Redox-chemistry of Pyramidanes: A DFT Study

Graphical Abstract

The reaction mechanisms for the reduction induced rearrangement of a series of pyramidanes into their cyclopentadienide derivatives were elucidated using density functional calculations. The calculations indicate that the reductions might proceed in a facile manner. However, the re-oxidation of the cyclopentadienide might yield meta-stable cyclic species. The latter represent intriguing synthetic targets.

Abstract

Based on previous experimental findings, a DFT study on the redox-induced rearrangement of a series of germa-, phospha- and borapyramidanes is presented. Upon stepwise two-electron reduction, these 5-vertex nido-clusters are predicted to form their respective monocyclic derivatives (germole diides, (tri)phospholides and borole diides) which are formally related to the cyclopentadienide anion. Hence, it is likely that these rearrangements are a common reactivity of pyramidanes. Based on the calculations, the oxidation of these monocyclic derivatives is expected to result in the formation of meta-stable dimers for germanium and phosphorus species, and monomeric borole derivatives for boron species. Consequently, investigating the redox chemistry of pyramidanes presents an exciting opportunity to discover new and unique main-group species.

Introduction

Pyramidane, [C(η⁴-C₄H₄)], is a 5-vertex nido-cluster where all four substituents of the apical C atom lie within the same hemisphere. For such a structure, the term “inverted tetrahedral” environment was coined by Wiberg.¹ Due to the unusual bonding situation, pyramidane has attracted attention from theoretical chemists starting from the 1970s.^2-7 While the parent species [C(η⁴-C₄H₄)] remains elusive as of today, several heteroatom-substituted derivatives were prepared in the last two decades. These derivatives might also be regarded as complexes where a dianionic, four membered base acts as a 6π-donor toward BCl²⁺,⁸ E²⁺ (E=Si, Ge, Sn, Pb)^9-13 or P³⁺.^{14, 15} As such, most of these derivatives feature either a [tBu₂C₂P₂]²⁻ or [TMS₄C₄]²⁻ base. Recently, the germapyramidane [Ge(η⁴-IPr₂C₂P₂)]²⁺ was reported, which features the neutral IPr₂C₂P₂ base (IPr=1,3-bis(2,6-diisopropylphenyl)imidazolium-2-ylidene).¹⁶ This base is formally derived from replacing the tert-butyl groups in [tBu₂C₂P₂]²⁻ with imidazolium moieties (Scheme 1). Note, that a second borapyramidane derivative with an unusual boryl-substituted C₄ base, [BC₆F₅(η⁴-TMS₂R'R’’C₄)] (R’=H, R’’=B(C₆F₅)₂) was reported as well.¹⁷

Scheme 1

Redox chemistry of [BCl(η⁴-C₄TMS₄)] and [Ge(η⁴-IPr₂C₂P₂)]²⁺ (top, counterions ([C₄TMS₄BCl]²⁻: Li⁺, [Ge(η⁴-IPr₂C₂P₂)]²⁺: BArF₂₄⁻ or OTf⁻) are omitted for clarity). Bottom: pyramidane derivatives investigated in this computational study.

In comparison to their structural diversity, little is known about the redox properties of pyramidanes. The first example was reported in 2018 by Lee and coworkers:⁸ Reduction of the borapyramidane [BCl(η⁴-C₄TMS₄)] (Scheme 1) with elemental lithium led to a facile rearrangement of the cluster to the planar, aromatic borole diide [C₄TMS₄BCl]²⁻. In 2022, a similar behavior was reported for the dicationic germapyramidane [Ge(η⁴-IPr₂C₂P₂)]²⁺ (Scheme 1): Two-electron reduction of

[Ge(η⁴-IPr₂C₂P₂)]²⁺ afforded the planar aromatic bis(imidazolium)-substitued germole diide IPr₂C₂P₂Ge. This process is reversible, i. e., oxidation of IPr₂C₂P₂Ge results in formation of [Ge(IPr₂C₂P₂)]²⁺ and the mechanism was deduced using experimental and computational methods.¹⁶ Both [C₄TMS₄BCl]²⁻ and IPr₂C₂P₂Ge may formally be regarded as main-group analogues of the ubiquitous cyclopentadienide anion. In addition, it is interesting to note that the related cyclopentadienide derivative of [P(η⁴-tBu₂C₂P₂)]⁺ is also known.¹⁴ However, it was not prepared via a two-electron reduction of the parent pyramidane.

The redox-induced transformations of five-vertex clusters into aromatic five-membered planar ring systems is of fundamental interest as pointed out by Canac and Bertrand.¹⁸ Such a reaction links two concepts which relate the valence electron count of a compound to their structure/properties, namely the Wade-Mingos-Rudolph rules (clusters) and the Hückel-rules (aromaticity of cyclic species).

In light of these findings, two questions arise. First, if the reduction of pyramidane derivatives would generally induce the rearrangement to the respective cyclopentadienide analogue and secondly, if the oxidation of those species would regenerate the parent pyramidane. To provide a possible answer, a detailed DFT study is presented here. The study in total covers seven pyramidanes with three different apexes (Ge²⁺, P³⁺ and BCl²⁺) based on the common [tBu₂C₂P₂]²⁻ and [TMS₄C₄]²⁻ bases as well as the neutral IPr₂C₂P₂ base (Scheme 1); the five known pyramidanes [Ge(η⁴-tBu₂C₂P₂)], [Ge(η⁴-TMS₄C₄)], [P(η⁴-tBu₂C₂P₂)]⁺, [P(η⁴-TMS₄C₄)]⁺ and [BCl(η⁴-TMS₄C₄)], as well as the hypothetical species [P(η⁴-IPr₂C₂P₂)]³⁺ and [BCl(η⁴-IPr₂C₂P₂)]²⁺.

Results and Discussion

Throughout the computational study, the ORCA¹⁹ program package was used and structures and thermal corrections were obtained using B97-3c.²⁰ Dipp substituents in species based on the IPr₂C₂P₂ base were replaced by Ph groups to save computational cost. For the calculation of final electronic energies, two functionals were considered. First, the meta-GGA functional M06 L,²¹ as it was used to investigate the dicationic germapyramidane [Ge(η⁴-IPr₂C₂P₂)]²⁺ and yielded a good agreement with the experimental data, considering redox-potentials and kinetic barriers. Secondly, the double-hybrid functional PWPB95²² was used in its DLPNO variant. The original PWPB95 functional was used to study borapyramidanes and yielded energies close to the accurate DLPNO-CCSD(T)^{23, 24} method in case of [BCl(η⁴-TMS₄C₄)].¹⁷ Both functionals were used in combination with the def2-TZVPP basis,²⁵ the respective dispersion correction^{26, 27} and the CPCM solvent model for acetonitrile.²⁸ The DLPNO-PWPB95 results will be discussed at the end of results and discussion section.

The obtained reduction pathways for the germanium species [Ge(η⁴-tBu₂C₂P₂)] and [Ge(η⁴-TMS₄C₄)] are similar to the one found for the dicationic germapyramidane [Ge(η⁴-IPr₂C₂P₂)]²⁺ (Schemes 2 and 3).Two single-electron reduction steps convert the nido-clusters first into the radical anions [Ge(η³-tBu₂C₂P₂)]⋅⁻ and [Ge(η²-TMS₄C₄)]⋅⁻ and subsequently into the arachno-clusters [Ge(η³-tBu₂C₂P₂)]²⁻ and [Ge(η²-TMS₄C₄)]²⁻, respectively. As can be seen from the hapticity changes, reduction of these pyramidanes is accompanied by vertex opening of the clusters. Compared to the dicationic germapyramidane [Ge(η⁴-IPr₂C₂P₂)]²⁺, the reduction potentials are, as expected, more negative (−1.2 and −1.4 V vs. −2.8 and −3.0 V for [Ge(η⁴-tBu₂C₂P₂)], −3.3 and −3.4 V for [Ge(η⁴-TMS₄C₄)]). Next, the reduced clusters undergo an exergonic rearrangement via TS_2e to form the aromatic germole-diides [tBu₂C₂P₂Ge]²⁻ and [TMS₄C₄Ge]²⁻. The activation barriers are lowered compared to [Ge(η³-IPr₂C₂P₂)] (31.4 vs. 30.0 for [Ge(tBu₂C₂P₂)]²⁻ and 26.5 for [Ge(TMS₄C₄)]²⁻, all values in kcal ⋅ mol⁻¹). Thus, a reduction-induced rearrangement of the germapyramidanes to dianionic germole diides upon two-electron reduction seems possible. Note, that according to the Eyring equation, an activation barrier of 26.5 kcal ⋅ mol⁻¹ corresponds to a half-life of 26 days at 300 K. However, small changes in the activation barrier cause large changes in the calculated half-lifes. For example, the rearrangement of [Ge(η³-IPr₂C₂P₂], for which a barrier of 31.4 kcal ⋅ mol⁻¹ was calculated, is completed within 2 days.¹⁶

Scheme 2

Proposed redox-chemistry of [Ge(η⁴-tBu₂C₂P₂)]. All calculated potentials are given in V vs. Fc/Fc⁺.

Scheme 3

Proposed redox-chemistry of [Ge(η⁴-TMS₄C₄)]. All calculated potentials are given in V vs. Fc/Fc⁺.

Thus, comparably small inaccuracies in the calculated activation barriers will lead to large discrepancies between calculated and measured reaction times. Therefore, throughout the study, comparisons of calculated activation barriers will be used to make a qualitative estimate about the reaction times relative to the ones calculated for the original [Ge(η⁴-IPr₂C₂P₂)]²⁺ system.

Overall, the reduction-induced rearrangements of the germanium species follow an electron transfer/electron transfer/chemical reaction (EEC) mechanism (marked in red in Schemes 2 and 3). Note, that in principle, already the one-electron reduced germanium clusters [Ge(η³-tBu₂C₂P₂)]⋅⁻ and [Ge(η²-TMS₄C₄)]⋅⁻ might rearrange to five-membered ring species: At the one-electron reduced stage, the rearrangement to the planar radical species [tBu₂C₂P₂Ge]⋅⁻ and [TMS₄C₄Ge]⋅⁻ via TS_1e might occur.

These radicals carry a significant spin population on the germanium atoms (0.45 and 0.54, see the SI, section 2 for a depiction) and might thus rapidly form the dimeric digermole diides [(tBu₂C₂P₂Ge)₂]²⁻ and [(TMS₄C₄Ge)₂]²⁻ in an exergonic Ge−Ge bond formation reaction according to [XGe]⋅⁻→0.5 [(XGe)₂]²⁻ (Δ_RG°=−14.8 kcal ⋅ mol⁻¹ for X=tBu₂C₂P₂ and −10.1 kcal ⋅ mol⁻¹ for X=TMS₄C₄). The synthetic viability of this pathway was demonstrated for [Ge(η⁴-IPr₂C₂P₂)]²⁺. However, this reaction was rather slow, meaning that in the presence of two equivalents of reducing agent a second electron transfer to [Ge(η³-IPr₂C₂P₂)]⋅⁺ proceeded much faster than the rearrangement and subsequent dimerization.¹⁶ Indeed, also for the germanium species [Ge(η³-tBu₂C₂P₂)]⋅⁻ and [Ge(η²-TMS₄C₄)]⋅⁻ the transition states TS_1e for the rearrangement to [tBu₂C₂P₂Ge]⋅⁻ and [TMS₄C₄Ge]⋅⁻ are significant and even higher than TS_2e.

While the planar radical species [tBu₂C₂P₂Ge]⋅⁻ and [TMS₄C₄Ge]⋅⁻ might not be of relevance for the two-electron reductive pathway of the germapyramidanes, they are indeed relevant intermediates in the oxidative pathways (marked in blue in Schemes 2 and 3). One-electron oxidation of the dianions [tBu₂C₂P₂Ge]²⁻ and [TMS₄C₄Ge]²⁻ at −1.6 V and −2.1 V, respectively, leads to the radical anions [tBu₂C₂P₂Ge]⋅⁻ and [TMS₄C₄Ge]⋅⁻ and after rapid dimerization to the dimeric digermole diides [(tBu₂C₂P₂Ge)₂]²⁻ and [(TMS₄C₄Ge)₂]²⁻ (vide supra). The digermole diides are then further oxidized to the neutral digermenes (tBu₂C₂P₂Ge)₂ and (TMS₄C₄Ge)₂ in two single-electron steps ([(tBu₂C₂P₂Ge)₂]²⁻: −1.1 and −0.6 V, [(TMS₄C₄Ge)₂]²⁻: −1.7 and −0.7 V). These digermenes might dissociate in a slightly endergonic reaction to the respective germylenes according to 0.5 (XGe)₂→XGe (Δ_RG°=1.7 kcal ⋅ mol⁻¹ for X=tBu₂C₂P₂ and 7.2 kcal ⋅ mol⁻¹ for X=TMS₄C₄). These germylenes can then rearrange to the initial germapyramidanes via TS. Relative to the monomeric germylenes XGe, the activation barrier ΔG^≠ is 34.0 kcal ⋅ mol⁻¹ for X=tBu₂C₂P₂ and 32.7 kcal ⋅ mol⁻¹ for X=TMS₄C₄. The calculated total values for this respective step in the redox-cycle of the dicationic germapyramidane [Ge(IPr₂C₂P₂)]²⁺ are Δ_RG°=7.4 kcal ⋅ mol⁻¹ for the dissociation step and ΔG^≠=16.4 kcal ⋅ mol⁻¹ for the activation barrier. Thus, the significantly higher activation barriers found for (tBu₂C₂P₂Ge)₂ and (TMS₄C₄Ge)₂ indicate that the digermenes, while being thermodynamically unstable with respect to the formation of the respective pyramidanes, might represent meta-stable species.

Moving from group 14 to group 15, the cationic phosphapyramidanes [P(η⁴-tBu₂C₂P₂)]⁺ and [P(η⁴-TMS₄C₄)]⁺ were investigated next. The reductive pathways are similar to those calculated for the analogues germapyramidanes (marked in red in Scheme 4 and 5): Two-single electron reduction steps open the phosphapyramidanes to the anionic clusters [P(η²-tBu₂C₂P₂)]⁻ and [P(η²-TMS₄C₄)]⁻. As expected, the cationic charge of those pyramidanes increases the reduction potential compared to the neutral germapyramidanes (−1.0 and −1.7 V for [P(η⁴-tBu₂C₂P₂)]⁺, −1.8 and −1.8 V for [P(η⁴-TMS₄C₄)]⁺). Subsequently, the reduced clusters rearrange via TS_2e to the respective monocyclic ring species, namely the (tri)phospholides [tBu₂C₂P₃]⁻ and [TMS₄C₄P]⁻. For [P(η²-tBu₂C₂P₂)]⁻, the activation barrier for the rearrangement to [tBu₂C₂P₃]⁻ is lowered compared to [Ge(IPr₂C₂P₂)] (31.4 vs. 29.0 kcal ⋅ mol⁻¹) again indicating the possibility of a facile reaction. In contrast, the respective barrier for [P(η²-TMS₄C₄)]⁻ is higher (33.5 kcal ⋅ mol⁻¹) indicating that the rearrangement to [TMS₄C₄P]⁻ might be slower or not even feasible in this case.

Scheme 4

Proposed redox-chemistry of [P(η⁴-tBu₂C₂P₂)]⁺. All calculated potentials are given in V vs. Fc/Fc⁺.

Scheme 5

Proposed redox-chemistry of [P(η⁴-TMS₄C₄)]⁺. All calculated potentials are given in V vs. Fc/Fc⁺.

Next, the oxidative pathways for [tBu₂C₂P₃]⁻ and [TMS₄C₄P]⁻ were investigated (blue in Schemes 4 and 5). Again, these are similar to the respective pathways calculated for the germanium species: One-electron oxidation of the (tri)phospholides results in the formation of the radical species [tBu₂C₂P₃]⋅ and [TMS₄C₄P]⋅ (see the SI section 2 for a depiction of the spin density). These form the di(triphosphole) (tBu₂C₂P₃)₂ and diphosphole (TMS₄C₄P)₂ in an exergonic reaction (−16.7 and −11.4 kcal ⋅ mol⁻¹).²⁹ Next, these neutral species are oxidized in two single-electron steps. Interestingly, the two resulting dications, [(tBu₂C₂P₃)₂]²⁺ and [(TMS₄C₄P)₂]²⁺, show completely different structures. [(TMS₄C₄P)₂]²⁺ might be best described as a diphosphole dication, where one lone pair of electrons had been formally removed from the parent diphosphole. In contrast, a polycyclic structure was obtained in the geometry optimization of [(tBu₂C₂P₃)₂]²⁺. Notwithstanding their structural differences, both dicationic species are predicted to form the respective monomers [tBu₂C₂P₃]²⁺ and [TMS₄C₄P]²⁺ in an endergonic reaction, followed by rearrangement to the original phosphapyramidanes. As for the germanium species, the rather high total activation barriers, i. e. the energetic difference between TS and [(tBu₂C₂P₃)₂]²⁺/[(TMS₄C₄P)₂]²⁺, respectively indicate that these dications are again meta-stable species.

The final considered phosphapyramidane is the hypothetical trication [P(η⁴-IPr₂C₂P₂]³⁺ (Scheme 6). The reductive pathway differs slightly from the already discussed examples. One- and two-electron reduction of [P(η⁴-IPr₂C₂P₂]³⁺ produces the opened clusters [P(η³-IPr₂C₂P₂]²⁺ and [P(η³-IPr₂C₂P₂]⁺, respectively. In contrast to the previous examples, [P(η³-IPr₂C₂P₂]⁺ rearranges to the bis(imidazolium)-substituted triphospholide [IPr₂C₂P₃]⁺ in a two-step process. First, one C−P bond of the IPr₂C₂P₂ base is broken leading to the intermediate Int_2e. The five-membered heterocycle [IPr₂C₂P₃]⁺ is then formed via the transition state TS_2e. This step is rate-determining and has a total activation barrier of 29.0 kcal ⋅ mol⁻¹.

Scheme 6

Proposed redox-chemistry of [P(η⁴-IPr₂C₂P₂)]³⁺. All calculated potentials are given in V vs. Fc/Fc⁺. The circles in the dimeric pentacation denote delocalization of the unpaired electron over the whole molecule.

This barrier is again lower than the one reported for [Ge(η³-IPr₂C₂P₂)] indicating an efficient rearrangement process. The rearrangement of the one-electron reduced species [P(η³-IPr₂C₂P₂]²⁺ proceeds in a similar two-step process, but again, the very high total activation barrier of 41.2 kcal ⋅ mol⁻¹ makes this process not competitive with a rapid second reduction to the two-electron reduced species [P(η³-IPr₂C₂P₂]⁺.

Until the last step, the oxidative pathway calculated for [IPr₂C₂P₃]⁺ is identical to those discussed for the other phosphapyramidanes: Oxidation of [IPr₂C₂P₃]⁺ results in formation of the radical species [IPr₂C₂P₃]²⁺ which dimerizes to [(IPr₂C₂P₃)₂]⁴⁺. This tetracation is subsequently oxidized in two single electron steps. Due to the high positive charge, the calculated potentials for these steps are quite high (1.8 and 2.3 V, respectively). The high charge of the resulting hexacation in addition renders the dissociation into two tricationic monomers exergonic (0.5 [(IPr₂C₂P₃)₂]⁴⁺→[IPr₂C₂P₃]³⁺, Δ_RG°=−8.5 kcal ⋅ mol⁻¹). Rearrangement of this monomer to the phosphapyramidane [P(η⁴-IPr₂C₂P₂]³⁺ proceeds via a low barrier of only 11.8 kcal/mol indicating that the redox-cycle for this particular pyramidane can be closed, i. e. oxidation of the triphospholide [IPr₂C₂P₃]⁺, at least in silico, results in the rearrangement to the phosphapyramidane.

Finally, pyramidanes with an apical BCl unit were investigated. For the borapyramidane [BCl(TMS₄C₄)], the potentials of the calculated single-electron reduction steps are similar to the related germapyramidane [Ge(TMS₄C₄)] (−3.6 and −3.6 V vs. −3.3 and −3.4 V, Scheme 7). However, the kinetic barriers for the rearrangement of the thereby formed negatively charged clusters to their planar, five-membered counterparts are strongly reduced compared to the respective germanium counterparts (ΔG^≠=10.6 kcal ⋅ mol⁻¹ for [BCl(TMS₄C₄)]⋅⁻ and 5.8 kcal ⋅ mol⁻¹ for [BCl(TMS₄C₄)]²⁻).

Scheme 7

Proposed redox-chemistry of [BCl(TMS₄C₄)]. All calculated potentials are given in V vs. Fc/Fc⁺.

Thus, the redox process [BCl(TMS₄C₄)] +2e→[TMS₄C₄BCl]²⁻ might follow the EEC mechanism established for the germanium and phosphorus species. Since, unlike for the phosphorus and germanium species, TS_1e is very low in energy, already the one-electron reduced cluster might rearrange forming the planar borole radical anion [TMS₄C₄BCl]⋅⁻ This radical is subsequently reduced to the aromatic borole diide [TMS₄C₄BCl]²⁻ at −2.2 V (see the red paths in Scheme 4). The latter path corresponds to an ECE mechanism.

For both the EEC and ECE mechanism, the calculated low kinetic barriers agree with the observed rapid formation of [TMS₄C₄BCl]²⁻ when [BCl(η⁴-TMS₄C₄)] is reduced with lithium.⁸ The oxidation of the borole diide [TMS₄C₄BCl]²⁻ is predicted to proceed rather differently compared to the formally related germole diides and phospholides: Single-electron oxidation of [TMS₄C₄BCl]²⁻ leads to the planar radical anion [TMS₄C₄BCl]⋅⁻ which is now stable towards dimerization (see the SI section 5). In part, this might be explained by the rather delocalized spin-density in [TMS₄C₄BCl]⋅⁻, compared to the respective planar germole radical anions (see the SI, section 2). Further oxidation of [TMS₄C₄BCl]⋅⁻ at −1.2 V then leads to the neutral borole TMS₄C₄BCl which again is stable toward dimerization. The rearrangement of the borole TMS₄C₄BCl to the borapyramidane [BCl(η⁴-TMS₄C₄)] is predicted to proceed in two steps: The endothermic isomerization to the housane intermediate Int (via TS_b) which subsequently forms the borapyramidane via TS_a.³⁰ A similar two-step mechanism was calculated for the borapyramidane [BC₆F₅(η⁴-TMS₂R'R’’C₄)] reported by Erker and coworkers.¹⁷ The rate-limiting step in this sequence is the formation of the housane Int which, relative to the borole TMS₄C₄BCl, has a total activation barrier of ΔG^≠=27.5 kcal ⋅ mol⁻¹. Thus, like the digermenes discussed earlier (vide supra), the borole TMS₄C₄BCl corresponds to a meta-stable species which might be observable experimentally.

For the reduction of the hypothetical dicationic borapyramidane [BCl(η⁴-IPr₂C₂P₂)]²⁺, again two reductive mechanisms, EEC and ECE are plausible based on the calculated activation barriers (see the red paths in Scheme 8). Similar to the borole diide [TMS₄C₄BCl]²⁻, the neutral bis(imidazolium)-substituted borole diide IPr₂C₂P₂BCl is predicted to be oxidized in two single-electron steps at −0.5 and 0.4 V with no dimeric species being involved (see the SI section 5). However, the final rearrangement of the dicationic borole [IPr₂C₂P₂BCl]²⁺ to the borapyramidane [BCl(η⁴-IPr₂C₂P₂)]²⁺ is found to proceed in a single step, namely via the triplet transition state TS. The activation barrier for this process is rather high (ΔG^≠=29.3 kcal ⋅ mol⁻¹). Therefore, similar to the neutral borole TMS₄C₄BCl, the dicationic borole [IPr₂C₂P₂BCl]²⁺ is a meta-stable species. Notably, TS and thus the activation barrier is raised by +12.5 kcal ⋅ mol⁻¹ using DLPNO-PWPB95 (see below and the SI, section 3), and therefore this method predicts [IPr₂C₂P₂BCl]²⁺ to be even more kinetically stable towards rearrangement to the respective pyramidane. Thus, [IPr₂C₂P₂BCl]²⁺ might be an experimentally accessible, meta-stable borole. The predicted meta-stability of the boroles is corroborated by experimental findings by Erker and coworkers: The pyramidane [BC₆F₅(η⁴-TMS₂R'R’’C₄)], while stable at ambient temperatures, could indeed be interconverted to the borole TMS₂R'R’’C₄BC₆F₅ upon heating. This borole was characterized as its SMe₂ adduct, which in turn could be converted to the pyramidane [BC₆F₅(η⁴-TMS₂R'R’’C₄)] by radiation with UV light.¹⁷

Scheme 8

Proposed redox-chemistry of [BCl(IPr₂C₂P₂)]²⁺. All calculated potentials are given in V vs. Fc/Fc⁺.

In this computational study, DLPNO-PWPB95 was used as a second functional (see the SI, section 3). Compared to M06 L, all redox potentials are, on average, lowered by 0.5 V. The activation barriers TS_1e and TS_2e are reproduced with a mean average deviation (MAD) of 4.8 kcal ⋅ mol⁻¹ for TS_1e and a MAD of 2.4 kcal ⋅ mol⁻¹ for TS_2e. Thus, especially the values of TS_2e are in qualitative agreement with the M06 L data, supporting the facile rearrangement of two-electron reduced clusters to their cyclopentadienide analogues. In contrast, the transition states TS are estimated to be higher by 5.9 kcal ⋅ mol⁻¹ on average. Thus, the oxidized species are predicted to be even more kinetically stable towards rearrangement to the respective pyramidanes.

Conclusions

In summary, the redox chemistry of seven pyramidane derivatives was investigated computationally with the focus on two particular questions: First, if the reduction of pyramidane derivatives would generally induce the rearrangement to monocyclic species and secondly, if the oxidation of those species would regenerate the parent pyramidane.

In all the clusters that were examined, it was found that the two-electron reduction of pyramidanes could potentially lead to the formation of arachno-clusters as predicted by the Wade-Mingos rules. However, thermodynamically, the isomerization to the respective monocyclic, aromatic species was calculated to be more favorable. With one exception ([P(η²-TMS₄C₄)]⁻) these isomerizations are predicted to occur faster than the experimentally observed reaction [Ge(η⁴-IPr₂C₂P₂)]²⁺ 2e⁻→IPr₂C₂P₂Ge. To summarize the findings related to the first question, it appears that the reduction-induced rearrangement to monocyclic derivatives seems to be a common reactivity of pyramidanes.

Regarding the second question, only [P(η⁴-IPr₂C₂P₂)]³⁺ was found to exhibit a fully closed redox-cycle, i. e. oxidation of the five-membered two-electron reduced derivative is indeed predicted to regenerate the pyramidane. However, it is important to highlight that the dimers found along the oxidative pathway of [P(η⁴-IPr₂C₂P₂)]³⁺ are highly charged and therefore elusive and potentially unstable. Consequently, it may not be experimentally feasible to close the redox-cycle for these species. For all the other examples, the barriers for the rearrangement of two-electron oxidized cyclic species to their respective pyramidanes were found to be rather high although the pyramidanes are thermodynamically favored in all cases. Therefore, these oxidized species, which display a wide structural variety ranging from digermenes over diphosphole dications to boroles, might at least be meta-stable species. Therefore, the second question which was addressed in this DFT study cannot be answered conclusively based on the available data.

Thus, the synthetic exploration of the redox chemistry of pyramidanes, i. e. two-electron reduction to their planar cyclopentadienide analogues followed by two-electron oxidation seems to be a worthwhile scientific endeavor. Such experimental studies might offer synthetic access to unique main-group species with interesting properties and reactivities. Although some of those species, like the dicationic borole [IPr₂C₂P₂BCl]²⁺ and the highly charged dimers [(IPr₂C₂P₃)₂]^4+/5+/6+ are rather hypothetical, they might still be detectable in trapping experiments. It is therefore hoped that this computational study sparks further interest and progress in the field of pyramidane chemistry.

Computational Details

All calculations were carried out with the ORCA program package.¹⁹ Density fitting techniques, also called resolution-of-identity approximation (RI),³¹ were used for all B97-3c and M06 L calculations, whereas an additional chain-of-spheres approximation for the HF exchange (RIJCOSX)³² was used for DLPNO-PWPB95 calculations. Atom-pairwise dispersion corrections were used for all DFT calculations [B97-3c, DLPNO-PWPB95: D3BJ, M06L: D3(0)]. All geometries and thermal corrections were obtained with the B97-3c compound method on isolated molecules using a medium-tight grid (Grid5) and TIGHTSCF convergence criteria for SCF procedure and the default convergence criteria for geometry optimisations (see an exemplary input file in the SI, section 1). Electronic energies of the optimised species were obtained using the methods described in the main text, i. e. M06L or DLPNO-PWPB95 with the appropriate dispersion correction, def2-TZVPP basis sets, TIGHTSCF convergence criteria, medium-tight grids (Grid5) and the CPCM solvent correction for acetonitrile (see the SI, section 1 for an exemplary input file). The final Gibbs free energies were subsequently obtained by adding the thermal corrections obtained with B97-3c to the electronic energies. Approximate transition state structures were obtained using the nudged elastic band method. These approximate structures were used in a subsequent saddle-point geometry optimization.

Acknowledgments

P. C. gratefully acknowledges funding from the VCI (Liebig-fellowship). Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest

The authors declare no conflict of interest.

Open Research

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.