Electrophilic insertion and ring growth in 1,2,5-azadiborolidines: theoretical evidence for boron-driven expansion

Abstract

This study computationally investigates the reactivity of 1,2,5-azadiborolidine derivatives toward carbon monoxide (CO), extending ring-expansion mechanisms from borole chemistry. Establishing structural and electronic analogies through isosterism, we propose that endocyclic CO insertion operates in this new class of boron heterocycles. 1,2,5-Tri-tert-butyl-1,2,5-azadiborolidine emerged as the optimal candidate, exhibiting a favourable three-step pathway: CO insertion, dimerization of the ring-expanded intermediate, and subsequent double [1,2]-migration. Thermochemical analysis confirms viability under mild conditions, with solvents (DCM, n-pentane, THF) providing similar barriers and reaction Gibbs energies. Key reactivity indicators include B–C(O) and C–O bond lengths, while correlations between kinetic barriers and σ → π*(CO) backdonation energies provide predictive insight. This work broadens boron-based reactivity by proposing a fourth class of CO-inserting boracycles and highlights 1,2,5-azadiborolidines as versatile, metal-free frameworks for small-molecule activation.

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Introduction

Ring expansion reactions remain indispensable tools in synthetic organic chemistry, offering direct access to medium- and large-sized ring systems that are often challenging to construct via conventional cyclization methods. These reactions provide a strategic advantage by increasing ring size without dismantling pre-existing molecular complexity, a concept widely embraced in natural product synthesis and drug design.¹ Notably, recent work by Chouraqui and co-workers emphasized the growing utility of ring expansion methodologies for synthesising structurally diverse and conformationally rich scaffolds, often with enhanced biological relevance and physicochemical properties.²

Ring expansions can be broadly classified into three mechanistic categories, defined by the transformation driving the ring-size increase (Chart 1).^2,3 (A) Fragmentation reactions typically involve cleavage of a small ring or leaving group, followed by rearrangement or migration to form a larger ring. These processes often proceed through carbocationic or radical intermediates and are broadly applied in skeletal editing. (B) Pericyclic reactions (e.g., electrocyclic ring openings, sigmatropic rearrangements, and cycloadditions) proceed via concerted mechanisms governed by orbital symmetry and have been central in synthesising polycyclic and strained architectures. (C) Insertion reactions, the focus of this study, entail the formal incorporation of an external atom or functional group into a cyclic framework. These transformations frequently proceed under mild conditions with high regiochemical and stereochemical control, rendering them particularly attractive for constructing complex, functionalized ring systems.

Chart 1 Classification of ring expansion reactions.

Among the elements used in insertion strategies, boron stands out due to its unique electron-deficient character, which enables distinctive bonding modes and electrophilic reactivity not typically observed in classic organic systems.^4–9 The incorporation of boron atoms into molecular frameworks facilitates the development of advanced materials with potential applications across diverse fields, including energy storage,^10–17 optoelectronics,^17–21 drug design,^22–24 and small molecule activation.^9,17,25–27

Within this landscape, ring expansion reactions in boracycles constitute a powerful subclass, enabling access to structurally diverse and electronically tunable organoboron architectures.^28–31 However, there is a reduced number of heterocycles containing trivalent boron atoms that can activate carbon monoxide (CO) via a coordination–insertion mechanism (Chart 2). For instance, early work by Paetzold and Boese showed that a tert-butyl-substituted azadiboriridine (NB₂R₃) undergoes 1,1-insertion with carbon monoxide (CO), followed by dimerization and a [1,2]-migration to afford a six-membered diboroxan heterocycle.³² Siebert subsequently provided mechanistic insights into a related boron-mediated ring expansion via CO insertion, dimerization, and rearrangement.³³ More recently, Piers and co-workers expanded the synthetic utility of such transformations by developing transition-metal-free ring expansion of boroles, yielding larger boracycles with improved stability and applications in materials chemistry.³⁴

Chart 2 CO insertion-induced ring expansion reactions in boracycles.

Given that boroles and 1,2,5-azadiborolidines share analogous structural and electronic features, they can be viewed as isosteres. We thus hypothesized that 1,2,5-azadiborolidines could undergo similar reactivity toward CO insertion, ring expansion, or dimerization. Frontier molecular orbitals (particularly the LUMO centred on boron) could likewise behave analogously in electrophilic or π-system reactions, as shown for boroles. However, early experimental studies revealed different reactivity for azadiborolidines due to adjacent electron-deficient boron centres and a lone pair-bearing nitrogen.^35–39

Recent work highlights azadiborolidines as tunable reactivity platforms: Brown⁴⁰ and Hu and Cui⁴¹ showed strategic functionalization to modulate their reactivity with small molecules like CO, enabling ring-expanded heterocycles and synthetically relevant boron–heteroatom linkages. These transformations underscore the flexibility of the B–N–B core as both a structural and reactive unit.

Beyond small-molecule activation, azadiborolidines and related BN-heterocycles exhibit promising electronic and optical properties. Studies by Wu, Zeng and co-workers⁴² and Narita and Müllen⁴³ explain how N–B incorporation into π-conjugated systems influences aromaticity, stability, and electronic delocalization, highlighting their potential in organic electronic and optoelectronic applications. The polar N–B bond facilitates fine-tuning of HOMO–LUMO gaps while maintaining the planarity and delocalization essential for conjugated systems.

The present study investigates the hypothesis that borole and 1,2,5-azadiborolidine rings exhibit similar reactivity concerning the CO-induced ring expansion reaction, and subsequently, extending this to dimerization processes for the formation of highly complex fused boracycles. Herein, we employ density functional theory (DFT) to assess the viability of these reactions in 1,2,5-azadiborolidines, specifically addressing substituent effects. The main objective of this work is to predict the CO insertion reaction in any of the previously synthesised 1,2,5-azadiborolidine derivatives, for which no reaction with CO has been reported to date. Furthermore, this research aims to identify reactivity descriptors capable of explaining such a transformation, thereby broadening the theoretical insights into this class of reactions in boracycle chemistry.

Computational methods

DFT calculations were performed using Gaussian 09.⁴⁴ The long-range hybrid functional ωB97X-D was employed with the Ahlrichs split-valence def2-SVP basis set for all atoms.^45,46 Geometry optimisations were conducted in the gas phase without constraints. Initial coordinates were extracted from crystallographic data where available. Harmonic frequency calculations characterised stationary points. Thermal corrections to Gibbs energies were obtained under the ideal gas approximation at 298.15 K and 1 atm. Electronic energies were refined via single-point calculations using the def2-TZVPP basis set.⁴⁶ Solvent effects were incorporated via the polarizable continuum model (PCM) with SMD parameters, using dichloromethane (DCM), n-pentane, and tetrahydrofuran (THF) as representative solvents common in the synthesis of such molecules.⁴⁷ Gibbs energies thus correspond to the ωB97X-D/def2-TZVPP//ωB97X-D/def2-SVP level. This approach provides an effective balance between accuracy and computational cost.^48,49

The global electrophilicity index (ω),⁵⁰ defined as ω = μ²/2η, where μ is the chemical potential and η is the hardness, serves as a reactivity descriptor. Within the ground-state parabolic model, μ and η were approximated using the vertical ionization potential (I) and electron affinity (A), yielding ω = (I + A)²/8(I − A). Applying Pearson's principle⁵¹ and using Koopmans’ theorem,⁵² I and A can be approximated as the negative values of the HOMO and LUMO energies, ε_HOMO and ε_LUMO, respectively. This leads to the working equation: ω = (ε_HOMO + ε_LUMO)²/8(ε_LUMO − ε_HOMO). Although strictly valid for Hartree–Fock theory, the utility of this approximation in conceptual DFT is well established.^53–56 Frontier orbital energies were computed at the gas-phase single-point refinement level.

Geometrical descriptors, specifically the molecular planarity parameter (MPP) and the span of deviation from planarity (SDP),⁵⁷ were calculated for the starting heterocycles. Additionally, steric hindrance was evaluated by calculating buried volumes (%V_Bur) and generating steric maps using SambVca 2.1.^58–61

Further wavefunction analysis used NBO and Multiwfn software.^62,63 The Mayer⁶⁴ and Wiberg⁶⁵ bond indices (MBI and WBI) were estimated at the ωB97X-D/def2-TZVPP//ωB97X-D/def2-SVP level. The WBI values were calculated in the Löwdin orthogonalized basis.⁶⁶ The multicentre index (MCI) was computed within the natural atomic orbital (NAO) framework,^67–70 while σ → π*(CO) backdonation energies were quantified via second-order perturbation theory analysis of the Fock matrix in the NBO basis. Because of the delocalized nature of these interactions, diffusion functions were essential; analyses were therefore performed at the ωB97X-D/def2-TZVPPD level on optimised gas-phase geometries.⁷¹

Results and discussion

We initially explored the ring expansion reactivity of borole derivatives with CO, focusing on the parent borole (1), pentaphenylborole (2), and perfluoropentaphenylborole (3). Compounds 2 and 3 were previously studied experimentally by Piers and co-workers,³⁴ providing a benchmark to assess electronic and steric effects on the thermodynamics and kinetics of CO-mediated ring expansion. These boroles were later compared with 1,2,5-azadiborolidines to quantify energetic requirements for analogous pathways.

The proposed mechanism comprises two key steps (Scheme 1). First, the formation of Lewis adducts through CO coordination to boron, followed by 1,1-insertion of CO via endocyclic (ring B–C bond) or exocyclic (exterior B–C bond) pathways.

Scheme 1 A plausible reaction mechanism for the CO insertion into boroles (R = –H, –C₆H₅, –C₆F₅). The endocyclic product refers to the ring expansion reaction.

As shown in Fig. 1, CO coordination is spontaneous for all the boroles (ΔG_R→I-1) with low energy barriers (ΔG^‡_R→TS-1), indicating an equilibrium clearly shifted towards the adduct I-1. Furthermore, the energetic analysis indicates kinetically reversible CO coordination before ring expansion for 2 (ΔG^‡_I-1→TS-1 = 10.9; ΔG^‡_I-1→TS-2 = 17.9; ΔG_I-1→P-1 = 16.1 kcal mol⁻¹) and 3 (ΔG^‡_I-1→TS-1 = 11.4; ΔG^‡_I-1→TS-2 = 30.1; ΔG_I-1→P-1 = 16.3 kcal mol⁻¹), aligning with experimental findings.³⁴ Note that the endocyclic insertion is kinetically feasible at room temperature for 1 and 2, although only 1 affords a thermodynamically stable product (ΔG_R→P-1 = −2.9 kcal mol⁻¹).

Fig. 1 Relative Gibbs energy profiles (kcal mol⁻¹) in the gas phase for the ring expansion reaction of selected borole derivatives with CO.

The substituent effects in boroles 1–3 are significant in the thermochemistry of the ring expansion reaction. Firstly, a reduction in the exergonic character of the CO coordination step is observed, accompanied by an increase in the corresponding energy barriers. This destabilization occurs when phenyl (2), a modest π-donor group, and perfluorophenyl (3), a moderately inductive electron-withdrawing and weak π-donor group, are considered as substituents. Sterically, 1 is least hindered, whereas 2 and 3 present comparable aryl bulk. Consequently, the general thermodynamic and kinetic destabilization of the coordination step for 2 (R = –C₆H₅) and 3 (R = –C₆F₅) can be attributed to the increased volume of the substituents surrounding these rings compared to 1 (R = –H). Furthermore, Lewis adduct formation is favoured both kinetically and thermodynamically for 3 over 2. This outcome can be rationalized by examining the electronic structure of boroles: the perfluoro derivative (3) bears substituents that behave more as electron-withdrawing groups. This enhances the electrophilicity of the ring compared to 2. Therefore, the interaction with CO (a σ-donor/π-acceptor ligand) is expected to be more effective when utilising 3, a greater electrophile, than when using 2. The last reasoning is also supported by ω values: 1.519 (1), 1.446 (2), and 2.479 (3) eV.

A similar counterproductive effect is recognised for the thermodynamics of the endocyclic insertion step (ΔG_I-1→P-1), which can be explained by the same previous arguments: the thermodynamics is generally destabilized for 2 and 3, in comparison with 1, due to the presence of bulkier groups; the electronics of the substituents differentiate the energetic requirements for the phenyl (2) or perfluorophenyl (3) derivatives. Nevertheless, the kinetics of the endocyclic 1,1-insertion step (ΔG^‡_I-1→TS-2) depends primarily on electronics rather than steric effects. Notably, borole 2 has a smaller barrier height despite having bulkier substituents than 1; sterically, TS-2 of 2 and 3 have similar environments (Fig. S1), yet there is a 12.2 kcal mol⁻¹ difference in energy barriers (ΔΔG^‡_I-1→TS-2). Also, the trend of the ω values 2 < 1 < 3 correlates with the insertion barrier energies (ΔG^‡_I-1→TS-2), suggesting that higher ω stabilizes the pre-insertion complex but increases substrate distortion at TS-2, thereby elevating the barrier in 3 compared with 2. Interestingly, the C2–B and B–C lengths in Fig. S1 follow the same trend. Exocyclic pathways exhibit higher barriers and endergonic profiles (Fig. S2).

These computational findings align with experimental results reported by Piers and coworkers.³⁴ Compound 2 forms the Lewis adduct I-1 in CH₂Cl₂ at −78 °C. Upon warming to −10 °C, NMR spectroscopy reveals primarily the dimerized ring-expansion product rather than the monomer (Chart 3a). The absence of a monomer is consistent with thermochemical data identifying the ring-expansion intermediate as unstable (ΔG_R→P-1 = 14.3 kcal mol⁻¹). For 3, the Lewis adduct is well characterised by X-ray crystallography (CCDC 863188),³⁴ yet no insertion product is formed even at high temperatures (Chart 3b), consistent with the high energy barrier for the endocyclic CO insertion (ΔG^‡_I-1→TS-2 = 30.1 kcal mol⁻¹). In contrast, while experimental data for 1 remain unavailable, our results suggest that its ring expansion, a pivotal step before dimerization, is reversible and feasible under appropriate thermal control. Moreover, these results show excellent agreement with the energy profiles of Lin, including dimerization pathways and solvent effects.⁷²

Chart 3 Experimental evidence for the CO insertion reactions of 2 and 3.

Given the shared central heterocyclic framework of boroles 1–3, we focus on 1 for a detailed discussion. Note that 1,2,5-azadiborolidine (4) exhibits structural similarity to borole, theoretically derived by replacing a C=C double bond with an isoelectronic N=B double bond adjacent to the ring boron atom. This substitution, termed heteroatom doping, is a well-established strategy for tuning electronic properties.^73–78

As shown in Fig. 2, both 1 and 4 adopt C_2v symmetry and the ¹A₁ singlet ground state. Their adiabatic singlet–triplet energy gaps, ΔE_ST = 20.9 (1) and 51.0 (4) kcal mol⁻¹, confirm the singlet as the ground state for both cases. As 4π-electron systems, they display antiaromatic character, as evidenced by their low multicentre indices (MCI).^79–81 Notably, 4 shows greater electronic delocalization across the ring, reflected in its higher MCI value relative to 1. This enhanced delocalization in 4 correlates with a lower global electrophilicity index, indicating a reduced electrophilic character compared to 1. MCI analysis of the lowest-lying triplet states (C_2v, ³B₂) reveals increased delocalization in both molecules, in agreement with Baird's rule, which predicts aromaticity in triplet-state 4π-systems.^82–84 Accordingly, while 1 is more antiaromatic in the singlet state, it becomes more aromatic than 4 in the triplet state. This shift in aromatic character explains the significantly lower ΔE_ST observed in 1, as aromatic stabilization in the triplet state contributes to its energetic favourability.^85,86

Fig. 2 Comparison of the structural, symmetric, reactivity, and electronic features between borole (1) and 1,2,5-azadiborolidine (4). Bond lengths are expressed in Å, singlet- and triplet-state (italics) MCI values in electrons, and global electrophilicity (underline) in eV. MBI values in red.

Geometric analysis reveals similar B–C (1.587–1.592 Å) and C=C (1.343–1.349 Å) bond lengths in compounds 1 and 4. In 1,2,5-azadiborolidine, the N–B bonds are fully equalized, with bond lengths (1.432 Å) closely matching the borazine values from X-ray crystallography (1.429 Å (ref. 87) and 1.427–1.429 Å (ref. 88)). This supports a borazine-like bonding structure in the B–N–B fragment, consistent with Yáñez's computational studies,⁸⁹ indicating nitrogen lone-pair delocalization over the B–N–B moiety as the optimal Lewis representation (Fig. 2).

The MBI values indicate that the C=C bond is stronger at 1, whereas the B–C bond exhibits greater stability at 4. Furthermore, a comparison of the B–C and N–B bond indices in 4 reveals that the latter is of higher order, in agreement with preceding discussions.

Frontier molecular orbital analysis (Fig. S3) reveals a key distinction: while the HOMOs and LUMOs of 1 and 4 share identical symmetry and shape and comparable energies, their ordering is reversed, 1-HOMO resembles 4-LUMO, and vice versa. Consequently, these systems are not isolobal; however, they constitute isosteres under current IUPAC definitions.^90,91

Despite lacking isolobal equivalence, their isosteric properties suggest analogous reactivity. Therefore, we examined the two-step CO reaction mechanism (coordination followed by 1,1-insertion) for 1,2,5-azadiborolidine derivatives. Given asymmetric endocyclic bonds adjacent to boron (N–B vs. B–C), we also evaluated insertion at the N–B bond—termed NB-endocyclic insertion (Scheme 2).

Scheme 2 A plausible reaction mechanism between 1,2,5-azadiborolidine derivatives and CO. The endocyclic products refer to the ring expansion reaction.

We used previously synthesised azadiborolidines as starting materials (Chart 4). Haubold and co-workers reported the first synthesis in 1980 (1,2,3,4,5-pentamethyl derivative 5),³⁵ followed months later by Siebert's 3,4-diethyl-1,2,5-trimethyl-1,2,5-azadiborolidine (6).³⁶ Köster and co-workers advanced the field in 1994 by introducing trimethylsilyl substituents (e.g., 7).³⁸ Paetzold's pioneering work on azadiboriridine reactivity subsequently enabled derivatives 1,2,5-tri-tert-butyl-1,2,5-azadiborolidine (8) and 1,2,5-tri-tert-butyl-3,4-dimethyl-1,2,5-azadiborolidine (9).^37,39 These compounds have only been characterised by NMR and MS to date.

Chart 4 Overview of 1,2,5-azadiborolidine derivatives considered in this work.

Hypothetical pentaphenyl (10) and fluorinated pentaphenyl (11) analogues, designed by similarity to boroles 2 and 3, were also computationally examined. Conversely, compounds 12–15 have been structurally authenticated: 12 by Müllen (CCDC 1412367);⁴³ dianion 13²⁻ by Zeng (CCDC 1555140);⁴² 14 by Cui (CCDC 2045630),⁴¹ and 15 by Lindley (CCDC 2122486).⁴⁰ Beyond these, only the 1,2,5-azadiborolidines by Piers, in 2004, and Li, in 2020, have been reported.^92,93

Given the experimental confirmation that borole 2 undergoes ring expansion, while 3 does not, we then evaluated CO insertion feasibility in 1,2,5-azadiborolidines using previously derived kinetic and thermodynamic profiles.

In contrast to boroles 2 and 3, the CO coordination for 1,2,5-azadiborolidine derivatives is endergonic, exhibiting higher energy barriers in all cases (Table 1). The rate-determining step remains ring expansion (R → TS-2), yet the reaction Gibbs energy (ΔG_R→P-1) is consistently lower than that for borole 2 (ΔG_R→P-1 = 14.3 kcal mol⁻¹). This indicates thermodynamic favourability upon replacing the borole with a 1,2,5-azadiborolidine unit. For instance, compounds 4, 12, and 13 show ΔG_R→P-1 values near equilibrium (0.1, −0.4, and 1.3 kcal mol⁻¹, respectively). Kinetically, however, endocyclic CO insertion faces higher barriers than 2. In particular, heterocycles 8 and 9 show barriers (ΔG^‡_R→TS-2 = 23.9 and 26.8 kcal mol⁻¹, respectively) exceeding 2 but below 3, suggesting ring expansion at increased temperatures or extended reaction times; a comparison of relevant TS-2 structural parameters for 1–3 and 8 is presented in Fig. S1. In contrast, 4 and 7 exhibit barriers near 30.0 kcal mol⁻¹, rendering ring expansion unlikely under standard conditions. The remaining derivatives (entries 5–12) display even higher barriers (ΔG^‡_R→TS-2 > 30.1 kcal mol⁻¹), substantially diminishing the prospect of CO insertion under experimental conditions.

Table 1 Relative Gibbs energy values (kcal mol⁻¹) in the gas phase for the ring expansion reaction between different 1,2,5-azadiborolidine derivatives and CO^a

Entry	Reactant	TS-1	I-1	TS-2	P-1
a Entries follow a natural order with respect to TS-2.
1	8	15.2	11.2	23.9	11.4
2	9	17.4	14.2	26.8	11.0
3	4	11.8	8.2	30.0	0.1
4	7	15.1	12.3	30.5	7.1
5	10	15.9	13.7	31.9	13.9
6	5	16.4	15.9	33.8	4.7
7	6	16.3	15.7	34.9	5.2
8	15	22.5	21.6	37.5	4.8
9	12	22.0	21.4	37.8	−0.4
10	14	14.8	14.2	39.2	6.6
11	11	12.4	10.1	41.1	12.3
12	13	22.4	22.1	45.9	1.3

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Exocyclic insertion is noncompetitive for 5–7, 11–12, and 15, yet it yields the kinetic product for 4 and 13–14 (Table S1). Conversely, it affords the thermodynamic product for 8–10. NB-endocyclic insertion, tested representatively for 4, 5, 8, and 10, proved noncompetitive (Table S2), likely due to cleavage of the delocalized B–N–B bond during insertion, which compromises ring stability. This underscores the greater strength of the N–B bond relative to the inherently labile B–C bond in boroles,^29,94 as suggested by bond lengths, MBI and WBI reported in Tables S3–S8.

Given the presence of an electron-rich nitrogen and an electron-deficient boron in 1,2,5-azadiborolidines, dimerization was considered plausible and then examined computationally. Calculations for all derivatives (Fig. S4), except 12–15 (for which single-crystal X-ray data show monomeric structures incompatible with the dimeric motif evaluated), reveal favourable dimerization only for 4. For 5, the reaction Gibbs energy (5.9 kcal mol⁻¹) and barrier (17.1 kcal mol⁻¹) align with the experimental detection of only a trace dimer by NMR.³⁵ Increasing the substituent size elevates both the energy and barrier, confirming high steric sensitivity.

Across the examined 1,2,5-azadiborolidines, the optimised geometries reveal an average N–B bond length of 1.446 Å (σ = 0.009 Å). Despite the lost bond equalization in the B–N–B moiety, the N–B lengths remain borazine-like, supporting similar electronic character. This observation is replicated when analysing MBI and WBI data (Tables S4 and S5). Notice that most rings are planar, except 8, 9, and 14, as revealed by large MPP and SDP values (Table S3); their out-of-plane distortions relieve steric strain from bulky substituents (e.g., tert-butyl groups in 8 and 9).

For the adduct I-1, the average B–C(O) and C–O bond lengths are 1.622 Å (σ = 0.043 Å) and 1.129 Å (σ = 0.003 Å), respectively (Table S6). The MBI specifies a bond order of 0.575–0.877 for B–C(O), and 2.301–2.427 for the C–O bond (Table S7), whereas the WBI estimates slightly stronger bonds (Table S8): 0.910–1.178 and 3.056–3.130 values, respectively. The initial delocalization along the B–N–B fragment is lost when forming the Lewis adduct, as supported by both MBI and WBI values (Tables S4, S5, S7 and S8). Moreover, as illustrated in the Lewis structures in Table S7, MBI examination suggests a dative bond between the CO fragment and the boracycle, i.e., a B ← C(O) bond, while highlighting a general decrease in the C–O bond order, thus indicating a likely donor → π*(CO) backdonation.

A systematic analysis quantified key thermochemical correlations across azadiborolidine and borole derivatives (Fig. 3). The strongest correlation (R² = 0.9544) was found between the energy barrier for CO coordination (ΔG^‡_R→TS-1) and its reaction Gibbs energy (ΔG_R→I-1). A secondary correlation (R² = 0.8487) was obtained between the ring expansion barrier and B–C(O) bond length. Second-order perturbation analysis of I-1 quantified stabilization energies from donor–acceptor NBO interactions, specifically concerning σ → π*(CO) backdonation. The total energetic stabilization performed by the two endocyclic σ-NBOs related to the boron centre reveals a significant correlation with the B–C(O) bond length (R² = 0.8491) and with the total barrier (R² = 0.8539). Notably, using average backdonation energies (cf. Piers et al.³⁴) substantially reduced the correlation coefficients (Fig. S5). We thus recommend employing total (not average) σ → π*(CO) backdonation energies for future studies of such adducts. Remarkably, a moderate correlation coefficient (R² = 0.8291) was calculated between the backdonation energy and WBI for the C–O bond. Also, when considering the MBI of the B–C(O) bond, a significant coefficient (R² = 0.8343) emerged in relation to the total energy barrier.

Fig. 3 Analysis of linear correlations from gas-phase thermochemistry data for the endocyclic CO insertion among compounds 1–15. (a) Energy barrier and reaction energy of the CO coordination step. (b) Total energy barrier and σ → π*(CO) backdonation energy related to the B–C(O) bond length. (c) Total energy barrier and backdonation energy. (d) Energy barrier of the second reaction step and the C–O bond length. The σ → π*(CO) backdonation energies and the B–C(O) and C–O bond lengths were calculated for the adduct I-1.

A reasonable correlation was found between the CO insertion barrier (ΔG^‡_I-1→TS-2) and the C–O bond length (R² = 0.7280). However, no meaningful correlations emerged between the C–O bond length and either the B–C(O) bond length or backdonation energy. A weak correlation was also noted between ω and the ring expansion barrier (R² = 0.6950, Fig. S5c). This trend contradicts Parr's principle, which states that higher ω values correspond to greater electron-accepting ability and, therefore, higher reactivity.⁵⁰ Piers previously identified this apparent paradox,³⁴ suggesting that the dependency of σ → π*(CO) backdonation on the initial electrophilicity of the ring may explain it. However, our computations indicated that the correlation between ω and backdonation is negligible (Fig. S5d), and is weaker than those shown in Fig. 3. Complete electrophilicity and σ → π*(CO) backdonation data are provided in Tables S3 and S9–S10, respectively.

Additional insights were obtained from the analysis of the steric environment in I-1 (Fig. S6). First, steric hindrance remains largely unchanged upon replacing the borole ring with a 1,2,5-azadiborolidine core. Second, %V_Bur is more sensitive to the substituent size at positions 1, 2, and 5 than at positions 3 and 4 of the heterocycle. Third, substitution of hydrogen with fluorine significantly increases %V_Bur. Although fluorination is often employed to enhance ring electrophilicity, it may also compromise the steric environment of the Lewis adduct. Nonetheless, neither the planarity of the starting ring (e.g., MPP and SDP) nor the steric hindrance (e.g., %V_Bur) in I-1 was found to be a significant predictor of the thermochemistry of the CO-induced ring-expansion reaction.

Given that the experimental final product of borole 2 is its dimer rather than the ring-expanded monomer, we explored the dimerization energy profile for 1,2,5-azadiborolidine derivatives. Focusing on 8, the most promising candidate based on ring expansion energetics, we calculated the extended profile (Fig. 4). Following CO-induced ring expansion of 8 (R → P-1), viable dimerization (P-1 → I-2) occurs, succeeded by double [1,2]-migration of boron substituents (I-2 → P-2). Here, P-1 is a kinetically trapped, low-temperature isolable intermediate, whereas P-2 is the thermodynamically preferred product formed upon subsequent conversion of P-1. Dimerization proceeds concertedly through TS-3, aligning with the product hierarchy of borole 2 ³⁴ but differing mechanistically: 8 dimerizes concertedly, whereas 2 follows a stepwise pathway.⁷² The transformation is highly exergonic (ΔG_R→P-2 = −62.2 kcal mol⁻¹) with a thermally accessible total barrier (ΔG_R→TS-3 = 25.3 kcal mol⁻¹).

Fig. 4 Relative Gibbs energy profile for the ring expansion of 8 with CO, followed by a dimerization process and a subsequent double [1,2]-migration of the central tert-butyl substituents. Energy values (kcal mol⁻¹) were calculated in the gas phase and three solvents: dichloromethane (DCM), n-pentane, and tetrahydrofuran (THF).

To better approximate experimental conditions (where 1,2,5-azadiborolidine syntheses typically employ DCM, n-pentane, or THF), we analysed solvent effects. For compound 8, the energetic impact is most pronounced during 1,1-endocyclic CO insertion (R → P-1). The barrier ΔG^‡_R→TS-2 decreases from 23.9 kcal mol⁻¹ (gas-phase) to 19.0 kcal mol⁻¹ in THF, while ΔG_R→P-1 drops from 11.4 kcal mol⁻¹ to 4.8 kcal mol⁻¹ in DCM. For the full profile, dimerization of the expanded ring P-1 remains rate-determining. The barrier ΔG^‡_R→TS-3 is consistent across solvent environments: 25.9 (THF), 25.4 (DCM), 25.3 (gas), and 25.3 kcal mol⁻¹ (n-pentane). Although solvents slightly destabilize the overall reaction (ΔG_R→P-2 = −60.6 to −62.2 kcal mol⁻¹), deviations are minimal. Therefore, across THF, DCM, and n-pentane, the computed solvent effects are modest: the differences in ΔG^‡ are ≤0.5 kcal mol⁻¹ at 298 K. THF and DCM afford essentially comparable kinetic and thermodynamic profiles, while n-pentane shows a slightly lower barrier; however, the magnitude of these differences lies within the uncertainty of the method. We therefore conclude that all three solvents provide functionally similar outcomes under our conditions.

Conclusions

We performed a computational study to elucidate the mechanism of endocyclic CO insertion into borole rings. Establishing a structural analogy via isosterism between boroles and 1,2,5-azadiborolidines enabled the transposition of CO ring expansion to this unexplored boron heterocycle. For the optimal candidate (8), the pathway comprises: (1) CO-induced ring expansion, (2) dimerization, and (3) double [1,2]-migration, mirroring borole mechanisms. These results confirm that 8 exhibits comparable CO reactivity alongside structural similarity to boroles. Computations predicted viable CO insertion⁹⁵ for 8, yielding polycyclic P-2. Within the accuracy of our calculations, no single solvent is uniquely optimal; THF, DCM, and n-pentane provide similar barriers and reaction Gibbs energies.

Mechanistically, the B–C(O) and C–O bond lengths in Lewis adducts correlate with ring expansion kinetics. A significant correlation between σ → π*(CO) backdonation energies and reaction barriers highlights its utility as a predictive descriptor for boron systems. We encourage experimental validation to establish 1,2,5-azadiborolidine as the fourth trivalent-boron-containing heterocycle undergoing CO coordination–insertion, highlighting the metal-mimetic behaviour of boron and enabling design of novel functional materials.

Author contributions

Victor A. Lucas-Rosales: investigation, validation, formal analysis, writing – original draft. Miguel A. Vázquez: investigation, writing – review. Gabriel Merino: investigation, writing – review. Albert Poater: supervision, formal analysis, computational resources, funding acquisition. J. Oscar C. Jiménez-Halla: conceptualization, supervision, formal analysis, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the SI: Cartesian coordinates of optimised geometries and electronic structure analyses. See DOI: https://doi.org/10.1039/d5qo01081k.

Acknowledgements

V. A. L.-R. thanks SECIHTI for his M.Sc. student scholarship (#1312084). J. O. C. J.-H. acknowledges Laboratorio Nacional de Cómputo de Alto Desempeño (PIPILA) and Universidad de Guanajuato (DCNE). A. P. is a Serra Húnter Fellow and thanks the Spanish MINECO for project PID2021-127423NB-I00, and the Generalitat de Catalunya for project 2021SGR623. The authors acknowledge the computing time supported by Conacyt (Grant CB-2015-252356), and additional resources provided by BSC supercomputing facilities.

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