σ-Aromatic MAl6S6 (M = Ni, Pd, Pt) Stars Containing Planar Hexacoordinate Transition Metals

Hypercoordinate transition-metal species are mainly dominated by the 18-valence-electron (18ve) counting. Herein, we report ternary MAl6S6 (M = Ni, Pd, Pt) clusters with the planar hexacoordinate metal (phM) centers, which feature 16ve counting instead of the classic 18ve rule. These global-minimum clusters are established via unbiased global searches, followed by PBE0 and single-point CCSD(T) calculations. The phM MAl6 units are stabilized by six peripheral bridging S atoms in these star-like species. Chemical bonding analyses reveal that there are 10 delocalized electrons around the phM center, which can render the aromaticity according to the (4n + 2) Hückel rule. It is worth noting that adding an (or two) electron(s) to its π-type lowest unoccupied molecular orbital (LUMO) will make the system unstable.


Introduction
The design, synthesis, and characterization of new two-dimensional (2D) materials have attracted wide attention in recent years, for unexpected properties and wide applications [1][2][3][4][5]. As its units or fragments, the corresponding planar clusters have gradually become one of the focuses in cluster science. Planar hypercoordinate carbon species have been explored for half a century due to their exotic structures, unusual chemical bonding, as well as potential applications since Hoffmann et al. put forward the strategies for stabilizing planar tetracoordinate carbon (ptC) structures in 1970 [6][7][8][9][10][11][12][13]. A variety of ptC, planar pentacoordinate carbon (ppC), planar hexacoordinate carbon (phC) species were predicted theoretically or characterized experimentally [14][15][16][17][18][19][20][21][22][23][24][25]. The atypical planar hypercoordination is not limited to carbon, which can be extended to other main group elements and transition metals. Due to the electron-deficiency nature of boron, B n − clusters in the size range of n = 3-40 have been confirmed to assume planar or quasi-planar structures, in which some species can possess even higher coordination numbers [26,27]. Planar heptaand octacoordinate boron (p7B, p8B) centers can be stabilized in the beautiful molecular wheels B 8 − and B 9 − , which were experimentally observed by Zhai in 2003 [28]. The wheellike ppB B 6 H 5 + , ppBe BeCu 5 , p8Be BeB 8 2− , p7Sc ScCu 7 , ppAl Cu 5 Al 2+ , ppGa Cu 5 Ga 2+ , and star-like ppB BBe 5 Au 5 , phGa GaBe 6 Au 6 were identified as the global minima [29][30][31][32][33][34][35]. Using size-selected anion photoelectron spectroscopy combined with ab initio calculations, a series of transition-metal-centered monocyclic boron wheel clusters M©B n (n = [8][9][10] were reported by Wang and Boldyrev [36]. Among them, D 8h -Co©B 8 − , D 9h -Ru©B 9 − , D 10h -Ta©B 10 − are the most representative molecular wheels, containing the planar octacoordinate cobalt, planar nonacoordinate ruthenium, and planar decacoordinate tantalum, respectively [37,38]. More importantly, an effective principle was proposed for designing the stable M©B n k− , that is x =12-n-k, where x is the required valence of the transition-metal M atom. Obviously, Co©B 8 − and Ru©B 9 − follow the formula exactly. For D 10h -Ta©B 10 − , the corresponding electron counting formula needs to upgrade to x =16-n-k. It should transition-metal M atom. Obviously, Co©B8 − and Ru©B9 − follow the formula exactly. For D10h-Ta©B10 − , the corresponding electron counting formula needs to upgrade to x =16-n-k. It should be noted that these beautiful molecular wheels possess σ and π double aromaticity. In 2015, a series of planar wheel-type D6h M©B6H6 −/0/+ (M = Mn, Fe, and Co) clusters were theoretically designed by Hou [39]. The H-bridged BenHn rings can be used to stabilize the ppC, phB, and p7Au [40][41][42]. However, it is a failure to stabilize the transition metal atom with a BenHn ring. Recently, the ppB BAl5S5 + , ppC CAl5O5 + , and CB5S5 + molecular stars were predicted in theory [43][44][45]. Very recently, the MB7O7 + (M = Ni, Pd, Pt) stars were reported as the global minima by Wu, which contain the p7M centers and possess the σ aromaticity alone [46]. To better broaden the research field of the planar hypercoordinate transition metals species, it is highly desirable to design the phM clusters, which is the theme of our present study. To host a planar hypercoordinate transition metal center, the M atom and surrounding ligands ring must match both geometrically and electronically. One interesting question arises regarding how to design molecular stars containing the planar hexacoordinate Ni/Pd/Pt centers.
Our design idea is shown in Scheme 1. Geometrically, the star-like B6O6 ring is too small to hold a Ni atom. It is imperative to increase the geometrical size of the ligand ring. Our preliminary calculations show that D6h NiAl6O6 is only a transition state structure. Can we stabilize the Ni/Pd/Pt atoms using a larger Al6S6 ring? The answer is positive. Geometrically, the Al6S6 ring is suitable to hold the Ni/Pd/Pt transition metal center. As we all know, 18-valence-electron (18ve) counting is popular for transition metal species. It is easy to think of MAl6S6 2− (M = Ni, Pd, Pt) systems first. However, MAl6S6 2 − (M = Ni, Pd, Pt) are the third-order saddle points on the corresponding energy surfaces, at the PBE0/def2-TZVP level. Removing one electron from MAl6S6 2 − , the MAl6S6 − (M = Ni, Pd, Pt) are formed. Unfortunately, MAl6S6 − (M = Ni, Pd, Pt) are still unstable, which are only the second-order saddle points. Thus, both 18ve and 17ve counting are invalid. Frequency analyses indicate that neutral MAl6S6 (M = Ni, Pd, Pt) are the true minima at the PBE0/def2-TZVP level. Thus, 16ve counting seems to be an appropriate electronic rule to design the phM species. The present paper reports ternary S-bridged MAl6S6 (M = Ni, Pd, Pt) molecular stars, which contain the planar hexacoordinate transition metal centers. Interestingly, MAl6S6 (M = Ni, Pd, Pt) possesses 10σ aromaticity alone, whose transition metal centers follow the 16ve counting instead of the typical 18ve rule. The MAl6S6 (M = Ni, Pd, Pt) species reported in this paper will provide new candidates for further exploration of 2D materials. The present paper reports ternary S-bridged MAl 6 S 6 (M = Ni, Pd, Pt) molecular stars, which contain the planar hexacoordinate transition metal centers. Interestingly, MAl 6 S 6 (M = Ni, Pd, Pt) possesses 10σ aromaticity alone, whose transition metal centers follow the 16ve counting instead of the typical 18ve rule. The MAl 6 S 6 (M = Ni, Pd, Pt) species reported in this paper will provide new candidates for further exploration of 2D materials.

Computational Details
The potential energy surfaces of MAl 6 S 6 (M = Ni, Pd, Pt) were explored by the Coalescence Kick (CK) algorithm [47,48], at the PBE0/Lanl2DZ level of theory [49]. Both singlet and triplet surfaces were considered. More than 8000 stationary points (4000 singlets and 4000 triplets) were probed for each of the MAl 6 S 6 (M = Ni, Pd, Pt) clusters. Subse-quent structural optimizations were carried out for the low-lying isomers using the PBE0 method with the def2-TZVP basis set [50]. Frequency calculations were performed at the same level to ensure that all the structures are true minima on the potential energy surface. The energies were refined by the single point CCSD(T)/def2-TZVP calculations at the PBE1PBE/def2-TZVP geometries [51]. The final relative energies were determined by the CCSD(T)/def2-TZVP energy plus the PBE0/def2-TZVP zero-point energy corrections. Born-Oppenheimer molecular dynamic (BOMD) simulations were performed at the PBE0/def2-SVP level [52].

Structures and Stability
The optimized global minima (GMs) structures of ternary MAl 6 S 6 (M = Ni, Pd, Pt) clusters were depicted in Figure 1, at the PBE0/def2-TZVP level. The phM GMs (1-3) assume the perfect D 6h symmetry, which is composed of the M center, Al 6 ring, and six S bridges at the periphery. Geometrically, the star-like Al 6 S 6 ring is suitable for hosting these hexacoordinate planar transition metals (phMs) with the high symmetry of D 6h , which has good tolerance and can be adjusted according to the size of the central atom. Frequency analyses indicate that the empty D 6h Al 6 S 6 ring is unstable, which is only a transition state at PBE0/def2-TZVP level. Introducing a transition metal atom into its center can help to stabilize it. Alternative optimized low-lying structures are shown in Figure 2. To check for consistency in terms of structures and energetics, the corresponding B3LYP/def2-TZVP calculations and vibrational analyses were further done for 1-3 and the low-lying isomers, as well as the single-point CCSD(T)/def2-TZVP//B3LYP/def2-TZVP calculations [61,62]. As shown in Figure 2, the CCSD(T)//B3LYP energetics data (in square brackets) are closely consistent with those at single-point CCSD(T)//PBE0. Thus, we shall only discuss the PBE0 and CCSD(T)//PBE0 data in the following discussion. and 4000 triplets) were probed for each of the MAl6S6 (M = Ni, Pd, Pt) clusters. Subseq structural optimizations were carried out for the low-lying isomers using the method with the def2-TZVP basis set [50]. Frequency calculations were performed a same level to ensure that all the structures are true minima on the potential energy sur The energies were refined by the single point CCSD(T)/def2-TZVP calculations a PBE1PBE/def2-TZVP geometries [51]. The final relative energies were determined b CCSD(T)/def2-TZVP energy plus the PBE0/def2-TZVP zero-point energy correct Born-Oppenheimer molecular dynamic (BOMD) simulations were performed a PBE0/def2-SVP level [52].

Structures and Stability
The optimized global minima (GMs) structures of ternary MAl6S6 (M = Ni, Pd clusters were depicted in Figure 1, at the PBE0/def2-TZVP level. The phM GMs (1-3 sume the perfect D6h symmetry, which is composed of the M center, Al6 ring, and bridges at the periphery. Geometrically, the star-like Al6S6 ring is suitable for hosting hexacoordinate planar transition metals (phMs) with the high symmetry of D6h, whic good tolerance and can be adjusted according to the size of the central atom. Frequ analyses indicate that the empty D6h Al6S6 ring is unstable, which is only a transition at PBE0/def2-TZVP level. Introducing a transition metal atom into its center can he stabilize it. Alternative optimized low-lying structures are shown in Figure 2. To chec consistency in terms of structures and energetics, the corresponding B3LYP/def2-T calculations and vibrational analyses were further done for 1-3 and the low-lying isom as well as the single-point CCSD(T)/def2-TZVP//B3LYP/def2-TZVP calculations [6 As shown in Figure 2, the CCSD(T)//B3LYP energetics data (in square brackets) are cl consistent with those at single-point CCSD(T)//PBE0. Thus, we shall only discuss the and CCSD(T)//PBE0 data in the following discussion.  At the CCSD(T)//PBE0 level, the GMs 1, 2, 3 lie 5.36, 19.25, and 23.69 kcal mol −1 lower than the second low-lying isomers 1B, 2B, and 3B, respectively. Their optimized Cartesian coordinates for GMs 1-3 and the low-lying isomers 1B-3E are provided in Table S1 (ESI †). In these low-lying isomers, all Al atoms tend to coordinate directly to the M center, whereas most of the S atoms are situated on the periphery and link with Al atoms as the bridges (µ 2 -S). It should be noted that there is one µ 3 -S atom is bound to the M center as the facecapping group in 1B/1C/1D/2B/2D/3B/3C/3E. However, there is no terminal µ 1 -S atom in these low-lying isomers. The central M atom has a coordination number of six/seven, while the coordination number of the Al atom is three/four in 1B-3E. The most stable triplet structures are obviously higher than 1E, 2E, and 3E in energy at the CCSD(T) level, respectively. Thus, the phM 1, 2, and 3 stars are the GMs on the potential energy surfaces.
In these low-lying isomers, all Al atoms tend to coordinate directly to the M center, whereas most of the S atoms are situated on the periphery and link with Al atoms as the bridges (μ 2 -S). It should be noted that there is one μ 3 -S atom is bound to the M center as the face-capping group in 1B/1C/1D/2B/2D/3B/3C/3E. However, there is no terminal μ 1 -S atom in these low-lying isomers. The central M atom has a coordination number of six/seven, while the coordination number of the Al atom is three/four in 1B-3E. The most stable triplet structures are obviously higher than 1E, 2E, and 3E in energy at the CCSD(T) level, respectively. Thus, the phM 1, 2, and 3 stars are the GMs on the potential energy surfaces. The bond distances, Wiberg bond indices (WBIs), and natural population analysis (NPA) charges can help us to explore the bonding characters of 1-3, which are shown in Figure 1 and Table 1. As shown in Figure 1, the calculated Ni-Al bond distance in 1 is 2.54 Å, which is longer than the Ni-Al covalent single bond length (2.36 Å) based on covalent atomic radii proposed by Pyykkö [63]. Because of the perfect D6h symmetry, the Al-Al bond distance in 1 is also 2.54 Å, which is close to the recommended single bond (2.52 Å). The Al-S distance 2.18 Å, is between the Al-S single bond (2.29 Å) and Al=S double bonds (2.07 Å). Considering the differences in electronegativity of the elements (Ni:1.9, Al:1.5, S:2.5), Ni-Al and Al-S bonding can be sort of polar in nature. Thus, it is not easy to judge the bond strength just by the bond distances. WBIs and NPA charges offer valuable bonding information. As shown in Table 1, the WBINi-Al 0.22 and WBIAl-Al 0.40, are less than 0.5, indicating their delocalized bonding nature. The WBIAl-S in 1 is 0.88, suggesting that the Al-S bonding is quite strong, which is consistent with the conclusions from the analyses of bond distances. With the increases in the size of central M atoms, the changes in the corresponding bond distances have almost the same trends. Interestingly, the Pd-Al in 2 The bond distances, Wiberg bond indices (WBIs), and natural population analysis (NPA) charges can help us to explore the bonding characters of 1-3, which are shown in Figure 1 and Table 1. As shown in Figure 1, the calculated Ni-Al bond distance in 1 is 2.54 Å, which is longer than the Ni-Al covalent single bond length (2.36 Å) based on covalent atomic radii proposed by Pyykkö [63]. Because of the perfect D 6h symmetry, the Al-Al bond distance in 1 is also 2.54 Å, which is close to the recommended single bond (2.52 Å). The Al-S distance 2.18 Å, is between the Al-S single bond (2.29 Å) and Al=S double bonds (2.07 Å). Considering the differences in electronegativity of the elements (Ni:1.9, Al:1.5, S:2.5), Ni-Al and Al-S bonding can be sort of polar in nature. Thus, it is not easy to judge the bond strength just by the bond distances. WBIs and NPA charges offer valuable bonding information. As shown in Table 1, the WBI Ni-Al 0.22 and WBI Al-Al 0.40, are less than 0.5, indicating their delocalized bonding nature. The WBI Al-S in 1 is 0.88, suggesting that the Al-S bonding is quite strong, which is consistent with the conclusions from the analyses of bond distances. With the increases in the size of central M atoms, the changes in the corresponding bond distances have almost the same trends. Interestingly, the Pd-Al in 2 has exactly equal bond distance with the Pt-Al (2.58 Å) in 3. The WBI Pd-Al and WBI Pt-Al are 0.23 and 0.25, respectively. It should be noted that the periphery Al-S bond distances in 1-3 seem to be almost unchanged (from 2.18 to 2.19 Å), as well as their WBIs. Indeed, the bridging S atoms can help to make the relatively flexible Al 6 ring more rigid to some extent. Due to the electronegativity differences, there is obvious electron transfer from the Al atoms to the central M and periphery S atoms. As shown in Table 1 For a thermodynamically stable cluster, its kinetic stability is equally important for experimental realization. Are these perfect phM MAl 6 S 6 (M = Ni, Pd, Pt) stars dynamically stable? Born-Oppenheimer molecular dynamics (BOMD) simulations were performed for clusters 1-3, at the PBE0/def2-SVP level, for 30 ps at room temperature (298 K). The root-mean-square deviations (RMSD, relative to the PBE0/def2-SVP optimized structures) of the structures are depicted in Figure 3. The average RMSD values of 1-3 are in the 0.28~0.36 Å range, indicating that their original structures can be maintained during the 30 ps simulations. As a technical note, the major spikes in 1 are due to the inversion vibration of Al/S up and down the molecular planes, suggesting that the Al 6 ring is relatively soft. As the size of the central M atom increases, the vibration decreases. The BOMD data suggest that 1-3 species also have reasonable kinetic stability against isomerization and decomposition.

Chemical Bonding
To further understand the electronic structures and stability of MAl 6 S 6 (M = Ni, Pd, Pt) clusters, it is essential to perform in-depth chemical bonding analyses. Here, we chose to carry out AdNDP analyses for these phM stars. AdNDP is an extension of the NBO analysis, which recovers not only the Lewis bonding elements (lone pairs and 2c-2e bonds) but also delocalized nc-2e bonds. The AdNDP scheme for NiAl 6 S 6 is illustrated in Figure 4, which is relatively straightforward for comprehension. There are 64 valence electrons in NiAl 6 S 6 , which can be attributable to five subsets from (a) to (e), according to the CMO orbital composition and structural characteristics. As shown in Figure 4a, there are three 1c-2e lone pairs (LPs) on the central Ni atom, with the occupation numbers (ON) from 2.00 to 1.97 |e|. Subset (b) indicates that there are six 1c-2e LPs of the periphery S atoms (ON = 1.96 |e|). Subset (c) contains 12 typical 2c-2e Al-S localized σ bonds on the peripheral Al 6 S 6 ring (ON = 1.96 |e|). In Subset (d), there are six delocalized 3c-2e π bonds on the Al-S-Al triangles, with the ON 2.00 |e|. The residual 10 electrons can correspond to five 7c-2e delocalized σ bonds on the NiAl 6 unit, which are depictured in subset (e). Thus, the phM NiAl 6 S 6 possesses 10σ aromaticity, according to the classical (4n + 2) Hückel rule. The orbital composition of occupied CMOs for 1 is listed in Table S2, which further supports the above AdNDP results. The AdNDP bonding patterns of 2 and 3 are very similar to 1, which are shown in Figure S1 and Figure S2, respectively. the structures are depicted in Figure 3. The average RMSD values of 1-3 are in the 0.28~0.36 Å range, indicating that their original structures can be maintained during the 30 ps simulations. As a technical note, the major spikes in 1 are due to the inversion vibration of Al/S up and down the molecular planes, suggesting that the Al6 ring is relatively soft. As the size of the central M atom increases, the vibration decreases. The BOMD data suggest that 1-3 species also have reasonable kinetic stability against isomerization and decomposition.

Chemical Bonding
To further understand the electronic structures and stability of MAl6S6 (M = Ni, Pd, Pt) clusters, it is essential to perform in-depth chemical bonding analyses. Here, we chose to carry out AdNDP analyses for these phM stars. AdNDP is an extension of the NBO analysis, which recovers not only the Lewis bonding elements (lone pairs and 2c-2e bonds) but also delocalized nc-2e bonds. The AdNDP scheme for NiAl6S6 is illustrated in Figure  4, which is relatively straightforward for comprehension. There are 64 valence electrons in NiAl6S6, which can be attributable to five subsets from (a) to (e), according to the CMO orbital composition and structural characteristics. As shown in Figure 4a, there are three 1c-2e lone pairs (LPs) on the central Ni atom, with the occupation numbers (ON) from 2.00 to 1.97 |e|. Subset (b) indicates that there are six 1c-2e LPs of the periphery S atoms (ON = 1.96 |e|). Subset (c) contains 12 typical 2c-2e Al-S localized σ bonds on the peripheral Al6S6 ring (ON = 1.96 |e|). In Subset (d), there are six delocalized 3c-2e π bonds on the Al-S-Al triangles, with the ON 2.00 |e|. The residual 10 electrons can correspond to five 7c-2e delocalized σ bonds on the NiAl6 unit, which are depictured in subset (e). Thus, the phM NiAl6S6 possesses 10σ aromaticity, according to the classical (4n + 2) Hückel rule. The orbital composition of occupied CMOs for 1 is listed in Table S2, which further supports the above AdNDP results. The AdNDP bonding patterns of 2 and 3 are very similar to 1, which are shown in Figure S1 and Figure S2, respectively. A total of 64 valence electrons are ideal for these σ aromatic phM stars, and even one additional electron can deteriorate their electronic stability. Table S3 listed the LUMOs A total of 64 valence electrons are ideal for these σ aromatic phM stars, and even one additional electron can deteriorate their electronic stability. Table S3 listed the LU-MOs and atomic composition of 1-3. For such delocalized orbitals, intuitively, adding electrons to them will be beneficial to the stability of the systems. However, the result is counter-intuitive. As depictured in Figure 5, D 6h NiAl 6 S 6 − ( 2 A 2u ) is only a second-order saddle point on the potential energy surface, with two small imaginary frequencies at the PBE0/def2-TZVP level. It should be noted that the singly occupied molecular orbital (SOMO) of NiAl 6 S 6 − is a typical delocalized π orbital. In general, the electron on π-SOMO should be beneficial to the stability of the system. Even then, the D 6h NiAl 6 S 6 − anion is not stable. Why is the phM NiAl 6 S 6 − star unstable? We briefly answer this question. The electron on SOMO has both positive and negative effects on the stability of the plane structure of NiAl 6 S 6 − . On the one hand, π delocalization can help to disperse electrons from the central transition metal Ni atom. However, the charge on Ni is only −0.34 |e|, which makes this effect contribute a little to the stability of the NiAl 6 S 6 − star. In addition, although the SOMO is a bonding orbital in general, it has some antibonding components. The π-LPs of S atoms play a crucial role in the anti-bonding characters, which account for 27.2% of the total. The combination of these two factors makes the electrons on SOMO contribute very little to the stability of the system. On the other hand, both Ni-Al and Al-Al bond distances are equal to 2.49 Å, which is obviously shorter than those in NiAl 6 S 6 (2.54 Å). According to the NPA distribution, the charge of the Al atom is +0.75 |e| in NiAl 6 S 6 − . The relatively short Al-Al bond distances make the electrostatic repulsion between them increase obviously, which makes the plane structure of D 6h NiAl 6 S 6 − become unstable. Similarly, D 6h NiAl 6 S 6 2− dianion is the third-order saddle point on the potential energy surface, whose Ni center satisfies the 18ve rule. Thus, 18ve counting is not a prerequisite for the planar hypercoordinate transition metals species.
Molecules 2023, 28, x FOR PEER REVIEW 7 of 11 and atomic composition of 1-3. For such delocalized orbitals, intuitively, adding electrons to them will be beneficial to the stability of the systems. However, the result is counterintuitive. As depictured in Figure 5, D6h NiAl6S6 − ( 2 A2u) is only a second-order saddle point on the potential energy surface, with two small imaginary frequencies at the PBE0/def2-TZVP level. It should be noted that the singly occupied molecular orbital (SOMO) of NiAl6S6 − is a typical delocalized π orbital. In general, the electron on π-SOMO should be beneficial to the stability of the system. Even then, the D6h NiAl6S6 − anion is not stable. Why is the phM NiAl6S6 − star unstable? We briefly answer this question. The electron on SOMO has both positive and negative effects on the stability of the plane structure of NiAl6S6 − . On the one hand, π delocalization can help to disperse electrons from the central transition metal Ni atom. However, the charge on Ni is only −0.34 |e|, which makes this effect contribute a little to the stability of the NiAl6S6 − star. In addition, although the SOMO is a bonding orbital in general, it has some antibonding components. The π-LPs of S atoms play a crucial role in the anti-bonding characters, which account for 27.2% of the total. The combination of these two factors makes the electrons on SOMO contribute very little to the stability of the system. On the other hand, both Ni-Al and Al-Al bond distances are equal to 2.49 Å, which is obviously shorter than those in NiAl6S6 (2.54 Å). According to the NPA distribution, the charge of the Al atom is +0.75 |e| in NiAl6S6 − . The relatively short Al-Al bond distances make the electrostatic repulsion between them increase obviously, which makes the plane structure of D6h NiAl6S6 − become unstable. Similarly, D6h NiAl6S6 2− dianion is the third-order saddle point on the potential energy surface, whose Ni center satisfies the 18ve rule. Thus, 18ve counting is not a prerequisite for the planar hypercoordinate transition metals species. ) and the number of imaginary frequencies are shown. The SOMO and its compositions are also listed.

σ-Aromaticity
In general, many beautiful planar molecules are associated with aromaticity, which is very important for the stability of the system. Aromaticity can be described not only qualitatively but also quantitatively. To further strengthen the AdNDP analyses presented above, detailed ELF analyses were performed for the MAl6S6 (M = Ni, Pd, Pt) stars. As shown in Figure 6, the bifurcation values of ELFσ in 1-3 are 0.80, 0.74, and 0.74, respectively. Thus, the MAl6S6 (M = Ni, Pd, Pt) stars are σ aromatic according to the ELF criteria, which are consistent with our conclusion of AdNDP analyses.

σ-Aromaticity
In general, many beautiful planar molecules are associated with aromaticity, which is very important for the stability of the system. Aromaticity can be described not only qualitatively but also quantitatively. To further strengthen the AdNDP analyses presented above, detailed ELF analyses were performed for the MAl 6 S 6 (M = Ni, Pd, Pt) stars. As shown in Figure 6, the bifurcation values of ELF σ in 1-3 are 0.80, 0.74, and 0.74, respectively. Thus, the MAl 6 S 6 (M = Ni, Pd, Pt) stars are σ aromatic according to the ELF criteria, which are consistent with our conclusion of AdNDP analyses.
As an independent, semi-quantitative measure of aromaticity in the systems, NICS plays an important role in the characterization of aromaticity. The negative NICS(0) and NICS(1) values can reflect σ and π aromaticity, respectively. As shown in Figure S3 (1) values are from −4.0 to −6.5 ppm, indicating they have a certain degree of π aromaticity. However, evaluating NICS values at some point seems to be inadequate. To more intuitively observe the aromaticity, the color-filled maps of ICSS zz (0) of 1-3 are plotted in Figure 7. It should be noted that positive ICSS zz values indicate diatropic ring currents and aromaticity. The calculated ICSS zz data provide a quantitative assessment, fully supporting the idea of σ aromaticity in MAl 6 S 6 (M = Ni, Pd, Pt) stars. As an independent, semi-quantitative measure of aromaticity in the systems, NICS plays an important role in the characterization of aromaticity. The negative NICS(0) and NICS(1) values can reflect σ and π aromaticity, respectively. As shown in Figure S3

Simulated IR Spectrums
To facilitate future experimental characterization, the IR spectrums of the phM stars 1, 2, and 3 were simulated at the PBE0/def2-TZVP level. As depictured in Figure 8, the strongest IR absorption peak occurs at 568 cm −1 , which mainly originates from inplane asymmetrical Al-S stretching vibrations. The peak at 461 cm −1 , is mainly generated by coupled vibrations of Al-S, Al-Ni, and Al-Al in-plane asymmetrical stretching vibrations. The weak peak at 248 cm −1 , corresponds to asymmetrical Ni-Al in-plane stretching vibrations. The weak peak at 67 cm −1 is the result of the up-and-down movements of the phNi center within the Al6 ring along the molecular axis. As shown in Figure S4, the locations and intensity of absorption peaks in 2 (PdAl6S6) and 3 (PtAl6S6) are basically like those of 1.  As an independent, semi-quantitative measure of aromaticity in the systems, NICS plays an important role in the characterization of aromaticity. The negative NICS(0) and NICS(1) values can reflect σ and π aromaticity, respectively. As shown in Figure S3

Simulated IR Spectrums
To facilitate future experimental characterization, the IR spectrums of the phM stars 1, 2, and 3 were simulated at the PBE0/def2-TZVP level. As depictured in Figure 8, the strongest IR absorption peak occurs at 568 cm −1 , which mainly originates from inplane asymmetrical Al-S stretching vibrations. The peak at 461 cm −1 , is mainly generated by coupled vibrations of Al-S, Al-Ni, and Al-Al in-plane asymmetrical stretching vibrations. The weak peak at 248 cm −1 , corresponds to asymmetrical Ni-Al in-plane stretching vibrations. The weak peak at 67 cm −1 is the result of the up-and-down movements of the phNi center within the Al6 ring along the molecular axis. As shown in Figure S4, the locations and intensity of absorption peaks in 2 (PdAl6S6) and 3 (PtAl6S6) are basically like those of 1.

Simulated IR Spectrums
To facilitate future experimental characterization, the IR spectrums of the phM stars 1, 2, and 3 were simulated at the PBE0/def2-TZVP level. As depictured in Figure 8, the strongest IR absorption peak occurs at 568 cm −1 , which mainly originates from inplane asymmetrical Al-S stretching vibrations. The peak at 461 cm −1 , is mainly generated by coupled vibrations of Al-S, Al-Ni, and Al-Al in-plane asymmetrical stretching vibrations. The weak peak at 248 cm −1 , corresponds to asymmetrical Ni-Al in-plane stretching vibrations. The weak peak at 67 cm −1 is the result of the up-and-down movements of the phNi center within the Al 6 ring along the molecular axis. As shown in Figure S4, the locations and intensity of absorption peaks in 2 (PdAl 6 S 6 ) and 3 (PtAl 6 S 6 ) are basically like those of 1.

Summary
In summary, we have designed the phM MAl6S6 (M = Ni, Pd, Pt) stars. Based on extensive searches and high-level calculations, these perfect phM stars turned out to be the global minima on the potential energy surfaces. In addition, the dynamic simulations re-

Summary
In summary, we have designed the phM MAl 6 S 6 (M = Ni, Pd, Pt) stars. Based on extensive searches and high-level calculations, these perfect phM stars turned out to be the global minima on the potential energy surfaces. In addition, the dynamic simulations revealed that they possess good kinetic stabilities. The formation of peripheral 2c-2e Al-S σ bonds, 3c-2e Al-S-Al π bonds, and the 10σ aromaticity contribute to the stabilization of phM-containing structures in MAl 6 S 6 (M = Ni, Pd, Pt) species. Thus, these phM species may be targeted in future experiments and enrich the planar hypercoordinate transition metals chemistry.