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

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}axis of rotation in three-dimensional hexaborane(12).

## 1. Introduction

_{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].

_{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.

_{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.

## 2. Computational Methods

_{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.

^{3}density, which is accurate to two significant figures, and carried out by Monte-Carlo integration.

## 3. Results

#### 3.1. Intrinsic-Reaction-Coordinate (IRC) and Stationary Points in the 3D → 2D Isomerisation of Hexaborane(12)

_{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.

^{−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.

_{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}.

_{1}, with an energy barrier of 75 kJ·mol

^{−1}from R, the B(4)-B(6) distance (grey line in Figure 3) decreases by 0.2 Å and the B(5)-B(6) distance increases by the same amount, while the remaining B-B distances remain similar. However, as displayed in Figure 4, the B(6)-H(10) and B(6)-H(17) distances undergo significant changes with a decrease and increase of 1 Å, respectively. The remaining B-H distances remain almost unaltered along the R → TS

_{1}step. As we move from TS

_{1}to the first intermediate I

_{1}, the B-B distances remain almost unaltered with the exception of B(4)-B(6) and B(5)-B(6) which seem to exchange their profiles, returning to the original values in R. As for the B-H distances, Figure 4, there is an increase of 0.3 Å for B(3)-H(11), B(4)-H(16), B(6)-H(10), and B(6)-H(17). For B(2)-H(7) and B(2)-H(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.

#### 3.2. QTAIM Analysis of the Stationary Points in the 3D → 2D Isomerisation of Hexaborane(12)

**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 $\overrightarrow{\nabla}\rho =\left(\frac{\partial \rho}{\partial x},\frac{\partial \rho}{\partial y},\frac{\partial \rho}{\partial z}\right)=\overrightarrow{0}$ and $\overrightarrow{\nabla}E=\left(\frac{\partial E}{\partial X},\frac{\partial E}{\partial Y},\frac{\partial E}{\partial Z}\right)=\overrightarrow{0}$, where lower and capital (x, y, z) Cartesian coordinates correspond to electrons and nuclei respectively, and they should not be confused. As shown in Figure 5, bond critical points (BCP) are depicted in yellow, ring critical points (RCP) in red, and the gradient bond-paths of the electron density are represented as black solid lines connecting atoms. For further details on the QTAIM calculations the reader is referred to Section 2 above. As shown in Figure 5, starting off with the upper left corner, R hexaborane(12) shows two equivalent RCP and several BCP between boron atoms and between boron and hydrogen atoms. The Ĉ

_{2}rotation axis passes through the midpoint of the B(3)-B(4) bond path, where the BCP lies, and is perpendicular to this bond. The above statement on the low B(1)-B(3) = B(4)-B(6) interactions is confirmed with the absence of a gradient path connecting these nuclei. At this point we should emphasize that the threshold in the electron density of BCP for bond path plotting is 0.1 au: solid line for ρ(BCP) > 0.1, and dashed line for ρ(BCP) < 0.1. The topological analysis of R further shows two types of hydrogens: the bridge hydrogens {H(14), H(15)}, and the equivalent {H(17), H(18)} through Ĉ

_{2}rotations, in which gradient paths split into two toward two neighbor boron atoms. For the remaining hydrogens, only one gradient path connects them to the neighbor boron atom. As we move from R to TS

_{1}with an energy barrier of 75 kJ·mol

^{−1}, an additional RCP appears inside the {B(1)B(2)H(14)} triad and lies very close to the new BCP between B(1) and B(2) and to the BCP between B(1) and H(14). Additionally, on the other side of the molecule the B(6)-H(17) gradient path with its corresponding BCP vanishes and a new B(4)-B(6) gradient path appears with the corresponding BCP between B(4) and B(6). Following the IRC from TS

_{1}to I

_{1}down 44 kJ·mol

^{−1}, the molecule seems to get back to the previous conformational structure of R but in fact this is not the case, with vanishing of the B(1)-B(2) and B(1)-H(14) bond paths with the subsequent vanishing of the RCP within the {B(1)B(2)H(14)} triad. This rearrangement brings the new B(1)-B(3) bond path with the respective BCP. On the other side of the molecule the B(4)-B(6) bond path vanishes and the new B(5)-B(6) bond path appears with the respective BCP. We now turn to the most energetic reaction step mechanism in the 3D → 2D isomerization of hexaborane(12), depicted with a thicker black arrow in Figure 5: an energy barrier of 240 kJ·mol

^{−1}with an interesting atomic rearrangement in the I

_{1}→ TS

_{2}step. A close look at TS

_{2}clearly shows a bond breaking of B(2)-B(3), B(3)-B(4)—the central boron-boron bond in the initial C

_{2}structure—and B(2)-H(15). These changes imply the formation of the new bonds B(2)-B(4), B(1)-H(14), B(1)-H(7), and B(2)-H(7). The central frame of TS

_{2}shapes almost to a hexagonal structure with the central RCP and another RCP within the {B(1)H(7)H(14)}B(2) moiety resembling a diborane(6) structure. The next reaction step TS

_{2}→ I

_{2}, downhill by 167 kJ·mol

^{−1}, involves for I

_{2}two new RCP within moieties {B(3)H(11)H(18)B(5)} and {B(4)B(5)H(10)B(6)}, the latter very close to the BCP between B(4) and B(5), a clear indication of ring collapse. It is noteworthy that in this reaction step there is no bond breaking, but rather bond formations with new gradient lines as follows: B(5)-B(6) and B(5)-H(11)-B(3). In the I

_{2}→ TS

_{3}step, with an energy barrier of 110 kJ·mol

^{−1}, the central hexagonal frame is more evident in TS

_{3}with three RCP, the central one and the same two satellite RCP forming the diborane moieties as in I

_{2}. The former RCP close to the BCP between B(4) and B(5) in I

_{2}has now collapsed, with a B(4)-B(5) bond breaking in TS

_{3}. In the final TS

_{3}→ P step, with a drop of 114 kJ·mol

^{−1}, a new RCP turns up within the {B(4)H(10)H(16)B(6)} moiety involving the new gradient line B(4)-H(16)-B(6), with the new B(4)-H(16) bond, leading to the final D

_{3h}structure.

## 4. Discussion

^{−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.

_{2}hexaborane(12) forms a parallelogram which transforms into a hexagon, where atoms B(1), B(2), and B(4) remain at the same point, but atoms B(3), B(5), and B(6) are shifted down along the line defined by B(3) and B(4), the two boron atoms which hold rigid the central boron rhombus in existing hexaborane(12).

_{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.

## 5. Conclusions

_{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.

## Supplementary Materials

_{6}H

_{12}, with their structures, Lipscomb’s valence structures, relative energies ΔE(kJ·mol

^{−1}) referred to lowest energy isomer R (styx 4212), and the labels according to stationary points (SP) in the main text, Table S2: Selected B-B distances (Å) for the stationary points from Figure 2 of the main text, Table S3: Selected B-H distances (Å) for the stationary points from Figure 2 of the main text, Tables S4–S11: Cartesian coordinates (Å) for the optimized geometries of the stationary points considered in this work, displayed in Figure 2 of the main text, and of styx isomer 3303.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

_{3h}hexaborane(12). This research was funded by Spanish MICINN, grant number CTQ2018-094644-B-C22 and Comunidad de Madrid, grant number P2018/EMT-4329 AIRTEC-CM.

## Conflicts of Interest

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**Figure 1.**Two projections of known 3D hexaborane(12) with C

_{2}symmetry (

**a**) perpendicular to the Ĉ

_{2}rotation axis and (

**b**) along the Ĉ

_{2}rotation axis, and two projections of unknown planar 2D hexaborane(12) with D

_{3h}symmetry (

**c**) perpendicular to the Ĉ

_{3}rotation axis and σ

_{h}plane and (

**d**) along the Ĉ

_{3}rotation axis and on the σ

_{h}plane. Atom labels are shown for boron (green) and hydrogen (white).

**Figure 2.**Reaction pathway along the IRC from reactant (R) 3D C

_{2}hexaborane(12) to product (P) 2D D

_{3h}hexaborane(12).

**Figure 3.**B(i)-B(j) distances (Å) for the Stationary Points (SP) along the R → P reaction pathway for the 3D → 2D isomerization of hexaborane(12).

**Figure 4.**Selected B(i)-H(j) distances (Å) for the Stationary Points (SP) along the R → P reaction pathway for the 3D → 2D isomerization of hexaborane(12).

**Figure 5.**QTAIM critical points and bond paths (solid black line) of the stationary points (SP) along the IRC from 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.

**Figure 6.**Simplified representation of the 3D → 2D isomerization of hexaborane(12): (

**a**) 2D projection of the boron frame in reactant (R) C

_{2}hexaborane(12), (

**b**) boron frame in 2D product (P) D

_{3h}hexaborane(12). The black arrows indicate the displacement of the B(3)B(5)B(6) moiety down parallel along the B(3)-B(4) line.

**Table 1.**Energy (a.u.) and energy differences ΔE

_{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.

SP | E | ΔE_{R} |
---|---|---|

R | −156.20882555 | 0.0 |

TS_{1} | −156.18016535 | 75.2 |

I_{1} | −156.19687483 | 31.4 |

TS_{2} | −156.10584340 | 270.4 |

I_{2} | −156.16931585 | 103.7 |

TS_{3} | −156.12728434 | 214.1 |

P | −156.17070415 | 100.1 |

**Table 2.**Electronic volumes (Å

^{3}) and B(3)-B(4) distance (Å) of the stationary points (SP) along the IRC for the 3D → 2D isomerization of B

_{6}H

_{12}—Figure 2.

SP | Volume | B(3)-B(4) |
---|---|---|

R | 146.7 | 1.788 |

TS_{1} | 160.5 | 1.720 |

I_{1} | 152.5 | 1.763 |

TS_{2} | 145.2 | 2.434 |

I_{2} | 161.5 | 2.822 |

TS_{3} | 168.6 | 3.385 |

P | 173.3 | 3.512 |

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**MDPI and ACS Style**

Oliva-Enrich, J.M.; Alkorta, I.; Elguero, J.; Ferrer, M.; Burgos, J.I.
On the 3D → 2D Isomerization of Hexaborane(12). *Chemistry* **2021**, *3*, 28-38.
https://doi.org/10.3390/chemistry3010003

**AMA Style**

Oliva-Enrich JM, Alkorta I, Elguero J, Ferrer M, Burgos JI.
On the 3D → 2D Isomerization of Hexaborane(12). *Chemistry*. 2021; 3(1):28-38.
https://doi.org/10.3390/chemistry3010003

**Chicago/Turabian Style**

Oliva-Enrich, Josep M., Ibon Alkorta, José Elguero, Maxime Ferrer, and José I. Burgos.
2021. "On the 3D → 2D Isomerization of Hexaborane(12)" *Chemistry* 3, no. 1: 28-38.
https://doi.org/10.3390/chemistry3010003