOs). They can be transformed to two two-center two-electron (2c-2e) Be-H σ single bonds. Subset (b) had three CMOs (including HOMO-5, HOMO-6 and HOMO-7), corresponding to delocalized three-center two-electron (3c-2e) Be–H–Be bonds. Subset (c) was the π framework on SiBe₄ unit, which involved only the HOMO. The 2π electrons were contributed by SiBe₄ core, which endowed the 2π aromaticity according to the (4n + 2) Hückel rule. Lastly, subset (d) included HOMO-1, HOMO-2 and HOMO-8, which was a 6σ system with major contributions from Be 2s/2p and Si 3s/3p atomic orbitals (AOs). It is stressed that both π and σ frameworks were truly delocalized over the SiBe₄ core; they could not be transformed to Lewis-type π/σ bonds. Thus, one π CMO (c) and three delocalized σ CMOs (d) suggest that there was two-fold delocalization in C_2v SiBe₄H₅⁻ (1), that is, double (2π and 6σ) aromaticity.

To gain insight into the bonding nature of 1–4, we performed the AdNDP analyses. AdNDP analysis is an effective tool developed by Zubarev and Boldyrev for revealing the chemical bonding nature of one molecular. As an extension of the NBO analysis, AdNDP is simpler and more intuitive than the CMOs. The AdNDP analysis, thus, recovers not only the classical Lewis bonding elements (such as lone-pairs and 2c-2e bonds) but also nonclassical, delocalized nc-2e bonds. Here, we still took 1 as an example to reveal the bonding nature of these clusters through AdNDP analysis. The AdNDP scheme for SiBe₄H₅⁻ (1) is illustrated in Figure 5. SiBe₄H₅⁻ (1) was a 18 ve system. As shown in Figure 5, there were two Be–H 2c-2e localized σ bonds and three 3c-2e Be–H–Be σ bonds in 1, with the idea ON 1.97|e|. These ten electrons were for peripheral σ bonding, which were irrelevant to the Si center. There were delocalized (5c-2e) one π and three σ bonds on the SiBe₄ cores in 1, with the idea occupation number (ON) from 1.97 to 1.99 |e|. The delocalized π/σ bonding around Si center involved eight electrons only, which confirmed the bonding pattern from CMOs analysis. Therefore, these four orbitals also offered 2π and 6σ double aromaticity according to the Hückel 4n + 2 rule, which was beneficial to stabilize the ptSi structure. The CMOs and AdNDP bonding pattern of XBe₄H₅⁻ (X = Ge, Sn, Pb) was similar to that of SiBe₄H₅⁻.

3.3. Double Aromaticity

The nucleus-independent chemical shift (NICS) calculations were performed to quantitatively characterize the aromaticity of XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters. NICS(0) and NICS(1) were calculated at the Be–X–Be, Be–H–Be triangles centers and at 1 Å above them, which can semi-quantitatively characterize the σ and π aromaticity, respectively. As shown in Figure 6, the NICS(0) values at the geometric center of Be–Si–Be triangles were −27.73/−19.77 ppm, suggesting that SiBe₄H₅⁻ possessed good σ aromaticity. Accordingly, the NICS(1) values of Be–Si–Be triangles were −20.39/−15.23 ppm, indicating that SiBe₄H₅⁻ also possessed good π aromaticity. In addition, the NICS(0) of Be–H–Be triangles was highly negative, revealing that the σ aromatic characteristics were present in these regions. The situations of XBe₄H₅⁻ (X = Ge, Sn, Pb) (2–4) were similar to those of SiBe₄H₅⁻ (1). Thus, 1–4 had both π and σ double aromaticity, which is consistent with the conclusion obtained from the AdNDP analysis. Boldyrev and Simons described in an early paper that one π and three σ bonds around C center are crucial for an 18ve ptC cluster. Similar to ptC clusters, one π and three σ bonds are also important for ptSi species, although total electrons of system do not need to obey the 18ve counting.

However, it seems a little inadequate to reveal the aromaticity of the system through the NICS values of a few points. The magnetic criterion isochemical shielding surface (ICSS) [57] calculation was handled in a three-dimensional grid of lattice points and direction and anisotropy effects can be quantified in a more straightforward way. To more intuitively observe the aromaticity, the color-filled maps of ICSS_zz (0) and ICSS_zz (1) are shown in Figure 7. Note here that positive ICSS_zz values indicate diatropic ring currents and aromaticity. Similarly, Figure 7a,b indicate that SiBe₄H₅⁻ had σ and π double aromaticity. The situation of XBe₄H₅⁻ (X = Ge, Sn, Pb) (2–4) was similar to that of SiBe₄H₅⁻ (1).

3.4. Simulated Photoelectron Spectra

Given the fact that ptSi/Ge/Sn/Pb clusters are scarce in chemistry, we shall compute their electronic properties. Anion XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) (1–4) clusters were reasonably well-defined on their potential energy surfaces. Photoelectron spectroscopy (PES) is a powerful tool to characterize anion clusters in the gas phase. To aid future experimental characterizations of the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters, their PESs were simulated at the time-dependent PBE0/def2-TZVPP (TD-PBE0) level. The simulated PES spectrum of SiBe₄H₅⁻ (1) is presented in Figure 8, which had three well-separated bands in the 3–7 eV binding energy regime. The ground-state vertical detachment energy (VDE) of 1 was calculated to be 3.47 eV at the CCSD(T)/def2-TZVPP/PBE0-D3(BJ)/def2-TZVPP level, respectively, which is relatively high in binding energies. As shown in Figure S1, the simulated PESs of XBe₄H₅⁻ (X = Ge, Sn, Pb) (2–4) clusters were basically the same as SiBe₄H₅⁻ (1).

4. Conclusions

In conclusion, we computationally designed the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters with ptSi/Ge/Sn/Pb centers, which were isoelectronic with the previously reported ptSi GM SiAl₄²⁻. The ptSi/Ge/Sn/Pb GM clusters had the perfect fan-shaped XBe₄ cores, which were protected by peripheral three bridging and two terminal H atoms. They were true global minima on the potential energy surfaces, through unbiased global structural searches and high-level quantitative calculations. The XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters represent the first ternary ptSi/Ge/Sn/Pb species with 18 ve. The NBO, CMOs and AdNDP analyses indicated that 18ve are ideal for these ptX clusters: delocalized one π and three σ bonds for the XBe₄ core, three Be-H-Be 3c-2e and two Be-H σ bonds for the periphery. According to the Hückel 4n + 2 rule, the XBe₄H₅⁻ (X = Si, Ge, Sn, Pb) clusters possess 2π + 6σ double aromaticity, which underlies their planarity and stability. The current finding suggests further opportunities to design novel planar hypercoordinate Si/Ge/Sn/Pb species, via tuning the ligands, auxiliary atoms and altering the electron counting.

Author Contributions

Y.-X.L. and J.-C.G. designed the works. L.-X.B. performed the global minima searching and the bonding analysis. Y.-X.L. wrote the draft. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All data reported in this study are available upon request by contact with the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

Sample Availability

Not applicable.

Footnotes

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Figures

Figure 1. Optimized global minimum (GM) structures of the XBe4H5− (X = Si, Ge, Sn, Pb) cluster at PBE0-D3(BJ)/def2-TZVPP level. The bond distances are presented (in Å).

Figure 2. Optimized global-minimum structures 1, 2, 3, 4 of XBe4H5− (X = Si, Ge, Sn, Pb) clusters and their four low-lying isomers (nB–nE) at the PBE0-D3(BJ)/def2-TZVPP level. Relative energies are listed in kcal mol−1 at the single-point CCSD(T)/def2-TZVPP//PBE0-D3(BJ)/def2-TZVPP level, with zero-point energy (ZPE) corrections at PBE0-D3(BJ).

Figure 3. (a) Wiberg bond indices (WBIs, in blue color), and (b) atomic natural population analysis (NPA) charges (q, |e|, in red color) for 1, 2, 3, 4.

Figure 4. Analysis of canonical molecular orbitals (CMOs) of C2v SiBe4H5− (1) cluster. (a) Two σ CMOs for Lewis-type two-center two-electron (2c-2e) terminal B-H single σ bonds. (b) Three σ CMOs for delocalized Be-H-Be 3c-2e bonds. (c) One delocalized π CMO. (d) Three delocalized σ CMOs.

Figure 5. Chemical bonding pattern for SiBe4H5− (1) cluster, according to the adaptive natural density partitioning (AdNDP) analysis. Occupation numbers (ONs) are shown. (a) two localized Be–H σ bonds; (b) three Be–H–Be 3c-2e σ bonds; (c) one delocalized π bond; (d) three delocalized σ bonds.

Figure 6. Nucleus independent chemical shifts (NICSs) for clusters 1–4. NICS (0), shown in blue, is calculated at the center of a triangle. NICS (1), shown in red, is calculated at 1 Å above the center of a triangle.

Figure 7. Color-filled maps of (a) ICSS(0)zz and (b) ICSS(1)zz (in ppm) for the SiBe4H5− (1) cluster. Positive values indicate aromaticity. 0 and 1 in parentheses represent the height above the molecular planes (in Å).

Figure 8. Simulated photoelectron spectra of SiBe4H5 cluster at the time-dependent PBE0/def2-TZVPP (TD-PBE0) level. The labeled electronic transitions are the ground state and excited states of the corresponding neutral SiBe4H5 cluster.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/1420-3049/28/14/5583/s1, Figure S1: Simulated photoelectron spectra of XBe₄H5⁻ (X = Ge, Sn, Pb) clusters at the time dependent PBE0/def2-TZVPP (TD-PBE0) level; Table S1: Cartesian coordinates for global minimum (GM) clusters minimum (GM) clusters 1–4 of the XBe4H5⁻(X = Si, Ge, Sn, Pb) series at the PBE0-D3(BJ)/def2-TZVPP level, along with four lowest-lying nB–nE isomeric structures; Table S2: Orbital composition analysis of canonical molecular orbitals (CMOs of the global minimum structure 1 (C_2v, ¹A₁ of SiBe₄H5⁻ cluster.

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