Planar Elongated B12 Structure in M3B12 Clusters (M = Cu-Au)

Here, it is shown that the M3B12 (M = Cu-Au) clusters’ global minima consist of an elongated planar B12 fragment connected by an in-plane linear M3 fragment. This result is striking since this B12 planar structure is not favored in the bare cluster, nor when one or two metals are added. The minimum energy structures were revealed by screening the potential energy surface using genetic algorithms and density functional theory calculations. Chemical bonding analysis shows that the strong electrostatic interactions with the metal compensate for the high energy spent in the M3 and B12 fragment distortion. Furthermore, metals participate in the delocalized π-bonds, which infers an aromatic character to these species.

However, this structural versatility makes it challenging to establish chemical bonding patterns that facilitate these systems' structural rationalization. In contrast to its carbon neighbor in the periodic table, there are very limited models for predicting the structures of boron-based molecular systems. Boron hydrides, for instance, are characterized using electron counting-based rules [11][12][13][14][15][16][17][18].
Structures of bare B n clusters have been thoroughly analyzed in recent years. These studies show that small clusters prefer planar structures up to a maximum size depending on the charge of the system. Cationic, neutral, and anionic clusters prefer planar structures up to 15, 20, and 40 atoms, respectively . This demonstrates the significant effect that even one electron has on the structural preference of boron clusters.
In recent years, it has been shown that adding alkali metals to the B 12 structure induces fascinating structural changes. For instance, in the LiB 12 global minimum (GM) structure, the naked cluster B 12 structure remains almost unchanged [43], but LiB 12 and NaB 12 -GMs prefer a conical shape with an inner B 4 ring and a higher concavity than the quasi-planar B 12 cluster [44]. More noticeable is the D 6d -Li 2 B 12 GM, a tubular structure consisting of two

Results and Discussion
The putative GM structures of M n B 12 (M = Cu-Au and n = 1-3) clusters are depicted in Figure 1, and relevant lowest energy isomers are depicted in Figures S1-S9. Figure 1 shows that the B 12 structure of the bare cluster is retained at the GM by adding one and two metal atoms. The first metal atom forms a bridged-like B-M-B bond with two boron atoms of the peripheral B 9 ring (1-M), while the second one is placed on one of the edges of the MB 2 triangle (2-M). Note that in previous reports the effect of doping B 12 with other transition metals was evaluated, revealing that metal is placed on the main axis, above the peripheral B 9 ring on the concave side of the B 12 structure [49][50][51][52][53][54], which in the present work has been identified as an isomer close in energy to the putative global minimum of CuB 12 (structure 1b, Figure S1). In the case of AgB 12 and AuB 12 , this structure does not correspond to a local minimum since it has an imaginary frequency, and therefore is not reported. Furthermore, the analogous to the GM structures reported for the ZrB 12 and AlB 12 combinations [55, 56] have relative energies higher than 20.0 kcal mol -1 , thus lying above the relative energy range considered in our report. For the M n B 12 (M = Cu-Au and n = 1-3) clusters, there are marginal changes in the B-B bond distances due to the addition of metals, more significant in the fragment where the metal is bonded. This agrees with the bond orders according to the WBI B-B values, which are in the range of 0.4-1.3 in both the B 12 and the M n B 12 clusters (M = Cu-Au, n = 1, 2), where values close to or greater than 1.0 are among the peripheral atoms, as can be seen in Figure S10. dicate a charge transfer from the M to the B12 fragment (qM = 0.2-0.7 |e|); however, it does not reach the magnitude of the alkali atoms, where almost one electron per metal atom is transferred ( Figures S10-S12). Additionally, the natural electron configurations of the Cu, Ag, and Au atoms in these systems are reported in Table S1. The charge transfer occurs mainly from the 4s and 5s orbitals of Cu and Ag, respectively. While for systems with Au, this transfer, to a lesser extent, occurs from the 5d orbitals.  After reviewing the identified structures, we realized that the counterpart structures of the LinB12 (n = 2, 3) GMs were missing. This prompted us to evaluate these geometries, and as shown in Figure 3, the relative energies when Li is replaced by group 11 metals change significantly. This underlines the importance of using suitable algorithms to explore the PES since it is unreliable to use structural knowledge of related systems, which could lead to entirely wrong conclusions. The structural counterparts are local minima, except for Au2B12 and Au3B12, with two and one imaginary frequencies. Remarkably, for M = Ag and Au, the relative energies are at least 50.0 kcal mol -1 above the GM identified by PES exploration. The WBI M-B values are less than 1.0 for the bridged metal and close to 1.0 for the metal bonded to one boron at the periphery, while the WBI M-M value in 2-M is less than 0.1, showing that metals lack a significant covalent bonding character. When one more metal is added, in M 3 B 12 , the minimum energy structure has a significantly different B 12 fragment than that of the B 12 GM. An elongated planar structure is now favored, 3-M ( Figure 1). The stabilizing role of M to tend planar elongated structure is significant, as evidenced in  Figures S10-S12). Additionally, the natural electron configurations of the Cu, Ag, and Au atoms in these systems are reported in Table S1. The charge transfer occurs mainly from the 4s and 5s orbitals of Cu and Ag, respectively. While for systems with Au, this transfer, to a lesser extent, occurs from the 5d orbitals.
showing that metals lack a significant covalent bonding character. When one more metal is added, in M3B12, the minimum energy structure has a significantly different B12 fragment than that of the B12 GM. An elongated planar structure is now favored, 3-M ( Figure 1). The stabilizing role of M to tend planar elongated structure is significant, as evidenced in Fig Figures S10-S12). Additionally, the natural electron configurations of the Cu, Ag, and Au atoms in these systems are reported in Table S1. The charge transfer occurs mainly from the 4s and 5s orbitals of Cu and Ag, respectively. While for systems with Au, this transfer, to a lesser extent, occurs from the 5d orbitals.  After reviewing the identified structures, we realized that the counterpart structures of the LinB12 (n = 2, 3) GMs were missing. This prompted us to evaluate these geometries, and as shown in Figure 3, the relative energies when Li is replaced by group 11 metals change significantly. This underlines the importance of using suitable algorithms to explore the PES since it is unreliable to use structural knowledge of related systems, which could lead to entirely wrong conclusions. The structural counterparts are local minima, except for Au2B12 and Au3B12, with two and one imaginary frequencies. Remarkably, for M = Ag and Au, the relative energies are at least 50.0 kcal mol -1 above the GM identified After reviewing the identified structures, we realized that the counterpart structures of the Li n B 12 (n = 2, 3) GMs were missing. This prompted us to evaluate these geometries, and as shown in Figure 3, the relative energies when Li is replaced by group 11 metals change significantly. This underlines the importance of using suitable algorithms to explore the PES since it is unreliable to use structural knowledge of related systems, which could lead to entirely wrong conclusions. The structural counterparts are local minima, except for Au 2 B 12 To gain further insights into the chemical bonding, we performed an AdNDP analysis. Orbital localization methods proved insightful in understanding chemical bonding in boron clusters [59,60]. The results of the AdNDP analysis for all systems are reported in Figures S13-S15. In the three systems 1-M, 2-M, and 3-M, five, ten, and fifteen 1c-2e lone pairs are identified, corresponding to the d orbitals of the metals of each system. For 1-M and 2-M, the bonding picture of the B12 fragment remains identical to that of the bare B12 cluster (see Figures S13-S14). In 1-M, the metal connects to the B12 fragment through a three-center one-electron (3c-1e) B-M-B σ-bond, as shown in Figure S13.
In the case of 2-M, the bonding situation is very similar, only now the second M atom is attached to one of the periphery B's by one M-B 2c-2e σ-bond. Furthermore, the bridged M is now linked via a B-M-B 3c-2e σ-bond at the cost of delocalization of the periphery B-B bond. The 3-M bonding will be discussed in more detail. For 3-Cu, the localized orbitals, excluding the lone pairs, recovered by AdNDP are reported in Figure 4. The other systems show similar bonding patterns (see the full bonding picture in Figure S15). Eight B-B 2c-2e σ-bonds link the nine periphery borons. Seven 3c-2e σ-bonds are also detected between each triangular fragment that forms the three internal boron with those of the periphery. The M extremes of the M3 fragment are linked to borons by M-B 2c-2e σ-bonds. The central M does not participate in any bonds, according to AdNDP. The remaining electrons, AdNDP locates in three π-orbitals, two of 6c-2e, and one of 4c-1e, for a total of five πelectrons. These results suggest the possibility of (anti)aromaticity, local or global, given both σ-and π-delocalized bonds. We will discuss below this possibility by analyzing the 3-M magnetic behavior. To gain further insights into the chemical bonding, we performed an AdNDP analysis. Orbital localization methods proved insightful in understanding chemical bonding in boron clusters [59,60]. The results of the AdNDP analysis for all systems are reported in Figures S13-S15. In the three systems 1-M, 2-M, and 3-M, five, ten, and fifteen 1c-2e lone pairs are identified, corresponding to the d orbitals of the metals of each system. For 1-M and 2-M, the bonding picture of the B 12 fragment remains identical to that of the bare B 12 cluster (see Figures S13 and S14). In 1-M, the metal connects to the B 12 fragment through a three-center one-electron (3c-1e) B-M-B σ-bond, as shown in Figure S13.
In the case of 2-M, the bonding situation is very similar, only now the second M atom is attached to one of the periphery B's by one M-B 2c-2e σ-bond. Furthermore, the bridged M is now linked via a B-M-B 3c-2e σ-bond at the cost of delocalization of the periphery B-B bond. The 3-M bonding will be discussed in more detail. For 3-Cu, the localized orbitals, excluding the lone pairs, recovered by AdNDP are reported in Figure 4. The other systems show similar bonding patterns (see the full bonding picture in Figure S15). Eight B-B 2c-2e σ-bonds link the nine periphery borons. Seven 3c-2e σ-bonds are also detected between each triangular fragment that forms the three internal boron with those of the periphery. The M extremes of the M 3 fragment are linked to borons by M-B 2c-2e σ-bonds. The central M does not participate in any bonds, according to AdNDP. The remaining electrons, AdNDP locates in three π-orbitals, two of 6c-2e, and one of 4c-1e, for a total of five π-electrons. These results suggest the possibility of (anti)aromaticity, local or global, given both σand π-delocalized bonds. We will discuss below this possibility by analyzing the 3-M magnetic behavior.  The shape of the 3-M structure evokes the geometry of an isomer of its valence isoelectronic B13 cluster, which is 3.7 kcal mol -1 above the GM (at the PW91/TZ2P level) [61]. The AdNDP analysis of this system is shown in Figure 5, where it is seen that there are significant differences with 3-M, the B9 contour is closed by 10B-B 2c-2e σ-bonds, there are six delocalized 4c-2e σ-bonds connecting the internal B3 fragment to the B9 contour, and AdNDP places seven electrons formingπ-bonds. These bonding differences, i.e., having 4n delocalized σ-bonds, could be responsible for the non-planarity of B13. The isomerization energy decomposition analysis (IEDA) allows us to analyze quantitatively the structural preference between two isomers in terms of energy components [45]. A hypothetical thermodynamic cycle used to perform the IEDA in the M3B12 systems The shape of the 3-M structure evokes the geometry of an isomer of its valence isoelectronic B 13 cluster, which is 3.7 kcal mol -1 above the GM (at the PW91/TZ2P level) [61]. The AdNDP analysis of this system is shown in Figure 5, where it is seen that there are significant differences with 3-M, the B 9 contour is closed by 10 B-B 2c-2e σ-bonds, there are six delocalized 4c-2e σ-bonds connecting the internal B 3 fragment to the B 9 contour, and AdNDP places seven electrons forming π-bonds. These bonding differences, i.e., having 4n delocalized σ-bonds, could be responsible for the non-planarity of B 13 .  The shape of the 3-M structure evokes the geometry of an isomer of its valence isoelectronic B13 cluster, which is 3.7 kcal mol -1 above the GM (at the PW91/TZ2P level) [61]. The AdNDP analysis of this system is shown in Figure 5, where it is seen that there are significant differences with 3-M, the B9 contour is closed by 10B-B 2c-2e σ-bonds, there are six delocalized 4c-2e σ-bonds connecting the internal B3 fragment to the B9 contour, and AdNDP places seven electrons formingπ-bonds. These bonding differences, i.e., having 4n delocalized σ-bonds, could be responsible for the non-planarity of B13. The isomerization energy decomposition analysis (IEDA) allows us to analyze quantitatively the structural preference between two isomers in terms of energy components [45]. A hypothetical thermodynamic cycle used to perform the IEDA in the M3B12 systems is shown in Figure S16. Thus, we compare 3-Cu vs. the first Cu3B12 isomer that preserves the B12 fragment of the naked cluster (ΔEiso = 13.0 kcal mol −1 ); the relative energy is slightly The isomerization energy decomposition analysis (IEDA) allows us to analyze quantitatively the structural preference between two isomers in terms of energy components [45].
Molecules 2023, 28, 236 6 of 12 A hypothetical thermodynamic cycle used to perform the IEDA in the M 3 B 12 systems is shown in Figure S16. Thus, we compare 3-Cu vs. the first Cu 3 B 12 isomer that preserves the B 12 fragment of the naked cluster (∆E iso = 13.0 kcal mol −1 ); the relative energy is slightly different from that reported in Figure S7 since the IEDA calculations were performed at the PBE0-D3-BJ/ZORA/TZ2P level. The values summarized in Table 1 show that interactions favor GM in the orbital (∆∆E orb = 115.3 kcal mol -1 ) contribution, compensating for the electrostatic (∆∆V elstat = -7.9 kcal mol -1 ) and Pauli repulsion (∆∆E Pauli = -19.5 kcal mol -1 ) terms which favor the higher energy isomer; the difference in the dispersion interaction is negligible. These results show that the covalent interactions between M 3 and the B 12 are enhanced and are more important in terms of magnitude than ionic interactions in the GM, thus accounting for its preference. However, ∆E iso also depends on the distortion energy of each fragment, favoring, in this case, the higher energy isomer (∆∆E dist (total) = -74.5 kcal mol -1 ). Note that the major contribution of this term comes from the distortion of the M 3 fragment, while the B 12 fragment slightly prefers the geometry it has in the GM. Therefore, Cu 3 B 12 prefers the planar elongated shape granted by better orbital interactions between the Cu 3 and B 12 fragment, compensating for the energy cost to distort its M 3 moiety, and to a lesser extent, the unfavorable electrostatic interaction and Pauli repulsion terms. IEDA predicts a similar trend for Ag 3 B 12 with the difference that the Pauli repulsion term, in this case, also favors GM. Finally, for Au 3 B 12 , the results are slightly different. The distortion energies follow the same trends and magnitudes as for its lighter analogs, and the orbital interaction remains the most important term; however, the electrostatic interaction, which, as in Cu 3 B 12 and Ag 3 B 12 , favors the second isomer, is now comparable in magnitude to the orbital term, so that the balance of all the terms that make up ∆E iso leaves both isomers virtually isoenergetic at the PBE0-D3-BJ/ZORA/TZ2P level. Note that although at the PBE0-D3/def2-TZVP level, the planar elongated system is still predicted to be the global minimum of Au 3 B 12 , the difference in energy between it and the highest energy isomer is much smaller (2.1 kcal mol -1 ) than for Cu 3 B 12 and Ag 3 B 12 .
AdNDP analysis reveals the presence of delocalized π-bonds, which could be associated with a possible (anti)aromatic character. To investigate this possibility, we have evaluated the current densities induced by an external magnetic field (perpendicular to the molecular plane). According to the magnetic criteria, an (anti)aromatic system is characterized by the presence of (diatropic) paratropic ring currents circuits. Figure 6 shows that 3-Cu exhibits both local and global diatropic ring currents circuits. The local circuits are internal and around the inner B atoms. At the same time, the global ring current surrounds the cluster decorating the external M 3 B 9 chain. By analyzing the integrated current profiles (Figures S17-S19), it has been possible to estimate the ring current strength (RCS) of each circuit (see Figure 6). RCS values are significant, considering benzene has a net RCS of 11.8 nA T -1 at the same level. The magnetic behavior of 3-Ag and 3-Au are similar, as shown in Figures S17-S19. Therefore, the 3-M are classified as local and global aromatic species according to the magnetic criterion.

Materials and Methods
We systematically explored the potential energy surfaces employing the AUTOMA-TON program [57,62], with an initial screening (in the singlet states) at the PBE0 [63]/SDDALL [64] level. The low-lying energy isomers (<20.0 kcal mol -1 above the putative global minimum) were re-minimized at the PBE0-D3 [65]/def2-TZVP [66] level. The top isomers were optimized in the triplet state at the PBE0-D3/def2-TZVP level to test the relative energies at this multiplicity. To provide more reliability in our energetic analysis, relative energies were computed using the domain-based local pair-natural orbital-based single-, double-, and perturbative triple excitations coupled cluster DLPNO-CCSD(T) method [67] as implemented in ORCA-4.2.1 [68,69] in conjunction with extrapolation to the complete basis set limit via the def2-SVP and def2-TZVP basis sets [70,71] (labeled as DLPNO-CCSD(T)/CBS). This refinement was performed for isomers up to 10.0 kcal mol -1 above the putative global minimum. The chemical bonding was analyzed (at the PBE0-D3/def2-TZVP level) using the Wiberg bond index (WBI) and natural population analysis (NPA), as implemented in the NBO 6.0 program [72]. Furthermore, the adaptive natural density partitioning (AdNDP) method [73,74] was performed with the Multiwfn program [75]. AdNDP represents the electronic structure in n-center-two-electron (nc-2e) bonds, with n ranging from one to the total number of atoms in the molecule, recovering the Lewis' electron pair concept as the fundamental chemical bonding component complemented with delocalized bonds, when they are present. Isomerization energy decomposition analysis (IEDA) [45] was computed. IEDA allows the decomposition of the isomerization energy (ΔEiso) in terms of the distortion energy of the fragments (ΔEdist) and the change in the interaction energies between the fragments of each isomer (ΔΔEint). The latter term, in turn, is decomposed as the sum of the changes in the orbital (ΔΔEorb) and electrostatic (ΔΔVelstat) interaction, the Pauli repulsion (ΔΔEPauli), and the dispersion energy (ΔΔEdisp). This analysis was performed at the PBE0-D3-BJ [76]/ZORA [77]/TZ2P [78] level using ADF2012 [79].
To assess aromaticity, we have analyzed the current densities induced by an external magnetic field applied perpendicularly to the molecular plane (at the PBE0-D3/def2-TZVP level) using the GIMIC program [80,81], which employs the gauge-included atomic orbitals (GIAO) method [82]. For vector plots, we used the Paraview 5.10.0 software [83,84]. The ring current strengths (RCS), a quantitative descriptor of aromaticity, were obtained by integrating the ring current flow in a perpendicular plane using the two-dimensional Gauss-Lobatto algorithm [80,85] as implemented in GIMIC. The integration planes correspond to cut-off planes perpendicular to the chosen bonds of the interest annular moiety and extend horizontally for 3.6 Å along the ring's plane, with 2.6 Å above and below the bond. Positive (diatropic), negative (paratropic), and near-zero RCS values indicate

Materials and Methods
We systematically explored the potential energy surfaces employing the AUTOMA-TON program [57,62], with an initial screening (in the singlet states) at the PBE0 [63]/ SDDALL [64] level. The low-lying energy isomers (<20.0 kcal mol -1 above the putative global minimum) were re-minimized at the PBE0-D3 [65]/def2-TZVP [66] level. The top isomers were optimized in the triplet state at the PBE0-D3/def2-TZVP level to test the relative energies at this multiplicity. To provide more reliability in our energetic analysis, relative energies were computed using the domain-based local pair-natural orbital-based single-, double-, and perturbative triple excitations coupled cluster DLPNO-CCSD(T) method [67] as implemented in ORCA-4.2.1 [68,69] in conjunction with extrapolation to the complete basis set limit via the def2-SVP and def2-TZVP basis sets [70,71] (labeled as DLPNO-CCSD(T)/CBS). This refinement was performed for isomers up to 10.0 kcal mol -1 above the putative global minimum. The chemical bonding was analyzed (at the PBE0-D3/def2-TZVP level) using the Wiberg bond index (WBI) and natural population analysis (NPA), as implemented in the NBO 6.0 program [72]. Furthermore, the adaptive natural density partitioning (AdNDP) method [73,74] was performed with the Multiwfn program [75]. AdNDP represents the electronic structure in n-center-two-electron (nc-2e) bonds, with n ranging from one to the total number of atoms in the molecule, recovering the Lewis' electron pair concept as the fundamental chemical bonding component complemented with delocalized bonds, when they are present. Isomerization energy decomposition analysis (IEDA) [45] was computed. IEDA allows the decomposition of the isomerization energy (∆E iso ) in terms of the distortion energy of the fragments (∆E dist ) and the change in the interaction energies between the fragments of each isomer (∆∆E int ). The latter term, in turn, is decomposed as the sum of the changes in the orbital (∆∆E orb ) and electrostatic (∆∆V elstat ) interaction, the Pauli repulsion (∆∆E Pauli ), and the dispersion energy (∆∆E disp ). This analysis was performed at the PBE0-D3-BJ [76]/ZORA [77]/TZ2P [78] level using ADF2012 [79].
To assess aromaticity, we have analyzed the current densities induced by an external magnetic field applied perpendicularly to the molecular plane (at the PBE0-D3/def2-TZVP level) using the GIMIC program [80,81], which employs the gauge-included atomic orbitals (GIAO) method [82]. For vector plots, we used the Paraview 5.10.0 software [83,84]. The ring current strengths (RCS), a quantitative descriptor of aromaticity, were obtained by integrating the ring current flow in a perpendicular plane using the two-dimensional Gauss-Lobatto algorithm [80,85] as implemented in GIMIC. The integration planes correspond to cut-off planes perpendicular to the chosen bonds of the interest annular moiety and extend horizontally for 3.6 Å along the ring's plane, with 2.6 Å above and below the bond. Positive (diatropic), negative (paratropic), and near-zero RCS values indicate aromaticity, antiaromaticity, and non-aromaticity. The bisected current densities (sigma and pi) were calculated using AIMAll software [86] at the PBE0-D3/def2-TZVP level. As previously established in other studies, the different ring current circuits have been identified by analyzing the RCS profiles in appropriate planes [87,88].

Conclusions
The effect of doping the B 12 cluster with group 11 metals, in M 3 B 12 (M = Cu-Au) clusters is evaluated to compare with the impact of alkali metals, especially Li, where the minimum energy structures of Li 2 B 12 and Li 3 B 12 consist of B 12 arrays quite different from those of the bare B 12 cluster. Exploration of the potential energy surface, using genetic algorithms and DFT calculations, reveals that adding one or two metal atoms induces substantial changes in the B 12 fragment, with minor modifications in bond distances, especially of the fragments in contact with the metals. However, when the third M atom is added, in M 3 B 12 , a structure containing a planar elongated B 12 fragment (3-M), whose shape is high-energy in the bare cluster, is favored. This is evidence of the wealth of structural possibilities by doping boron clusters with metals, where the nature of the metal may have unexpected effects. The latter also evidences the need for adequate methods to identify minimum energy structures since no structural preferences can be assumed based on similar systems. For example, the GM analogous structures of Li 2 B 12 are less stable by at least 7 kcal mol -1 , while the Li 3 B 12 analogs are not even all local minima and are more than 50 kcal mol -1 away from the most stable one. Bonding analysis evidences the presence of delocalized σand π-bonds in 3-M. Furthermore, magnetically induced current density analysis evidences the existence of local and global diatropic ring currents, characterizing them as aromatic.