On the 3D → 2D Isomerization of Hexaborane(12)

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).


Introduction
The chemistry of boron is usually treated as a separate chapter in inorganic chemistry textbooks and is considered as more diverse and complex than that of any other element in the periodic table, with the exception of carbon [1]. Boranes are compounds combining boron and hydrogen B n H m . For low molecular weights they are sensitive to air and moisture, toxic, and volatile [2], such as pentaborane(9) B 5 H 9 , which is very flammable and acutely toxic; however, they can also be stable solids which can be handled under ambient conditions, such as B 10 H 14 and B 18 H 22 . The unique three-dimensional (3D) structural and bonding patterns of boranes confer to them a rich variety of architectural molecular constructs [3], and the combination of boranes with metals and other elements of the periodic table leads to compounds included in emerging fields of current fundamental and applied research [4].
On the other hand, two-dimensional (2D) planar borane molecules are unknown due to the 3D clusterization of boron atoms when forming many-electron multicenter bonds [5]. However, recent experiments [6] called our attention to the possibility of isolating planar finite borane molecules. Moreover, a one-to-one correspondence between any conjugated hydrocarbon C n H m and the structurally equivalent borane B n H m+n can be easily drawn [7]. For instance, benzene C 6 H 6 can be transformed into planar hexaborane(12) B 6 H 12 by substituting carbon atoms with boron atoms and every π two-electron bond with one perpendicular H 2 moiety at the mid-point of the former C=C bond; in other words, with three {C=C} → {BH 2 B} substitutions [7,8]. Therefore, potential synthesis of planar borane molecules encompasses a new field of research within boron chemistry.
We know that arachno-B 6 H 12 , hexaborane (12), is a colorless liquid that, like most boron hydrides, is readily hydrolyzed and flammable, and usually prepared from [B 5 H 8 ] − , the conjugate base of pentaborane (9), B 5 H 9 [9]. Derivatives of hexaborane (12) have been synthesized and characterized [10][11][12], and its thermal gas-phase decomposition has been studied [13]. This molecule has a 3D (curved) structure with C 2 symmetry, as shown in Figure 1a,b [14]. Thus, the 3D → 2D isomerization of hexaborane (12) to the unknown planar D 3h structure, Figure 1c,d, corresponds to a flattening and swelling of the B 6 skeleton into a planar B 6 hexagon. According to Lipscomb's styx notation [15], there are four possible isomers with the B 6 H 12 formula: 6030, 5121, 4212, and 3303. In styx notation, s stands for number of bridge hydrogens, t for the number of two-electron three-center boron bonds, y for the number of two-center two-electron boron bonds, and x for the number of BH 2 groups. Reactant (C 2 ) and Product (D 3h ) [7,8] in the 3D → 2D hexaborane (12) isomerization correspond to isomers 4212 and 6030, respectively, and structure 5121 to an intermediate of the 3D → 2D isomerization, as shown below. Isomer 3303 lies 13 kJ·mol −1 above R (4212). Isomers 6030 (P) and 5121 lie 100 kJ·mol −1 and 104 kJ·mol −1 higher than R (4212). A summary of the structural description and relative energies of hexaborane(12) isomers with styx notation is included in the Supplementary Information, Table S1. The question that we would like to answer in this work, dedicated to Professor Josef Michl, is related to the possibility of transforming 3D hexaborane(12) into a 2D planar structure through chemical reaction steps. Synthesis of planar borane molecules mimicking planar conjugated hydrocarbons is certainly a scientific challenge. What follows is an attempt to give an acceptable answer to this question.  (12) with C 2 symmetry (a) perpendicular to theĈ 2 rotation axis and (b) along theĈ 2 rotation axis, and two projections of unknown planar 2D hexaborane (12) with D 3h symmetry (c) perpendicular to theĈ 3 rotation axis and σ h plane and (d) along theĈ 3 rotation axis and on the σ h plane. Atom labels are shown for boron (green) and hydrogen (white).

Computational Methods
The electronic structure calculations presented in this work were carried out with the scientific software Gaussian16 [16] and the M06-2X/aug-cc-pVDZ level of theory [17][18][19], which consists of a hybrid functional combining density-functional and Hartree-Fock theory, which includes dispersion corrections, and an augmented double-ζ basis set with polarization and diffuse functions for all atoms. The transition states (TS), stationary points with one imaginary frequency, were located by combining synchronous transit and quasi-Newton methods [20,21]. In order to locate the intermediates (I) at either site of the TS col point we followed the vibrational mode of the imaginary frequency-forward and backward-along the intrinsic reaction coordinate (IRC) [22,23] and relaxed the geometry for searching an energy (local) minimum. All TS and I were checked with frequency computations at the same level of theory, with one and zero imaginary frequencies, respectively. The quantum theory of Atoms-in-Molecules (QTAIM) [24,25] calculations were carried out with the AIMAll program [26]. In this theory, the electron density is analyzed from a topological point of view, with gradient and Laplacian operators, → ∇ρ and ∇ 2 ρ, respectively.
The critical points of the electron density are those with → ∇ρ c = 0; the three eigenvalues of ∇ 2 ρ c are classified according to the number of non-zero values and the sum of the signs as follows: A maximum (3,−3) critical point is associated with nuclei positions, the saddle points (3,−1) and (3,+1) are associated with bond (BCP) and ring critical points (RCP), respectively, and the minima (3,+3) correspond to cage critical points. The molecules included in this work provide BCP and RCP, apart from the maxima corresponding to nuclear positions. A gradient path-line connects two nuclei through a BCP, where the electron density ρ BCP is a maximum in two directions and a minimum in one direction. In an RCP, the ρ RCP is a minimum in one direction and a maximum in two directions.
The molecular volume was computed with the Gaussian16 scientific software, as the volume inside a contour of 0.0067 e/Å 3 density, which is accurate to two significant figures, and carried out by Monte-Carlo integration.

Intrinsic-Reaction-Coordinate (IRC) and Stationary Points in the 3D → 2D Isomerisation of Hexaborane(12)
In Figure 2 we plot the energy profile of the reaction pathway along the intrinsic reaction coordinate (IRC) from reactant (R), C 2 hexaborane(12), to product (P), D 3h planar hexaborane (12), with the structures of transition states (TS) and intermediates (I). The nature of all stationary points (SP)-TS and I-along the reaction pathway were checked with frequency computations, with one and zero imaginary frequencies, respectively. Between R and P we found five stationary points on the energy hypersurface along the IRC, with three transition states, TS 1 , TS 2 , and TS 3 , and two intermediates, I 1 and I 2 . In Table 1 we gather the energies of these SP and the energy differences with respect to R, the lowest energy isomer. Table 1. Energy (a.u.) and energy differences ∆E R = E(SP) − E(R) (kJ·mol −1 ) for the stationary points (SP) of the 3D → 2D isomerization in hexaborane (12). R = Reactant, SP = Stationary Point, TS = Transition State, I = Intermediate. M06-2X/aug-cc-pVDZ calculations. As gathered in Table 1 and displayed in Figure 2, unknown planar hexaborane(12)-P-lies 100 kJ·mol −1 above existing hexaborane(12)-R. The three energy barriers from (local) energy minima to TS along the IRC are 75 kJ·mol −1 , 239 kJ·mol −1 , and 110 kJ·mol −1 for TS 1 , TS2, and TS 3 respectively and the intermediates I 1 and I 2 lie 31 kJ·mol −1 and 104 kJ·mol −1 above R, respectively. From a chemical point of view, as shown in Figure 2, the reaction determining step corresponds to the I 1 → TS 2 process, with the largest barrier: 240 kJ·mol −1 . In this process the B 2 -B 3 and B 3 -B 4 bonds are broken, thus opening the central tilted B 4 rhombus. The first two steps, R → TS 1 → I 1 correspond to hydrogen bridge atoms moving so that the boron-frame structure rearranges, with an energy barrier of 75 kJ·mol −1 , comparable to energy barriers in S N 2 chemical reactions in organic chemistry [27]. After TS 1 we reach intermediate I 2 , the predicted styx isomer 5121 (see Supplementary Information). As compared to R, the I 2 structure has one more bridge hydrogen atom, one less three-center B-B-B bond, an additional two-center B-B bond, and one less BH 2 group. From a chemical point of view I 2 has a similar energy as compared to P, with a difference of 3.6 kJ·mol −1 only. The transition state TS 3 , separating I 2 and P, lies 110 kJ·mol −1 above I 2 .

SP
Given the complexity of the borane cage rearrangements along the IRC, we have selected boron-boron B(i)-B(j)- Figure 3-and boron-hydrogen B(i)-H(j) distances- Figure 4in the SP, along the reaction coordinate from R to P. Thus, as displayed in Figure 1a Tables S2 and S3 respectively. In the Supplementary Information file we also provide the optimized geometries of all SP points included in this work, Tables S4-S11. In Figures 3 and 4 all B(i)-B(j) and selected B(i)-H(j) distances-in the latter those with major changes, respectively-are plotted along the IRC for the 3D → 2D isomerization of hexaborane (12).
In Figure 3 one can clearly envisage two subsets of B(i)-B(j) connectivities. We should take into account that in R, the equivalent B(1)-B(3) and B(4)-B(6) distance is 1.904 Å, and therefore the interaction between boron atoms is not so strong as compared to the stiffer central tilted rhombus formed by B (2) 15) there is a slight decrease and increase of 0.1 Å respectively. At this point we should emphasize that the largest energy barrier for the planarization of B 6 H 12 corresponds to the reaction step I 1 → TS 2 , as displayed in Figure 2, with an energy barrier of 240 kJ·mol −1 from I 1 . This is the reaction determining step in the isomerization process.

QTAIM Analysis of the Stationary Points in the 3D → 2D Isomerisation of Hexaborane(12)
The electron density of the SP along the IRC in the 3D → 2D isomerization of hexaborane (12) was also analyzed with the quantum theory of atoms in molecules (QTAIM), in order to further assess the geometrical and electronic structure changes along the IRC, as shown in Figure 5. QTAIM defines the chemical bonding and structure of a chemical system based on the topology of the electron density ρ(r), with stationary (critical) points and gradient-bond-paths of the electron density that originate and terminate at these points. Thus, the critical points found between two atoms, called bond critical points (BCP), provide information about the nature of such bond. At this point we should emphasize that QTAIM ( Figure 5) and IRC (Figure 2) stationary points correspond, respectively, to   Figure 2 for the 3D → 2D isomerization of hexaborane(12), with energy barriers separating the SP. Red and yellow circles correspond to ring critical points (RCP) and bond critical points (BCP), respectively. The two arrows in I 1 indicate the collapsing of the two RCP into one RCP in TS2. M06-2X/aug-cc-pVDZ computations.

Discussion
Reactant and Product in the 3D → 2D isomerization process of hexaborane(12) resemble, at first, two valence isomers [28]; namely, they can be transformed into each other through some reaction mechanism. In organic chemistry valence isomers are connected through pericyclic reactions [29]. The organic chemistry analogue for our case in point here could be the 3D → 2D valence isomerization of prismane to benzene [30,31]. Other benzene valence isomers have also a 3D structure, like benzvalene [32]. A quantum-chemical computation at the same level of theory shows that benzvalene and prismane lie 290 kJ·mol −1 and 455 kJ·mol −1 above in energy respectively, as compared to benzene, and therefore the borane isomerization is inverse, with the 2D system lying higher in energy than the 3D molecule. However, the problem here seems to be more complex: the stiffness of the central boron rhombus in R is evident given the large energy barriers involved in the isomerization process, especially the I 1 → TS 2 step, with an energy barrier of 240 kJ·mol −1 .
This barrier increases to 270 kJ·mol −1 if we consider the energy difference of TS 2 with respect to R. Similar energy barriers can be found in organoboron chemistry, such as in the isomerization of borirane BC 2 H 5 -a triangular cyclic structure isoelectronic with the cyclopropyl cation [33]-to methyl methylideneborane, as shown in Equation (1) below. In this isomerization the computed energy barrier is 250 kJ·mol −1 , computed with highly correlated methods [33], and involves a C-C bond breaking and a hydrogen shift from B-H to one CH 2 group in borirane. (1) Hydrogens in boranes play an interesting role since they provide the missing 2p electron in boron in order to resemble carbon, but an electron is~2000 times lighter than hydrogen and the Coulombic force of the additional proton, and a boron nucleus instead of a carbon nucleus also has to be taken into account; hence the 3D diversity of borane shapes with closo, nido, arachno, and hypho structures, depending on the number of loss vertices in borane closed (closo) polyhedra [34]. The 3D → 2D isomerization of hexaborane (12) can be simplified in a 2D model of parallelogram → hexagon, as displayed in Figure 6. A 2D projected C 2 hexaborane (12)   Recently, we reported the reaction mechanism of the photochemical and thermal isomerization between two isomers of B 20 H 18 (2−) [35], involving Lipscomb's diamond-square-diamond (DSD) mechanism [36], with a thermal barrier of 193 kJ·mol −1 . Although this amount of energy is still far from the 240 kJ·mol −1 barrier needed for the 3D → 2D isomerization of hexaborane (12), it gives us a clue that large energy barriers can be surpassed in boron chemical reaction mechanisms. Indeed, the DSD mechanism is useful for predicting 3D → 3D isomerizations, but in our particular case the planarization of a 3D borane structure is, by no means, straightforward. Thus, major changes in the geometrical parameters of 3D B 6 H 12 involve the central tilted {B(2), B(3), B(4), B(5)} rhombus, as shown in Figure 3. Other boron-boron distances undergo minor changes along the reaction mechanism. Clearly, in the I 1 → TS 2 step, two RCP in the central rhombus collapse toward the BCP between B(3) and B(4), creating a single RCP and expanding the rhombus, as in the DSD mechanism, but with no returning to a 3D borane shape. On the other hand, the calculation of the electronic volumes in the SP along the IRC-defined as the volume inside a contour of 0.0067 e/Å 3 density-gathered in Table 2, provides information on the shape changes in the molecule. The molecular volume provides information on the extent of the electron density distribution of a molecule using an isodensity value. The comparison of the molecular volumes in a reaction coordinate provides some clues of the contraction or expansion of the electronic cloud along the chemical process. Thus, in the first step R → TS 1 , the molecular volume expands by 15 Å 3 and the B(3)-B(4) distance shortens by 0.07 Å. In the next step TS 1 → I 1 , there is a shrinking of 8 Å 3 in the volume and a shortening of 0.04 Å in the B(3)-B(4) bond. In the limiting reaction step, I 1 → TS 2 , there is surprisingly a further volume shrinkage of the molecule, even lower than in R, but a striking increase of the B(3)-B(4) distance, 0.67 Å, which implies the breaking of this bond. From the TS 2 point onwards the volume and B(3)-B(4) distance increase up to the final product P, in the latter with a volume swell of 27 Å 3 as compared to R.

Conclusions
The goal of this work was to study the possibility of transforming 3D polyhedral boranes, with the particular example of existing hexaborane (12), into 2D planar borane molecules. The fact that planar D 3h hexaborane(12) resembles benzene structurally and electronically and that 3D hexaborane (12) exists led us to this study: the 3D → 2D isomerization of hexaborane (12). By means of quantum-chemical computations we have been able to connect, through three transition states and two intermediates, the 3D and 2D structures. Along the reaction path, the most energetic step from one intermediate to a transition state involves a 240 kJ·mol −1 energy barrier, which corresponds to expansion of the central rhombus in B 6 H 12 and breaking of two boron-boron bonds. This is a large amount of energy when compared to organic chemical reactions and the proposed reaction mechanism of the 3D → 2D isomerization of hexaborane(12) throws some light on the intricacies of boron chemistry reaction mechanisms, as in the recently revisited isomerization of B 20 H 18 (2−) [35]. Thermodynamic and kinetic aspects are of paramount importance in every chemical reaction and therefore further reaction mechanisms must be studied within borane chemistry in order to understand how structures transform into one another. Finally, we should emphasize that the reaction mechanism exposed in this work is purely theoretical. Reaction mechanisms in boron chemistry are scarce, as opposed to organic chemistry, with thousands of named reactions and very well determined reaction mechanisms. The first problem in the 3D → 2D isomerization of hexaborane (12) is that the energy difference between reactant and product is very large from a thermochemical point of view. However, as mentioned above, the organic chemistry "analogue" of our case in point is somehow inverted: the very stable 2D benzene can be transformed into 3D benzvalene, lying much higher in energy, even higher than the energy difference between P and R in hexaborane (12). Perhaps using photochemical processes one could surpass the large barrier separating R and P in the 3D → 2D isomerization process of B 6 H 12 . The determination of reliable reaction mechanisms in boranes is by no means trivial, but we hope that this work can throw some light on the research field of boron chemistry.