Metallo-boranes : a class of unconventional superhalogens defying electron counting rules †

Superhalogens are a class of highly electronegative atomic clusters whose electron affinities exceed those of halogens. Due to their potential for promoting unusual reactions and role as weakly coordinating anions as well as building blocks of bulk materials, there has been considerable interest in their design and synthesis. Conventional superhalogens are composed of a metal atom surrounded by halogen atoms. Their large electron affinities are due to the fact that the added electron is distributed over all the halogen atoms, reducing electron–electron repulsion. Here, using density functional theory with a hybrid exchange–correlation functional, we show that a new class of superhalogens can be developed by doping closo-boranes (e.g., B12H12) with selected metal atoms such as Zn and Al as well as by replacing a B atom with Be or C. Strikingly, these clusters defy electron counting rules. For example, according to the Wade–Mingos rule, Zn(B12H12) and Al(BeB11H12) are closed-shell systems that should be chemically inert and, hence, should have very small electron affinities. Similarly, Zn(B12H11), Al(B12H12), and Zn(CB11H12), with one electron more than needed for electronic shell closure, should behave like superalkalis. Yet, all these clusters are superhalogens. This unexpected behavior originates from an entirely different mechanism where the added electron resides on the doped metal atom that is positively charged due to electron transfer.


Introduction
One of the important concepts that has emerged in cluster science is that of superatoms, 1 which are atomic clusters of given size and composition mimicking the chemistry of elements in the periodic table. Superhalogens 2 and superalkalis 3 are superatoms that mimic the chemistry of halogen and alkali atoms, respectively. The former have electron affinities (EA) larger than those of halogens, while the latter have vertical ionization energies (VIE) smaller than those of alkali atoms. EA is defined as the energy difference between the anion and the neutral cluster, both in their respective ground state configurations. VIE, on the other hand, is the energy difference between the neutral and positively charged cluster, both at the ground state geometry of the neutral. The highest electron affinity of a halogen atom is that of Cl, namely 3.6 eV, and the lowest ionization energy of an alkali atom is that of Cs, namely 3.89 eV. While early works on superhalogens and superalkalis were of academic interest, it has now been shown that these species can be used to form new supersalts 4 with unique properties. For example, superhalogens and hyperhalogens 5 (clusters with EAs even larger than those of superhalogens) can serve as the building blocks of hydrogen storage materials, 6 halogen-free electrolytes in metal-ion batteries, 7 hybrid perovskite solar cells resistant to moisture, 8 and ion conductors with enhanced ionic conductivities. 9 It has also been shown that superhalogens can be used in the design of multiferroic materials. 10 These promising technological applications have led to a surge of research in identifying novel superhalogen moieties.
According to the original design by Gutsev and Boldyrev, 2 superhalogens [11][12][13][14][15] with composition MX k+1 are composed of a metal atom (M) and k + 1 halogen atoms (X), where k is the maximal valence of the metal atom. The design principle has been based on the octet electron-counting rule 16 for low atomic number species and the 18-electron rule 17 for transition metals. In the former, outer s and p orbitals are filled with 2 and 6 electrons, while in the later s, p, and d orbitals are filled with 2, 6, and 10 electrons, respectively. Typical examples of superhalogens containing transition metal atoms include M@Au 12 (M = V, Nb, Ta). 18 In addition, there are superhalogens, such as H n F n+1 , 19 that do not contain any metal atom and MH n 20 (M being a non-transition metal element like Be, Mg, Al) that do not contain any halogen atom. The high EA of these superhalogens is due to the added electron being shared by multiple halogen atoms in the cluster, leading to reduced electron-electron repulsion. For nearly three decades since the prediction of superhalogens, the design and synthesis of these species fol-lowed the above Gutsev-Boldyrev strategy. Later, Jena and coworkers showed that electron counting rules such as the Wade-Mingos rule 21 and Huckel's rule 22,23 could also be used to design superhalogens composed of borane-based clusters 24,25 and organic molecules, 26 respectively. It was also shown that the electron affinity of superhalogens can be further increased by simultaneously satisfying multiple electron-counting rules. 27,28 All these species can be classified as "conventional" superhalogens.
In this paper, we show that, to create a superhalogen, it is not necessary for the added electron to be distributed over the electronegative sites nor for the cluster to follow specific electron counting rules; superhalogens can be created in defiance of the electron shell-closure rule. We demonstrate this by focusing on two types of metallo-boranes; closed-shell metalloboranes, e.g., Zn(B 12 H 12 ) and Al(BeB 11 H 12 ), and metalloboranes with one electron more than needed for electron shell closure, e.g., Zn(B 12 H 11 ), Zn(CB 11 H 12 ), and Al(B 12 H 12 ). However, as expected, metallo-boranes with one less electron than needed for shell closure, e.g., Zn(BeB 11 H 12 ) and Li(B 12 H 12 ), are conventional superhalogens. Note that the stability of closo-boranes, B n H n , is governed by the Wade-Mingos polyhedral skeletal electron pair theory (PSEPT). Here, (4n + 2) electrons are required for electron shell closure, where n is the number of vertices of the boron polyhedron. As B n H n clusters have 4n electrons, two more are needed for their stability, and B n H n 2− is a stable cluster. The second electron affinity, i.e., energy gained when the second electron is attached to B 12 H 12 − , is 0.9 eV. 29

Computational method
All calculations are performed using density functional theory 31 with the long-range corrected hybrid exchange-correlation functional ωB97XD 32 and 6-311+g(d,p) basis sets embedded in the Gaussian16 package. 33 The preferred site of the doped metal atom was determined by considering both endohedral and exohedral positions. Geometries are optimized without any symmetry constraint. Default convergence criteria are used for the force (4.5 × 10 −4 Hartree per Bohr) and displacement (1.8 × 10 −3 Bohr). The output symmetries given in Table S1 † are kept at a tolerance of 0.1 Å using the Gaussview. Our previous calculations 34 showed that the EAs and VIEs obtained using the above procedure are accurate to within 0.2 eV compared to the experiment. No imaginary frequency is found for the optimized geometries. VIE, EA, and vertical detachment energy (VDE) are calculated using the total energies of the clusters with different charge states. VDE is the energy difference between the anion and the neutral, both at the ground state geometry of the anion. The difference between EA and VDE, thus, is a measure of the effect of structural relaxation of the anionic cluster when the extra electron is removed. Natural bond orbital analysis (NBO) is performed to study the charge states of the atoms. 35 The nature of bonding between the adsorbed metal atom and the cluster is studied using Bader's Quantum theory of atoms in the molecule (QTAIM) 36 approach. This is illustrated by calculating the contour map of the Laplacian of the electron density 37 using the Multiwfn package. 38 To better understand the electronic structure, we have further calculated the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the projected density of states, and the charge density difference (CDD) of the studied clusters. CDD is obtained by subtracting the superimposed electron density of the selected fragments from the total electron density of the clusters. The projected density of states is obtained by using the C-squared population analysis (SCPA) method proposed by Ros and Schuit 39 as implemented in the Multiwfn package; during this calculation, we have removed the diffuse function. The original discrete molecular orbital energy levels are convoluted with a Gaussian function resulting in a smooth yet broadened DOS, as shown in Fig. 2. With the calculated DOS, our goal is to identify the electronic/elemental compositions of the frontal orbitals. Besides, thermally vibrational stability of the cluster is studied by using AIMD simulation; see ESI † for the details.  Fig. S1(a). † While in Al(BeB 11 H 12 ) the Al atom takes place of the Be atom in BeB 11 H 12 , independent of whether Al atom is placed in endohedral or exohedral site. This is consistent with the previous study on similar systems. 28 The optimized geometries of neutral and anionic Zn(B 12 H 12 ) are plotted in Fig. 1 It is interesting to note that Zn-H distance of 1.89 Å is shorter than that of the K-H distance of 2.29 Å in crystalline K 2 (B 12 H 12 ). 40 To see if this difference could be due to the fact that our study is based on an isolated cluster while K 2 (B 12 H 12 ) is crystalline, we optimized the geometry of K 2 (B 12 H 12 ) cluster. The calculated K-H distance of 2.55 Å is larger than that in the crystalline phase. Thus, one would expect that in Zn(B 12 H 12 ) crystal the Zn-H distance would be even smaller than 1.89 Å. The difference between the Zn-H and K-H distance is due to the size effectthe ionic radii of Zn and K are 74 pm and 138 pm, respectively.

Results and discussion
The equilibrium geometries of neutral and anionic Al (BeB 11 H 12 ) clusters are given in Fig. 1(c) and (d). It has been shown before that replacing a B atom with Be in the B 12 icosahedral cage would lead to a stable trianion. 41 Thus, we hypothesized that adding an Al atom to BeB 11 H 12 would make a closed-shell stable cluster, yielding a cluster where the Al atom is bound to an unperturbed BeB 11 H 12 cage. Geometry optimization, however, led to a different geometry of Al(BeB 11 H 12 ). As seen in Fig. 1(c), the Al atom formed the cage with 11 B atoms, with the Be atom bonded to AlB 11 H 12 . This structure ( Fig. 1(c)) was found to be 2.18 eV lower in energy than the one when Be forms the cage with the B atoms as shown on Fig. S1 Table 1, are 4.30 eV and 4.70 eV, respectively. This small difference is typical in cases where the ground state geometries of the neutral and its anion are not very different. However, the situation is different for Al(BeB 11 H 12 ), where the EA and VDE are 3.61 eV and 4.44 eV, respectively. This large difference of 0.83 eV is a consequence of significant changes in the geometries of the neutral and anionic clusters.
To understand the origin of this behavior, we have analyzed the electronic structure of the neutral and anionic clusters. First, we discuss the charge distribution. In the neutral Zn(B 12 H 12 ) cluster, the charge on the Zn atom is +1.50e, as can be seen from Fig. S2(a). † This is consistent with what we had hypothesized earlier, i.e., Zn would donate most of its two electrons to satisfy the charge requirement of B 12 H 12 , in keeping with the Wade-Mingos rule. Once an extra electron is added, the charge on the Zn site in Zn(B 12 H 12 ) − decreases to +0.79e. This clearly shows that instead of being distributed over the H atoms, the added electron goes to the positively charged Zn site. Note that the ionization energy of the Zn atom is 9.34 eV. Thus, as the added electron goes to the Zn site, it gains energy, not because it is distributed over a large phase space but because it neutralizes the Zn atom. Thus, Zn(B 12 H 12 ) is an unconventional superhalogen and can serve as a model for the design of many such species.
This is also what we see in Al(BeB 11 H 12 ). Here, in the neutral Al(BeB 11 H 12 ) cluster, Al and Be carry charges of +1.4e and +1.6e, respectively, as they donate the electrons to the cage needed for electronic shell closure. As an extra electron is added, we observe that the charges at the Al and Be sites in Al(BeB 11 H 12 ) − decrease to +1.19e and +1.45e, respectively (see Fig. S2(b) †). As the ionization energies of Al and Be atoms are respectively 5.99 eV and 8.83 eV, energy is gained as the added electron partially neutralizes these sites. Consequently, Al(BeB 11 H 12 ) is a superhalogen, although its EA of 3.61 eV is marginally larger than that of Cl, namely, 3.60 eV.
Next, we analyze the electronic structure and bonding characteristics by studying the HOMO-LUMO gap, the partial density of states, the charge density difference, and Bader's quantum theory of atoms in molecules (QTAIM) analysis. The computed HOMO-LUMO gaps of these clusters are shown in Table 1. What is surprising is that both Zn(B 12 H 12 ) and Al(BeB 11 H 12 ) clusters are superhalogens, in spite of being closed-shell systems and having large HOMO-LUMO gaps of 6.0 and 4.7 eV, respectively. HOMO-LUMO gap can be considered as an indicator of electronic stability and chemical reactivity of clusters. Note that the clusters with large HOMO-LUMO gaps are reluctant to donate or accept an electron from a low-lying HOMO or high-lying LUMO. In addition, the change in the gap, with the addition of an electron, can give us some clue about the stability of the anion compared to that of the neutral cluster. Fig. 2 shows the projected density of states of Zn(B 12 H 12 ) and Al(BeB 11 H 12 ) clusters. Orbital composition analysis shows that in neutral Zn(B 12 H 12 ), Zn s-p orbital has a significant contribution at LUMO, and HOMO is due to the B 12 H 12 cluster. On the other hand, in the anion, there is a significant contribution from Zn s-p orbital at HOMO. This increase in the density of states around HOMO for Zn indicates that the added electron resides on the Zn orbital, which is consistent with the NBO charge analysis shown in Fig. S2(a). † In the anionic Al(BeB 11 H 12 ), Al s-p orbital has a significant contribution at HOMO, which is negligible in the neutral. This also suggests that the added electron mainly resides on Al, consistent with the NBO charge analysis in Fig. S2(b). † Fig. 3 shows the 2D and 3D charge density difference (CDD) for Zn(B 12 H 12 ) and Al(BeB 11 H 12 ) clusters. The regions where electrons are accumulated and depleted are represented by yellow and blue colors, respectively, in the 3D CDD plot. In Zn(B 12 H 12 ), we observe positive charge density along the Zn-H bond. At the same time, the surrounding Zn regions show that there is an apparent charge depletion, indicating charge transfer from Zn during the formation of the Zn(B 12 H 12 ) complex. These observations suggest that the bonding of Zn with the cluster is primarily ionic. By analyzing the CDD for Al(BeB 11 H 12 ), a similar conclusion can be made.
To further understand the nature of bonding of the metal atoms in these clusters, we performed Bader's quantum theory of atoms in molecules (QTAIM) analysis. In addition, we calculated the Laplacian and gradient of the electron density. The existence of the bonds between atoms is characterized by the     Fig. 1(a and b). Contrary to our expectation, these clusters have VIEs higher than that of Na, which is 5.14 eV, and do not behave as superalkalis. Instead, the EAs of these clusters is higher than that of Cl, making these superhalogens. In the following, we discuss the reasons for this unusual behavior. We begin with the equilibrium geometries of neutral Zn(B 12 H 11 ), Al(B 12 H 12 ), and Zn(CB 11 H 12 ) clusters as shown in Fig. 4(a, b and c), respectively. Note that even when we remove one H atom or substitute one of the B atoms in the cage with C, the resulting cage structure remains intact. In Zn(B 12 Fig. 4(d, e and f), respectively. In anionic Zn(B 12 H 11 ), the Zn-H distances increase from its neutral and lie in the range 2.97-3.14 Å (the range in neutral is 1.98-2.24 Å) and Zn-B distance lies in the range 3.58-3.64 Å  To understand the reason for the superhalogen behavior of these clusters, which should be behaving like superalkalis, we examine the charge distribution. In neutral Zn(B 12 H 11 ), the charge on Zn is +0.87e, while that on the naked B on the cage is +0.68e. When an electron is added, it neutralizes the positive charge on the Zn atom, as shown by the natural distribution values (Zn has a null charge in anion) in Fig. S4(a). † Note that there is very little change in the charge on the naked B atom (+0.64e in the anion).
In Al(B 12 H 12 ), the difference in bond length and the distribution of additional electrons follow the same trend as in Zn(B 12 H 11 ). Al-H bond length increases from 1.88 Å in the neutral to 2.07 Å in the anion, indicating a weakening of the Al bonding (see Fig. 4(b and e)). Besides, the Al binding energies of 4.93 eV in the neutral and 4.65 eV in the anion are consistent with the differences in Al-(H/B) bond distances in their neutral and anionic states in Fig. 4(b and e). Similar reasoning holds for the Zn(CB 11 H 12 ) cluster (Fig. 4(c and f )). Natural charge distributions in neutral and anionic Al(B 12 H 12 ) and Zn(CB 11 H 12 ) in Fig. S4(b) and (c) † indicate a decrease in the charge on Al and Zn in the anionic cluster compared to that in the neutral. This suggests that the added electron mainly resides on the metal atom rather than being distributed on the borane cage.
We now analyze the electronic structure and nature of bonding in these clusters. Fig. 5 shows the projected density of states of the neutral and anionic Zn(B 12 H 11 ), Zn(CB 11 H 12 ), and Al(B 12 H 12 ) clusters. In the neutral and anionic Zn(B 12 H 11 ), Zn-s orbital has a significant contribution at HOMO. In the anionic Al(B 12 H 12 ) and Zn(CB 11 H 12 ) clusters, the HOMO is constituted mostly of the Al-s and Zn-s orbitals, respectively. Besides these observations, the NBO analysis presented in Fig. S4 † indicates that the additional electron in these clusters mainly resides on the metal adatom.
The CDD plots for these clusters in 2D and 3D are shown in Fig. 6. Note that there is an apparent deficiency in the charge around the region surrounding Zn and Al, indicating charge transfer from these metal atoms during the formation of the respective complexes.
The contour maps of the Laplacian of electron density with bond critical points highlighting the interaction of the adatom (Zn, Al) with the cluster atoms (H, B) in Zn(B 12 H 11 ), Zn(CB 11 H 12 ), and Al(B 12 H 12 ) are shown in Fig. 6, while the corresponding molecular graph representing the QTAIM topology of the critical points and possible bond paths are shown in Fig. S5. † In Zn(B 12 H 11 ), BCP is observed along the shortest Zn-H bond, which is further verified by the existence of the bond path along one H atom in Fig. S5(a). † The location of the BCP at the positive contour of the Laplacian (∇ 2 ρ(r) = 0.10) indicates the primarily ionic nature of the Zn-H interaction. No BCP is observed between Zn-B in Zn(B 12 H 11 ), which is reflected by the characteristic Zn-B bond length in Fig. 4. In Al (B 12 H 12 ), BCP is observed along the axis passing through the centroid of the triangle formed by three B atoms of the closoborane ring. The location of the BCP at the positive contour of Laplacian (∇ 2 ρ(r) = 0.08) indicates polar (very weak ionic, but no covalent) interaction of Al in Al(B 12 H 12 ). Since no BCP is observed along Al-H in Al(B 12 H 12 ), Al-H interactions are implicitly influenced by the electron densities along with Al-H and B-H atoms.
The bonding of Zn in Zn(CB 11 H 12 ) is similar to that in Zn (B 12 H 11 ). BCP is observed along the shortest Zn-H bond (namely 2.05 Å) in Zn(CB 11 H 12 ), as shown in Fig. 6(c).   Fig. S6. † In the anionic state, a slight change in the charge on the Zn (+1.15e in neutral vs. +0.94e in the anion) and Be (+1.57e in neutral vs. +1.52e in the anion) in Zn(BeB 11 H 12 ), and on the Li (+0.97e in neutral vs. +0.95e in the anion) atom in Li(B 12 H 12 ) is observed. This indicates that the additional electron mainly resides on the boron cage. The projected density of states for the neutral and anionic states of Zn(BeB 11 H 12 ) and Li(B 12 H 12 ) are shown in Fig. 8. In both clusters, in their neutral and anionic state, the adatom has no noticeable contribution at HOMO and LUMO. Besides, in both clusters, the CDD plot in Fig. 9 shows an apparent deficiency in the charge around the surrounding region of metal atoms during the formation of the complex. Unlike other clusters we studied, the higher value of the EA, namely, 3.67 eV in Zn(BeB 11 H 12 ) and 4.85 eV in Li(B 12 H 12 ), is due to the delocalization of the extra electron over the boron atoms forming the cage.
The contour map of the Laplacian highlighting the Zn and Be interaction with cluster atoms in Zn(BeB 11 H 12 ) and Li interaction with cluster atoms in Li(B 12 H 12 ) is shown in Fig. 9. In Zn(BeB 11 H 12 ), BCP is observed between Zn-B, Zn-H, and Be-H. The existence of BCP between Zn-B is along the shortest Zn-B distance, namely 2.13 Å, while no BCP is observed along Zn-Be. While in Li(B 12 H 12 ), BCP is observed along the axis passing through the centroid of the triangle formed by three B atoms of the closo-borane ring. The existence of the bond path between the metal atoms (Zn, Be, and Li) to the cluster atoms in Fig. S7 † further explains the bonding in these clusters. As before, the nature of Zn and Li bonding can be further understood by the corresponding Laplacian values at the BCP, in Fig. 9.

Limitations and future prospects
Now, we examine the limitations in the design of this new class of superhalogens and explore the future prospects of the metallo-borane class of superhalogens. First, the limitations:  . The bond length (in Å) between the adatom and the nearest atom in the cluster is presented. The color coding for the atoms is the same as in Fig. 1, except the atom in magenta color (in c and d) represents the lithium atom.  Thus, the choice of the negative ion components and high ionization energy of the metal atoms is important in the design of more unconventional superhalogens. For example, H in the B 12 H 12 can be replaced by more electronegative ligands such as halogens (F, Cl) and superhalogens (CN, BO). Previous studies have shown that the electron affinities of B 12 X 12 can be substantially increased when X is a halogen or a superhalogen. It will be interesting to study the electron affinities of Zn(B 12 X 12 ) (X = F, Cl, Br, CN, BO) species. Another promising study is to use transition metal (TM) elements other than Zn, noting that TM elements not only have large ionization energies but also, they carry magnetic moments. For example, could TM(B 12 X 12 ) be a magnetic superhalogen?

Conclusion
Using density functional theory with a long range corrected hybrid exchange-correlation functional (ωB97XD) and the 6-311+g(d,p) basis set, we have shown that a new class of superhalogens, called metallo-boranes, can be designed. A particularly interesting example is Zn(B 12 H 12 ). Note that the electron affinity of the Zn atom is −0.60 eV; this is due to the fact that Zn has a closed 4s 2 shell. Zn(B 12 H 12 ) also has a closed electronic shell with a HOMO-LUMO gap of 6.0 eV. Thus, Zn(B 12 H 12 ) should mimic the chemistry of noble gas atoms, and its electron affinity should be minimal. Yet, its electron affinity is 4.30 eV, making it a superhalogen. Among the studied metallo-boranes (i.e., clusters with closed shell and one extra electron than required for the electron shell closure), Al(B 12 H 12 ) has the highest EA, namely 4.43 eV, and Al(BeB 11 H 12 ) has the lowest, namely 3.61 eV. The basic difference between the traditional superhalogens and these metallo- boranes is the underlying principle governing superhalogen behavior. Unlike traditional superhalogens (with composition MX k+1 ) in which the added electron is distributed over a large phase space provided by the halogen atoms, in the metalloboranes, the added electron mainly resides on the doped metal site to neutralize its positive charge resulting from charge transfer. However, not all metal atoms bound to the B 12 H 12 cage can lead to superhalogens; only those that have high ionization energy can. More interestingly, we found that, unlike the conventional superhalogens, the metallo-borane class of superhalogens defy the electron shell closure rule, thereby expanding the scope for their design and synthesis. In addition, the discovery of this new class of superhalogens opens the door for the design of magnetic superhalogens by doping transition metal atoms. It will be interesting to study if materials synthesized with these magnetic superhalogens could potentially produce ferromagnetic semiconductors. The prospects of designing and synthesizing new materials with tailored properties can bring a new dimension to the superhalogen research.

Conflicts of interest
There are no conflicts to declare.