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

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.


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 transitionstate structure containing the planar tetracoordinate carbon (ptC) in 1968 [1]. Based on bonding analysis of hypothetical planar CH 4 , 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 V 2 (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 CAl 4 − , NaAl 4 C − , CAl 3 Si − and CAl 3 Ge − by using the photoelectron imentally achieved the ptSi(IV) compound [40]. Recently, a series of thermally stable ptSi [Tp (CO) 2 MSiC(R 1 )C(R 2 )M(CO) 2 Tp ] (M = Mo, W; R 1 = R 2 = Me or R 1 = H, R 2 = SiMe 3 , 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 XBe 4 H 5 − (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 XBe 4 H 5 − (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 XBe 4 H 5 − (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 XBe 4 H 5 − (X = Si, Ge, Sn, Pb) clusters. The ternary XBe 4 H 5 − (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.

Computational Details
The extensive global minimum (GM) structural searches for XBe 4 H 5 − (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 XBe 4 H 5 − (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 XBe 4 H 5 − (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.

Geometies and Stability
The current study was primarily motivated by the previously reported 18ve ptC CAl 4 2− [15] and ptSi SiAl 4 2− [29]. Using the isoelectronic BeH units to replace the Al atoms of ptSi SiAl 4 2− cluster and replace an electron with one H atom at the same time, the 18ve ptSi SiBe 4 H 5 − cluster was formed. Previous studies showed that the bridge H has an obvious advantage over the terminal H in the ternary CBe 5 H 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 XBe 4 H 5 − (X = Si, Ge, Sn, Pb) clusters possessed the fan-shaped XBe 4 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.

Geometies and Stability
The current study was primarily motivated by the previously CAl4 2− [15] and ptSi SiAl4 2− [29]. Using the isoelectronic BeH units to re of ptSi SiAl4 2− cluster and replace an electron with one H atom at the s ptSi SiBe4H5 − cluster was formed. Previous studies showed that the bri ous advantage over the terminal H in the ternary CBe5Hn n-4 (n = 2-5 optimized geometries of GM structures 1-4 are depicted in Figure 1, alo distances. The GMs of XBe4H5 − (X = Si, Ge, Sn, Pb) clusters possessed th core, three bridging H and two terminal H atoms. The X center was t plane by four Be atoms, whereas the H atoms were situated on the p acted only with Be atoms.  All GM clusters 1-4 assumed perfectly planar geometries with C 2v symmetry. The lowlying 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 XBe 4 H 5 − (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 Be 4 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. 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  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.

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 twoelectron (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 C2v SiBe4H5 − (1), that is, double (2π and 6σ) aromaticity. , 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.

Chemical Bonding
Why were these ptSi XBe 4 H 5 − (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 XBe 4 H 5 − (1) as an example to reveal the bonding characteristics of XBe 4 H 5 − (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 SiBe 4 unit, which involved only the HOMO. The 2π electrons were contributed by SiBe 4 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 SiBe 4 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 SiBe 4 H 5 − (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 SiBe 4 H 5 − (1) is illustrated in Figure 5. SiBe 4 H 5 − (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 SiBe 4 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 XBe 4 H 5 − (X = Ge, Sn, Pb) was similar to that of SiBe 4 H 5 − .
Molecules 2023, 28, x FOR PEER REVIEW 7 of 12 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 − .

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. Accord-

Double Aromaticity
The nucleus-independent chemical shift (NICS) calculations were performed to quantitatively characterize the aromaticity of XBe 4  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 SiBe 4 H 5 − possessed good σ aromaticity. Accordingly, the NICS(1) values of Be-Si-Be triangles were −20.39/−15.23 ppm, indicating that SiBe 4 H 5 − 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 XBe 4 H 5 − (X = Ge, Sn, Pb) (2-4) were similar to those of SiBe 4 H 5 − (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.
The nucleus-independent chemical shift (NICS) calculations wer quantitatively characterize the aromaticity of XBe4H5 − (X = Si, Ge, Sn, Pb) and NICS(1) were calculated at the Be-X-Be, Be-H-Be triangles centers a them, which can semi-quantitatively characterize the σ and π aromatic As shown in Figure 6, the NICS(0) values at the geometric center of Be were −27.73/−19.77 ppm, suggesting that SiBe4H5 − possessed good σ arom ingly, the NICS(1) values of Be-Si-Be triangles were −20.39/−15.23 ppm SiBe4H5 − also possessed good π aromaticity. In addition, the NICS(0) of Be was highly negative, revealing that the σ aromatic characteristics were regions. The situations of XBe4H5 − (X = Ge, Sn, Pb) (2-4) were similar to (1). Thus, 1-4 had both π and σ double aromaticity, which is consistent sion obtained from the AdNDP analysis. Boldyrev and Simons described that one π and three σ bonds around C center are crucial for an 18ve ptC to ptC clusters, one π and three σ bonds are also important for ptSi specie 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 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 ICSSzz (0) and ICSSzz (1) are shown in Figure 7. Note here that positive ICSSzz values indicate diatropic ring currents and aromaticity. Similarly, Figures 7a,b indicate that SiBe4H5 − had σ and π double aromaticity. The situation of XBe4H5 − (X = Ge, Sn, Pb) (2)(3)(4) was similar to that of SiBe4H5 − (1).

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).  Positive values indicate aromaticity. 0 and 1 in parentheses represent the height above the molecular planes (in Å).

Simulated Photoelectron Spectra
Given the fact that ptSi/Ge/Sn/Pb clusters are scarce in chemistry, we shall compute their electronic properties. Anion XBe 4 H 5 − (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 XBe 4 H 5 − (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 SiBe 4 H 5 − (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 XBe 4 H 5 − (X = Ge, Sn, Pb) (2-4) clusters were basically the same as SiBe 4 H 5 − (1).

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

Conclusions
In conclusion, we computationally designed the XBe 4 H 5 − (X = Si, Ge, Sn, Pb) clusters with ptSi/Ge/Sn/Pb centers, which were isoelectronic with the previously reported ptSi GM SiAl 4 2− . The ptSi/Ge/Sn/Pb GM clusters had the perfect fan-shaped XBe 4 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 XBe 4 H 5 − (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 XBe 4 core, three Be-H-Be 3c-2e and two Be-H σ bonds for the periphery. According to the Hückel 4n + 2 rule, the XBe 4 H 5 − (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.

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Informed Consent Statement: Not applicable.

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