Single—Not Double—3D-Aromaticity in an Oxidized Closo Icosahedral Dodecaiodo-Dodecaborate Cluster

3D-aromatic molecules with (distorted) tetrahedral, octahedral, or spherical structures are much less common than typical 2D-aromatic species or even 2D-aromatic-in-3D systems. Closo boranes, [BnHn]2– (5 ≤ n ≤ 14) and carboranes are examples of compounds that are singly 3D-aromatic, and we now explore if there are species that are doubly 3D-aromatic. The most widely known example of a species with double 2D-aromaticity is the hexaiodobenzene dication, [C6I6]2+. This species shows π-aromaticity in the benzene ring and σ-aromaticity in the outer ring formed by the iodine substituents. Inspired by the hexaiodobenzene dication example, in this work, we explore the potential for double 3D-aromaticity in [B12I12]0/2+. Our results based on magnetic and electronic descriptors of aromaticity together with 11B{1H} NMR experimental spectra of boron-iodinated o-carboranes suggest that these two oxidized forms of a closo icosahedral dodecaiodo-dodecaborate cluster, [B12I12] and [B12I12]2+, behave as doubly 3D-aromatic compounds. However, an evaluation of the energetic contribution of the potential double 3D-aromaticity through homodesmotic reactions shows that delocalization in the I12 shell, in contrast to the 10σ-electron I62+ ring in the hexaiodobenzene dication, does not contribute to any stabilization of the system. Therefore, the [B12I12]0/2+ species cannot be considered as doubly 3D-aromatic.


INTRODUCTION
Doubly aromatic compounds are species that have two different (nearly) orthogonal types of aromaticity.The discovery of new doubly aromatic systems not only provides new insights into the fundamental principles of chemistry and chemical bonding but may also result in the development of new materials with enhanced stability and unique physicochemical properties.−4 For instance, LiAl 4 − is doubly σand πaromatic, 5 Li 3 Al 4 − in the singlet state is σ-aromatic and πantiaromatic 6 and in the triplet state is Huckel σ-aromatic and Baird π-aromatic, 7 B 12 has double σand π-disk aromaticity, 8 B 6 2− is doubly σand π-antiaromatic, 9,10 Hf 3 has triple σ-, πand δ-aromaticity, 4,11 V 2 B 7 − is doubly σ/π aromatic, 12 and Pa 2 B 2 has been recently reported to be σand π-Mobius aromatic, 13 among many other examples.
Less common is the double aromaticity in organic compounds.Still, there are already a number of examples.The first reported doubly aromatic system was the 3,5dehydrophenyl cation with σand π-aromaticity. 14However, the most well-known example of double aromaticity in organic chemistry is the singlet ground-state dication of hexaiodobenzene, [C 6 I 6 ] 2+ (see Scheme 1a), synthesized by Sagl and Martin. 15[C 6 I 6 ] 2+ is doubly Huckel σ-(with 10 delocalized electrons through the hexaiodo substituents) and π-aromatic (with six delocalized electrons in the benzene ring). 15,16eoretical studies support the double σand π-aromaticity of [C 6 I 6 ] 2+17 as well as that of [C 6 At 6 ] 2+ . 18For the former, relativistic effects are not so relevant but are essential for the latter. 19−21 Borazine analogues of hexaiodobenzene and hexakis(selenyl)benzene dication [B 3 N 3 I 6 ] 2+ as well as [B 3 N 3 (TeH) 6 ] 2+ were also reported to be doubly aromatic, 22 although the π-aromaticity of borazine is known to be extensively lower than that of benzene. 23And very recently, the triplet state of [C 7 Br 7 ] 3+ has been found to be π-Huckel aromatic (with six π-electrons in the tropylium ring) and weakly σ-Baird aromatic (with 12 delocalized σelectrons in the Br 7 ring, Scheme 1b). 24−27 Other examples are the double σand π-aromaticity in bishomotriboriranide 28 and in twisted thienylene−phenylene structures in toroidal and catenated topologies. 29,30t has to be mentioned that to reach double aromaticity in [C 6 I 6 ] 2+ , double oxidation of C 6 I 6 is required to open a hole in one of the 5p orbitals of iodine that generate six possible resonance structures (Scheme 1c depicts only three), if we consider only resonance structures in which the two electrons are removed from the same I atom, all of them with the same weight.The existence of these resonance structures generates the double aromaticity, and the fulfillment of Huckel's rule in both the σand π-systems explains it.
−33 The concept of 3D-aromaticity was introduced by King and Rouvray 34 in 1977 and by Aihara 35 in 1978 when they analyzed polyhedral boranes using a Huckeltype molecular orbital (MO) theoretical approach.2D and 3Daromaticity were perceived as two independent systems until 2014, when it was shown 36 that the two were related, described as two sides of the same coin.In 2016, it was demonstrated 37 that each aromatic annulene had its aromatic counterpart in the boron closo hydrides that could be categorized based on the Huckel's 4n + 2 rule.Later on, some of us 38 established the conditions that must be fulfilled for a compound to be 3Daromatic, namely, (i) (at least) triply degenerate MOs as found in tetrahedral or higher symmetry molecules, (ii) a closed-shell electronic structure, which leads to a 6n + 2 electron count in the case of tetrahedral or octahedral molecules, (iii) extensive electron delocalization involving the complete 3D molecule leading to resonance stabilization, and (iv) similar (optoelectronic and magnetic) properties in the three xyz directions.Such conditions are obeyed only by a few compounds.The first known species with 3D-aromaticity were the closo boranes, such as [B 10 H 10 ] 2− or [B 12 H 12 ] 2− and derivatives, synthesized at the end of the 1950s. 39,40Not only closo boranes [B n H n ] 2− (5 ≤ n ≤ 14) but also their carboranes counterparts, which result from single or double substitution of BH by isoelectronic CH + units in closo boranes, are 3D-aromatic compounds. 31hese clusters obey the Wade's 2n + 2 rule 41 and the equivalent Mingos' 4n + 2 rule. 42−46 Moreover, the high thermal stability of these clusters 47−49 further supports their aromatic character. 47,50,51−67 With the present investigation, we would like to provide both evidence and counter-evidence of the potential double 3D-aromaticity of the dodecaiodo-dodecaborate cluster.There are several reasons, more exactly seven, for choosing [B 12 I 12 ] 2− .First, [B 12 H 12 ] 2− , which has the same boron cage as [B 12 I 12 ] 2− , is likely the most aromatic closo borane. 37,68Indeed, it is the one that has the highest heat of formation among [B n H n ] 2− (5 ≤ n ≤ 12) clusters, 69 it has large adiabatic and vertical electron detachment energies, which is an indication of its high stability, 70 it has the lowest average energy on a per-vertex basis, 44 and it has the highest resonance energy. 35Second, [B 12 I 12 ] 2− (and, in general all closo [B 12 X 12 ] 2− ; X = halogen) has a high structural and electronic stability and chemical inertness, especially in front of electrophilic attacks, as well as superweak basicity. 71,72Third, [B 12 I 12 ] 2− has the largest oxidation potential among all closo [B 12 X 12 ] 2− (X = halogen). 73ourth, the second electron in the double oxidation of closo [B 12 X 12 ] 2− (X = F, Cl) is taken from the boron cage, whereas for X = I is taken from the halogen shell (for X = Br, we have an intermediate situation with the electron partially removed from the boron cage and the bromide shell). 72 Hirsch rule 74 for spherical aromaticity, with n = 5.However, the required oxidation to open a hole changes this number of electrons.

METHODOLOGY
All DFT calculations were performed with the Amsterdam Density Functional (ADF) program 75,76 using dispersioncorrected density functional theory (DFT) with relativistic corrections at the ZORA-BLYP-D3(BJ)/TZ2P level of theory 77−80 for geometry optimizations and energy calculations, with the full electron model for all atoms (no frozen core).All stationary points were verified to be minima on the potential energy surface through vibrational analysis.
−87 It has to be stressed that energetic stabilization and electron delocalization are the two most important requirements for aromaticity, and the two are compulsory conditions, whereas ring currents and bond length equalization are usual conditions followed by most of the aromatic species, but not sufficient to prove aromaticity.We considered magnetic, electronic, and energetic descriptors of aromaticity since it is generally accepted that one should use a set of indices based on different properties to discuss the aromaticity of a given species. 88he magnetic properties of aromaticity were first evaluated by means of the nucleus-independent chemical shift (NICS), proposed by Schleyer and co-workers, as a magnetic descriptor of aromaticity. 89NICS is defined as the negative value of the absolute shielding computed at a ring center or at some other point in the system.Rings with large negative NICS values are considered aromatic.NICS values were computed using the gauge-including atomic orbital method (GIAO). 86,90NICS scans were carried out with the same ZORA-BLYP-D3(BJ)/ TZ2P method.To analyze the importance of relativistic effects, we also computed the NICS scans of [B 12 I 12 ] 2− and singlet [B 12 I 12 ] clusters as well as those of C 6 I 6 and C 6 I 6 2+ with the B3LYP/6-311++G**∼LANL2DZ method (Figures S21 and  S22).Results show that, except for C 6 I 6 2+ , there is an increase in the absolute NICS values (by less than 5 ppm) at the B3LYP/6-311++G**∼LANL2DZ level of theory, but when we compared the initial and the oxidized species, the trends remain the same.On the other hand, magnetically induced current-density susceptibility was obtained with gaugeincluding magnetically induced currents (GIMIC) method. 87,91GIMIC requires the basis set information, the atomic orbital density matrix, and the perturbed atomic orbital density matrices as input data, which have been obtained by performing NMR shielding calculations with the Gaussian 16 program package. 92The specific parameters used in the GIMIC calculations are summarized in Table S1.The NMR shielding calculations were performed with the B3LYP functional and the 6-311++G** basis set for boron and LANL2DZ basis set and pseudopotential for iodine using the ZORA-BLYP-D3(BJ)/TZ2P optimized geometries.Finally, the visualization of the current densities was carried out using ParaView 5.9.0. 93−96 The required information on the formatted checkpoint file and the density matrix within the representation of natural atomic orbitals (NAOs) was obtained using NBO 6.0 software coupled to the Gaussian 09 rev.D.01 version.Then, the RunEDDB code (version 26-Jun-2021) was used to perform the EDDB analysis at the B3LYP/6-311++G**∼LANL2DZ//ZORA-BLYP-D3(BJ)/TZ2P level of theory. 97For the visualization of EDDB G (r) surfaces, we used the Avogadro1.0molecular editor. 98hird, the aromatic stabilization energy was determined through homodesmotic reactions. 99,100Finally, steric effects were analyzed with the SambVca2.1 package of Cavallo and coworkers, calculating the %V Bur and depicting steric maps. 101−103

RESULTS AND DISCUSSION
This section begins with the experimental considerations based on 11 B{ 1 H} NMR spectra of a series of iodinate derivatives that result from the stepwise substitution of hydrogen atoms with iodine atoms in the neutral o-carborane (1,2-C 2 B 10 H 12 ).Then, the chemical oxidation of halogenated derivatives of icosahedral anionic boranes ([B 12 X 12 ] 2− , X = F, Cl, Br, I, with H as the reference) is presented.Subsequently, the discussion delves into the obtained computational results.

Initial Considerations.
The benzene ring is possibly the ideal core to generate an additional ring to produce a concentric and coplanar two-ring system in which the second ring may result in an aromatic ring.Moreover, iodine is easily polarizable, is large, and can be oxidized.Hence, C 6 I 6 was the best starting point to build a system with two aromatic rings orthogonal to each other.A perfect structure for double 3Daromaticity would be a 3D-system whose core is an icosahedron, ideally the periodinated "B 12 ", [B 12 I 12 ] 2− , which could give rise to B 12 I 12 by oxidation.A similar core structure would be that of the "C 2 B 10 ", i.e., periodinate C 2 B 10 I 12 .
To understand the electronic structure and the influence of iodine substitution, one may consider the study of the evolution of [B 12 H 12 ] 2− through the incorporation of iodine groups on the core cluster, step by step.Nevertheless, the stepby-step synthesis of these iodinated compounds cannot be achieved experimentally using the icosahedral cluster [B 12 H 12 ] 2− .However, it is feasible to accomplish this synthesis with the o-carborane cluster, as performed by some of us.The presence of two adjacent carbon atoms in the o-carborane cluster leads to variations in the charge density among its different vertices. 104As a result, it is experimentally feasible to obtain and isolate the step-by-step iodinated compounds derived from o-carborane while modulating both the number and the position of iodine atoms that replace the hydrogen atoms in the o-carborane cluster.The chemistry of mono-to ten-substituted boron-iodinated o-carboranes (I n -1,2-C 2 B 10 H 12-n , n = 1−10) has been widely developed because the usefulness of o-carborane units is dependent upon their functionalization.The 2000s were dominated by the catalyzed reactions under Kumada conditions, and palladium was the sought catalyst for the B−C bond formation from B−I vertices, but more available metals (Ni) as well as the presence of CuI as cocatalyst were also employed to obtain well-defined patterns of o-carborane substitution from different and welldefined iodo-o-carboranes.Conventional reactions in solution as well as new solvent-free methods permitted regioselective control of o-carboranes iodine substitution to generate iodine Journal of the American Chemical Society I n -1,2-C 2 B 10 H 12-n (n = 1−10) derivatives on demand.The synthesis of regioselective B-iodinated o-carboranes was achieved; nevertheless, in general, the reactivity of the halogen linked to the boron is low.−109 Focusing on the 11 B{ 1 H} NMR spectrum of 9,12-I 2 -o-carborane (Figure 1b) and comparing it with ocarborane (Figure 1a), it can be observed that its appearance is considerably modified by the presence of iodine atoms on the B(9) and B (12) vertices with respect to pristine o-carborane and that the chemical shifts of these boron atoms are especially affected, being largely shifted upfield (from −2.1 ppm in the parent o-carborane to −13.8 ppm in the diiodinated ocarborane derivative, which corresponds to a Δδ = 11.7 ppm). 110The explanation that the substitution of hydrogen by iodine causes significant shielding on boron atoms attached to the substituent is that lone pairs of iodine interact efficiently with the p orbitals of ipso B, which produces a π backdonation from the I atom to the B atom of the substituted vertices.This enriches considerably the electron density at this B vertex, increasing its shielding and consequently shifting its B resonance to a high field.
Important is the fact that the pattern of the 11 B{ 1 H} NMR spectra of the parent o-carborane and the periodinated ocarborane from high to low frequency is the same 2:2:4:2, but the mean chemical shift value (⟨δ⟩) moves slightly upfield from −10.5 to −13.7 ppm as B-iodination of o-carborane moves from 0 to 10 atoms, respectively (Figure 1).These results suggest that by increasing the number of I atoms, the π backdonation ability of I atoms decreases, consistent with the formation of intramolecular I•••I noncovalent bonding.In other words, the lone pairs of electrons on I are used in backdonation when there is no chance to interact with other neighboring iodine atoms, but when this possibility exists, there is a preference for noncovalent interactions.As a result, these electrons would be less prone for other endeavors, for instance, to be removed (oxidation) from the cluster.To evidence the presence of noncovalent intramolecular interactions in the boron periodinated I 10 -o-carborane, a search at the Cambridge Structural Database (CSD) 111,112 was done.The CSD showed just three hits (CEHWOC, WUNDAL, and WUNDOZ).CEHWOC 113 and WUNDAL 114 have solvents as adducts in the crystal cells, but WUNDOZ was obtained solvent-free. 114To avoid any interference in measuring the I•••I distances, these were measured on the WUNDOZ, giving values in the range 3.946−4.278Å (the van der Waals radius of the I atom is 1.98 Å, 115 Figure S2) that parallel with the theoretical distances reported by the C 6 H 5 I•••IC 6 H 5 homodimers via type I−IV halogen halogen interaction (3.96−4.15Å). 116 The boron periodinated I 10 -o-carborane crystal structure (WUNDOZ) supports the I•••I noncovalent bonding formation and the creation of a two adjacent vertices truncated icosahedral (the two adjacent C−H vertices) constituted by the ten connected I atoms.
A similar situation is expected for the periodinated [B 12 I 12 ] 2− that is even a better core than o-carborane to form a clustered onion-like structure.Removal of two electrons would seemingly lead to a clustered onion-like structure, but is this what occurs experimentally?When comparing the 11 B{ 1 H} NMR spectra in acetone of the parent Na 2 [B 12 H 12 ] and its iodinated Na 2 [B 12 I 12 ], it is seen that both display a singlet at the chemical shifts −15.4 ( 1 J(B,H) = 125 Hz) 48,117   I 12 ], respectively.This NMR data is consistent with the data obtained for the o-carborane, to say that, as in the [B 12 H 12 ] 2− , the [B 12 I 12 ] 2− cluster does not generate π backdonation to the ipso B atom, but most possibly, the iodine atoms are involved in intramolecular I•••I noncovalent bonding interactions.Again, we moved to the CSD to confirm this hypothesis. 111,112CSD showed just 16 hits for salts of [B 12 I 12 ] 2− , but only two hits (QAVVAO and ASIWAC) 118 were found for its sodium salts.QAVVAO If we consider the oxidation of periodobenzene C 6 I 6 , two methods were utilized.In one method, chlorine is bubbled into a suspension of orange C 6 I 6 in a mixture of triflic acid and trifluoroacetyl triflate (TFAT).In this process, besides [C 6 I 6 ] 2+ , the radical [C 6 ClI 5 ] •+ was obtained.In the same report, an alternative method to produce [C 6 I 6 ] 2+ involves the use of pertriflic acid (CF 3 SO 4 H) or H 2 O 2 in triflic acid as the oxidizing agent.The mass spectrum displays peaks at m/z 834 corresponding to [C 6 I 6 ] + and at m/z 417 corresponding to [C 6 I 6 ] 2+ .Remarkable was the 13 C{ 1 H} NMR spectrum that produced a unique 13 C resonance, indicating the equivalence of all C atoms and, indeed, that the compound was diamagnetic. 15f we now examine the 3D-aromatic core per excellence, the [B 12 H 12 ] 2− and its perhalogenated dianions [B 12 X 12 ] 2− (X= F, Cl, Br, I), it is seen that in liquid sulfur dioxide, they can be oxidized either by chemical or electrochemical methods to give stable radicals. 73The chemical oxidation is done with the strong oxidizing agent AsF 5 that yields the radical anions [B 12 X 12 ] •− (X = F, Cl, Br), but it fails to produce [B 12 I 12 ] •− .When an excess of AsF 5 was used, the neutral hyperclosoboranes B 12 X 12 (X = Cl, Br) were obtained but failed to produce B 12 I 12 .The explanation given was the weakness of the B−I bond that would agree with the lack of π backdonation argued above and consistent with the stepwise loss of I • radicals leading to B 12 demonstrated by electrospray ionization-trap mass spectrometry. 120B 12 Cl 12 and B 12 Br 12 were characterized by X-ray diffraction (XRD) and did show unequal B−B bonds characteristic of hypercloso species. 73Electrochemical oxidation of [B 12 X 12 ] 2− (X = F, Cl, Br, I) shows that the first and second oxidation processes are detected for X = F, Cl, Br but not for X = I.The ground state of  We have also analyzed the quartet state of [B 12 I 12 ] + because, in this state, the three orbitals of the triply degenerated HOMO are occupied with a single same spin electron, leading to an I h symmetric structure with bond length equalization.So, we expect this state to be particularly doubly aromatic since it reminds the electronic distribution of Baird aromatic species. 38owever, according to the NICS scans of Figure 3, this state has an aromaticity slightly smaller than that of closed-shell singlet [B 12 I 12 ] 2+ .Other systems with double 3D-aromaticity according to NICS values (Figures S8 and S12 73 To confirm that the results of the NICS scan stem from diatropic ring currents, we computed the current-density susceptibility and visualized the current at the plane located in the middle of the two boron 5-MRs (0.0 Å), the plane including one of the boron 5-MR (0.8 Å), and the plane of  S17 and S18), which also show an increase in the current-density around the iodine substituents after oxidation.

Molecular
3.4.Electronic Aspects.Yet, other aspects of the potential double 3D-aromaticity (electronic, energetic, and geometric) must also be assessed, and next, we have analyzed the electron delocalization using the electron density of delocalized bonds (EDDB) method.The EDDB method decomposes the oneelectron density in several "layers" corresponding to different levels of electron delocalization, 128 namely, the density of electrons localized on atoms (EDLA) representing inner shells, lone pairs, etc.; the electron density of localized bonds (EDLB)  representing typical (2-center 2-electron) Lewis-like bonds; and EDDB, which represents electron density that cannot be assigned to atoms or bonds due to its (multicenter) delocalized nature.The EDDB population of electrons delocalized in a 2Dor 3D-closed circuit can be used as an indicator of aromaticity. 129According to the EDDB, the number of delocalized electrons (or holes) increases upon oxidation of [B 12 I 12 ] 2− (Figure 5).The number of delocalized electrons in the borane cage remains more or less similar, while the electron delocalization of the iodine sphere increases from 0. Thus, a crucial question is if it is possible to have aromaticity without covalent bonding.The answer from magnetic and electronic indices seems to be yes for [C 6 I 6 ] 2+ and maybe for [B 12 I 12 ] 0/2+ .Yet, it is important to emphasize that aromaticity is linked to stability, and we already pointed out that the [B 12 I 12 ] 0/2+ compounds have not been isolated.To check whether these molecules are stabilized by the double 3Daromaticity, we designed several homodesmotic 83 reactions (Tables 1 and S2).We have chosen the position of the H atoms so that in [B 12 I 6 H 6 ] 0/2+ or in [C 6 H 3 I 3 ] 2+ , the potential double aromaticity is quenched (for instance, in [C 6 H 3 I 3 ] 2+ , the three H atoms are located in meta positions with respect to each other).As can be seen from reaction (3) in Table 1, there is a stabilization of [C 6 I 6 ] 2+ because of the double 2Daromaticity.In contrast, in the case of [B 12 I 12 ] 0/2+ , such stabilization does not take place (reactions (1) and ( 2)).Therefore, the energetic indicator of aromaticity does not support the double 3D-aromaticity of [B 12 I 12 ] 0/2+ , but it reinforces the conclusion that [C 6 I 6 ] 2+ is doubly 2D-aromatic.
So, the answer to the question of whether it is possible to have aromaticity without covalent bonding is that, in some particular cases such as in [C 6 −2.8 −6.5 (3) with antibonding I•••I character, and the large distance between I atoms far outside the sum of the covalent radii of two I atoms (r I cov = 1.39 Å). 130 In this context, let us mention the synthesized dismutational aromatic isomer of hexa-silabenzene (Si 6 R 6 ), 131 which shows strong diamagnetic response when exposed to an external magnetic field and has two unsubstituted silicon atoms with an interatomic distance that is significantly longer than the common covalent Si−Si single bond. 132urthermore, one can note the pseudo-π method of Steiner and Fowler that replaces CH units in conjugated hydrocarbons by H atoms with a single 1s function located at the original C positions. 133In that way, they reproduce the ring currents of πconjugated hydrocarbons at a low cost.However, in the pseudo-π model of benzene, there is no H•••H covalent bonding or only a very weak one 134 (the H atoms are placed far from each other and ρ BCP,H•••H = 0.056 au, whereas for the H 2 molecule, the ρ BCP,H−H is 0.266 au).Moreover, the energy of the cyclic H 6 system is higher than those of the three H 2 molecules by 128.5 kcal/mol.So, there is no aromaticity in these H cycles (lack of stabilization), but there are ring currents and extensive electron delocalization (EDDB G indicates that 5.43 e out of a total of 6 are delocalized, Figure S27).This situation is akin to that found for [B 12 I 12 ] 0/2+ .Finally, a lack of stability of B 12 I 12 explains why [B 12 I 12 ] 2− requires such high oxidation potentials or strong oxidizing agents to reach the first oxidation step, the monoanionic radical, and even higher potentials to produce the neutral species.I 12 ] and [B 12 I 12 ] 2+ .Calculations of magnetic and electronic descriptors of aromaticity suggest (the electronic to less extent) that these two oxidized forms of closo icosahedral dodecaiodo-dodecaborate cluster, [B 12 I 12 ] and [B 12 I 12 ] 2+ , can be classified as doubly 3D-aromatic compounds, much like [C 6 I 6 ] 2+ is considered doubly 2D-aromatic.However, consistent with experimentation, homodesmotic reactions rule out the existence of double 3D-aromaticity in [B 12 I 12 ] 0/2+ because these reactions are all endothermic and endergonic for these species.Aromaticity is a complex phenomenon; aromatic compounds have many interesting properties, but two are essential, namely, electron delocalization and energetic stabilization.A lack of one of these two effects precludes the existence of aromaticity.Although the two species display noticeable magnetic ring currents and electron delocalization (as expected from the multiple existing resonance structures with the same weight), we cannot conclude that there is aromaticity on the I 12 shell of [B 12 I 12 ] 0/2+ because homodesmotic reactions show that there is no resonance stabilization, one of the two main conditions required for aromaticity.These systems are good examples illustrating that analyses of aromaticity have to be exhaustive and are not focused only on one of the aspects (usually magnetic properties) that characterize aromatic compounds.[B 12 I 12 ] 0/2+ shows that diatropic ring currents and bond length equalization, leading to high symmetry, are important but not sufficient conditions for claiming aromaticity.

CONCLUSIONS
Finally, let us mention that the difficulty of generating B 12 I 12 with electrochemical procedures already foreshadowed its lack of double 3D-aromaticity.Aromaticity, which is associated with electron delocalization facilitated by efficient orbital overlap, generally assists the synthesis of aromatic compounds because of their increased stability.However, in the case of B 12 I 12 , inefficient orbital overlap avoids the formation of a stable compound.This case highlights the potential for alternative approaches to enhancing stability beyond aromaticity.One such possibility is the generation of multiple weak, noncovalent I•••I contacts, which, when combined, significantly boost stability.
Scheme 1.(a) Schematic Illustration of the Circular σ-Delocalization in Dicationic Hexahalo-or Hexachalco-Substituted Benzene Leading to Huckel σ-Aromaticity; (b) Schematic Representation of the Circular σ-Delocalization in Tricationic Hexabromotropylium Species in Its Lowest-Lying Triplet State Resulting in Baird σ-Aromaticity; (c) Double Aromaticity in C 6 E 6 2+ Requires the Opening of an Electronic Hole by Double Oxidation to Generate σ-Delocalization Journal of the American Chemical Society

[B 12 I
12 ] 2+ is a quintet that is more stable than the closedshell singlet state by 6.9 kcal/mol.The molecular structure of [B 12 I 12 ] 2− has I h symmetry with B−B bond length of 1.790 Å (see Figure2) and, therefore, the bond length alternation (BLA), i.e., the difference between the shortest and the longest B−B distance, is zero.Our optimized geometries indicate that the shortest I•••I distance in [B 12 I 12 ] 2− is 4.099 Å, 0.539 Å longer than that of C 6 I 6 (3.560 Å).Despite the relatively long I•••I distance in [B 12 I 12 ] 2− , there is almost no space left in the I 12 crown with a %V Bur = 91.4% in comparison to [B 12 H 12 ] 2− for which %V Bur = 41.7% (Figures S23−S26).Double oxidation removes two electrons from the triply degenerated HOMO orbital of [B 12 I 12 ] 2− , which is I•••I antibonding (Figure S1).As a consequence, the I•••I distance is reduced minutely to 4.082 Å (triplet) or to 4.069 Å (closed-shell singlet), and the B−B bond lengths become also somewhat shorter, ranging from 1.785 to 1.786 Å (triplet) or 1.787 to 1.794 Å (singlet) with a BLA of 0.001 Å for the triplet and 0.007 Å for the singlet.The two electrons are removed from the I 12 shell, which gets a positive charge of 0.410 (triplet) or 0.408 (singlet) electrons according to Voronoi deformation density (VDD) charges, 126 computed at the ZORA-BLYP-D3(BJ)/ TZ2P level of theory.Finally, oxidation to closed-shell singlet [B 12 I 12 ] 2+ leads to a minor reduction of the B−B and I•••I distances (BLA being 0.010 Å).Again, the electrons are removed from the I 12 shell, which becomes positive by 2.512 electrons (using Hirshfeld charges, 127 we got 0.609 and 2.657 e for the I 12 unit of 3 B 12 I 12 and B 12 I 12 2+ , respectively).The number of resonance structures that can be built in the I 12 shell is 12 for B 12 I 12 if the doubly positive charge on I 12 is located in a single I atom and 66 if the two positive charges are placed in two different I atoms.For [B 12 I 12 ] 2+ , we have 66 resonance structures if the two doubly positive charges are located in two I atoms and 495 resonance structures if the positive charges are placed in four different I atoms.In both cases, the boron core remains with 26 electrons.3.3.Magnetic Aspects.To determine the magnetic behavior of our systems, we first performed NICS scans moving from the center of the dodecahedron to the center of the closest X 3 (X = H, I) three-membered ring (3-MR).As seen in Figure 3, the NICS scans for [B 12 I 12 ] 2− and [B 12 H 12 ] 2− clusters point out a somewhat higher aromaticity for [B 12 H 12 ] 2− .The minimum of the NICS scan in all cases is found around the B 3 plane.NICS scans of [B 12 I 12 ] 2− and
iodine 5-MR (1.8 Å) for [B 12 I 12 ] 2− for the singlet and triplet states of [B 12 I 12 ] and [B 12 I 12 ] 2+ , as well as for [B 12 H 12 ], C 6 I 6 , and [C 6 I 6 ] 2+ (Figures S13−S16).As can be seen, the changes in the current-density susceptibility around the iodine substituents are similar on going from C 6 I 6 to [C 6 I 6 ] 2+ and from [B 12 I 12 ] 2− to [B 12 I 12 ].This further substantiates the potential double 3D-aromaticity in [B 12 I 12 ] and [B 12 I 12 ] 2+ when evaluated with magnetic aromaticity descriptors.Figure 4 shows the current-density susceptibility of [B 12 I 12 ] 2− , singlet and triplet [B 12 I 12 ], and [B 12 I 12 ] 2+ in the 0.8 Å plane, which is ∼1 Å above one of the I 5-MR planes.In this plane, differences between the differently oxidized clusters are more evident.From these pictures, one can see the generation of a current density around the iodine substituents when going from [B 12 I 12 ] 2− to [B 12 I 12 ] and [B 12 I 12 ] 2+ .This current is particularly intense for 3 [B 12 I 12 ].In addition, we have computed the ring currents for [C 2 B 10 I 12 ] and [C 2 B 10 I 12 ] 2+ in their singlet and triplet states (Figures

Figure 4 .
Figure 4. Current-density susceptibility in the magnified area (black rectangle) of the 1 [B 12 I 12 ] 2− , singlet and triplet [B 12 I 12 ], and 1[B 12 I 12 ] 2+computed in a plane at 0.8 Å (see FigureS13).The color scale corresponds to the strength of the modulus of the current-density susceptibility in the range 0.0001 (dark red) to 0.4 (white) nA/(TÅ 2 ).
38 e ([B 12 I 12 ] 2− ) to 6.18 e (singlet [B 12 I 12 ]), 5.67 e (triplet [B 12 I 12 ]), and to 10.93 e ([B 12 I 12 ] 2+ ).In the case of C 6 I 6 , we also have the delocalization around the I 6 circle going from 0.20 e in C 6 I 6 to 5.30 e in [C 6 I 6 ] 2+ .For [B 12 I 12 ] 2+ , the number of delocalized electrons in the iodine shell (10.93 e out of 48 e coming from the 24 electron pairs located in the spherical surface of I 12 ) is similar to that of the borane cage (11.86 e out of 26 e).However, the percentage of delocalized electrons is still much larger for the borane cage (46 vs 23%).Moreover, the EDDB surface does not cover the entire I 12 spherical surface.As a whole, the EDDB shows that there is electron delocalization among the I 12 atoms (as expected from the different resonance structures) but does not fully support the existence of double 3D-aromaticity in [B 12 I 12 ] and [B 12 I 12 ] 2+ , especially in the former.EDDB plots for [C 2 B 10 I 12 ] and [C 2 B 10 I 12 ] 2+ in their singlet and triplet states show very similar behavior (Figure S19), the electron delocalization being clearly higher for [C 2 B 10 I 12 ] 2+ than for [C 2 B 10 I 12 ], especially in its singlet state.3.5.Energetic Aspects and the Nature of the I•••I Chemical Bond.As discussed before, the relatively short I•••I distances in 3,4,5,6,7,8,9,10,11,12-I 10 -o-carborane support the existence of noncovalent I•••I bonding.We expect a similar situation in [B 12 I 12 ] 2− .Moreover, we know that the I•••I distance decreases when we move from [B 12 I 12 ] 2− to [B 12 I 12 ] 0/2+ .Do we reach a situation that can be defined as covalent I−I bonding in [B 12 I 12 ] 0/2+ ?To answer this question, we performed a quantum theory of atoms-in-molecules (QTAIM) analysis for these species, and the results show that none of them has a bond critical point (BCP) between the I atoms, thus unambiguously indicating that we have noncovalent I•••I interaction but not covalent bonding.On the other hand, in the case of [C 6 I 6 ] 2+ , we observe I•••I BCPs (Figure S20), although the density at these BCPs is very low (ρ BCP,I•••I = 0.019 au), thus precluding the existence of covalent bonding.The highest overlap between lone pair orbitals in two adjacent I atoms in C 6 I 6 and [B 12 I 12 ] 2− is 0.165 and 0.097 au, respectively.
I 6 ] 2+ , it seems possible.Lack of covalent I•••I bonding in [C 6 I 6 ] 2+ is substantiated by the low density of I•••I BCPs, by the population of molecular orbitals

a
All species computed in their closed-shell singlet state.In the case of reaction (1), if B 12 I 12 and B 12 I 6 H 6 are in a triplet state, ΔE = −37.9,and ΔG = −40.7 kcal mol −1 .

11 B
NMR spectra of I n -o-C 2 B 10 H 12-n are consistent with the existence of intramolecular noncovalent I•••I bonding when n is large and, in particular, in I 10 -o-C 2 B 10 H 2 .It is expected that such a bonding situation is also present in [B 12 I 12 ] 2− .Based on the example of double 2D-aromaticity in [C 6 I 6 ] 2+ , we analyzed the possibility of double 3D-aromaticity in [B 12 and −15.8 ppm for Na 2 [B 12 H 12 ] and Na 2 [B 12 Structure.First, we quantum chemically studied the singlet ground state of [B 12 I 12 ] 2− as a possible species with double 3D-aromaticity, the borane cage following the 2N + 2 Wade rule with N = 12, and the I 12 sphere with 72 electrons as lone pairs following the Hirsch rule.As said before, to reach double aromaticity, a double oxidation may be required to open a hole in one of the 5p orbitals of iodine.Therefore, we analyzed [B 12 I 12 ] and also [B 12 I 12 ] 2+ .The first gas-phase ionization Gibbs energy of [B 12 I 12 ] 2− to [B 12 I 12 ] •− is 35.2 kcal/mol, and the second ionization to produce singlet [B 12 I 12 ] requires 101.3 kcal/mol.It has to be said that the triplet state of [B 12 I 12 ] is the ground state, and it is more stable than the closed-shell and the open-shell singlet states by 5.7 and 3.7 kcal/mol, respectively.Further oxidation to singlet [B 12 I 12 ] 2+ costs 408.2 kcal/mol.

Table 1 .
Electronic and Gibbs Reaction Energies (in kcal/mol) of Selected Homodesmotic Reactions a