Multiconfigurational non-adiabatic molecular dynamics towards photochemical-N₂-extrusion reactions in borodiazenes

Abstract

We used state-of-the-art quantum-chemical calculations to study the photodenitrogenation of 1-methylborodiazene to 1-methylborirane. Vertical excitation energy calculations indicate that the S₀ → S₁ (n_N → π_NN*) and S₀ → S₂ (n_N → 2p_B) transitions are accessible (318 nm and 287 nm, respectively), and the S₀ → S₁ transition is the bright state. The minimum-energy path indicates near-degeneracy between the S₁ and S₂ surfaces in the Franck–Condon region, leading to the steepest descent path on the S₁ state to be towards fluorescent decay rather than denitrogenation. Our simulations indicate that denitrogenation primarily occurs shortly after an S₁/S₀ hopping event (79% of trajectories) and proceeds via three distinct pathways. The dominant pathway involves boron pyramidalization and partial π_NN isomerization in the S₁ state, with N₂ elimination shortly after an S₁/S₀ hop. Minor pathways include either π_NN isomerization or boron pyramidalization, with N₂ elimination occurring on the S₀ and S₁ states, respectively. We also observed that some trajectories rearrange to form a diazoborete intermediate. Our results show that the labile N₂ group can be used to access base-free boriranes.

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Introduction

Photochemistry exemplifies principles of green chemistry by utilizing renewable solar energy to facilitate reactions under mild conditions. Light activation enables spatiotemporal control over the activation and deactivation of chemical processes, such as cycloadditions,^1–3 isomerizations,^4–6 and gas evolutions.^7–9 These processes have excellent atom economy, minimal energy use, and high selectivity—traits that are highly valued in chemistry,^10–12 biology,^13–15 and materials science.^1,16–18 Photochemical activation provides access to reactive intermediates that would otherwise be thermally inaccessible by breaking^19–21 and forming bonds,^22–24 causing isomerizations,²⁵ and altering electronic properties (e.g., aromaticity/antiaromaticity^26–28). These light-triggered modifications have led to the application of these reactions in energy storage,^1,16,29 drug delivery,^30–32 and total organic synthesis.^33–35

These photochemical reactions are used in organic synthesis to introduce ring strain^23,36,37 into chemical systems that would otherwise be kinetically or thermally unfavorable. Researchers can then utilize these ring-strained compounds in additional chemical reactions to produce final products, such as grazoprevir,³⁸ 2-pyridylethylamine,³⁹ and lasalocid.^33,37,40,41 Three-membered rings, such as cyclopropanes,⁴² aziridines,⁴³ and epoxides/oxiranes^40,44,45 have garnered significant interest because of their distinctive reactivity, arising from inherent ring strain, which enables diverse synthetic applications.^41,45,46 Despite the high ring strain, these three-member rings are commonly found in natural products,^47–49 leading to increased interest in pharmaceutical chemistry⁴³ and chemical biology^44,50 (Fig. 1).

Fig. 1 Examples of cyclopropanes, aziridines, and oxiranes within pharmaceutical agents: (a) triglanol tiglate,⁴⁷ (b) aziridines mitosol,⁴⁹ and (c) triptolide,⁵¹ respectively. The three-membered rings are highlighted in red within the structures.

The synthetic methods for these rings include cyclopropanations,^52–54 aziridination,^53,55–57 and epoxidations,^53,58 each of which produces its respective three-membered ring and is well-established. The widespread application of aziridines and oxiranes has driven research into other hetero-analogues of cyclopropanes, such as thiiranes,^59–61 phosphiranes,^62–64 and siliranes.^65–67 Like cyclopropanes, aziridines, and oxiranes, these compounds are highly reactive, often undergoing ring-opening reactions with nucleophiles^62,65 or ring expansions with π-systems.^67–69 As a result, these three-membered rings have found uses in pharmaceutical chemistry^68,70 and polymer synthesis.^62,65 One hetero-analogue of cyclopropane, whose chemistry is not fully understood, is borirane, the boron analogue.

Pioneering work on the synthesis of borirane was conducted by Berndt and co-workers in 1983, in which the first B=C double bond was reported (Fig. 2a).⁷¹ Boriranes are highly reactive due to their ring strain and Lewis acidity.^72,73 In 1991, Denmark and coworkers further expanded the field by introducing the first report of a Lewis base-stabilized borirane through the photoirradiation of diphenyl-(E)-2-phenylethenyl-borane (Fig. 2b).⁷⁴

Fig. 2 Comparison between the first (a) base-free borirane and (b) base-stabilized borirane.

In the late 2000 s, Wang reported several N,C-chelated^75,76 and N-heterocyclic carbene chelated boriranes⁷⁷ (NHC-borirane) for potential use in optoelectronic and organic synthesis, stemming from their easy and reversible C–C/C–B bond rearrangements triggered by both light and heat. Braunschweig et al. reported the synthesis of NHC-boriranes through the salt elimination of NHC-dichloroboranes with the dianion of trans-stilbene towards trans-1,2,3-triphenyl NHC-boriranes.⁷⁸ Curran and coworkers later reported a high-yield (80%) novel synthetic approach to NHC-boriranes via double hydroboration of acetylenedicarboxylates with NHC-boranes.⁷³ The NHC-boriranes show exceptional inertness in gas-phase, aqueous, thermal, and photolytic conditions because of the Lewis base stabilization.^73,78,79 In 2019, Curran et al. reported the first ring-opening reaction of base-stabilized borirane towards a novel class of NHC-boralactones.⁸⁰ Recent works have reported access to borirane derivatives, such as carborane-fused boriranes,^81,82 which have expanded the range of ligated boriranes. Nonetheless, base-free boriranes remain difficult to isolate.

Previous synthetic works have utilized denitrogenation reactions to synthesize three-member rings (i.e., cyclopropanes,^11,83,84 aziridines,⁸⁵ oxiranes,⁸⁶ and thiiranes^87,88). Similarly, Dowd described the photodenitrogenation of a five-membered ring, 4-methylene-Δ-pyrazoline, targeting the formation of trimethylenemethane; this highly reactive intermediate rapidly cyclized to produce cyclopropane at temperatures >77 K (Scheme 1a).⁸³ Here, we present a proof of concept for using the labile azo group in a similar denitrogenation reaction toward a base-free borirane. We hypothesize that irradiation of a boron derivative of 4-methylene-Δ-pyrazoline, 1-borodiazene (bd), would promote N₂ extrusion and produce 1-methylborirane, 5 (Scheme 1b).

Scheme 1 (a) Photodenitrogenation of 4-methylene-Δ-pyrazoline towards a 1,3-diyl and subsequent cycloaddition towards functionalized five-member ring (3) and/or ring-closure towards methyl-cyclopropane (4). (b) Proof-of-concept photodenitrogenation reaction of 1-methyl-borodiazene (bd) towards base-free 1-methylborirane (5).

We conducted a computational investigation of the denitrogenation mechanism of bd using multiconfigurational (complete active space self-consistent field, CASSCF) and single-reference (time-dependent density functional theory, TD-DFT) quantum chemical methods. In this study, we comprehensively outlined the reaction pathways for the photochemical N₂ extrusion of bd towards 5 using our open-source Python rapid artificial intelligence ab initio molecular dynamics (PyRAI²MD), which enabled quantum-mechanical nonadiabatic molecular dynamics (QM-NAMD).

Results and discussion

Active space and characterization of excitation on the optimized global minimum

The first step in the proposed photochemical denitrogenation is the absorption of a photon by bd, inducing electronic excitation. Therefore, we initially calculated the photophysical properties—vertical excitation energies and nature of transitions—using TD-DFT and EOM-CCSD. We carried out TD-DFT calculations using CAM-B3LYP-GD3(BJ) and ωB97X-D with the cc-pVDZ basis set. The predicted vertical excitation energy for the ground-state-optimized structure of bd, designated as bd-S₀, was calculated to be 3.71 eV with CAM-B3LYP-GD3(BJ)/cc-pVDZ and 3.72 eV with ωB97X-D/cc-pVDZ. Both methods indicated that the S₀ → S₁ excitation is a n_N → π_NN* transition, with an oscillator strength of 0.003. To ensure the reliability of our TD-DFT results and due to the absence of experimental spectra, we compare them against EOM-CCSD calculations, which are considered a gold standard^25,26,89 in excited-state single-reference computations.^26,27 We calculated the S₀ → S₁ vertical excitation energy to be 4.07 eV using EOM-CCSD/cc-pVDZ. These results demonstrate that the TD-DFT values are 0.36 eV and 0.35 eV lower in energy than the EOM-CCSD values (CAM-B3LYP-GD3(BJ)/cc-pVDZ and ωB97X-D/cc-pVDZ, respectively).

We used the complete active space self-consistent field (CASSCF) method and CASSCF with a second-order perturbation theory (CASPT2), both of which require an active space selection. We examined the orbital transitions predicted by TD-DFT and EOM-CCSD, and those involved in the photodenitrogenation of bd, to identify which orbitals to incorporate into the active space. We included twelve electrons distributed across 11 orbitals in the active space of bd; Fig. S1 shows the orbitals and their average orbital occupancies.

We compared the CASSCF and CASPT2 excitation energies and orbital transitions with those computed using single-reference methods (i.e., TD-DFT and EOM-CCSD) to ensure an accurate characterization of vertical excitation energies with the CASSCF(12,11) active space. When the vertical excitation energies and the nature of the transitions align between multiconfigurational and single-reference methods, this indicates that the selected active space sufficiently captures the photophysical properties of the molecule (i.e., bd-S₀). Due to the lack of experimental spectra for bd, we used the gold-standard^26,89 EOM-CCSD method as a reference. The vertical excitation energy for bd-S₀ was calculated using state-averaged CAS(12,11) over the first five singlet states with the cc-pVDZ basis set (i.e., SA5-CASSCF(12,11)/cc-pVDZ) to be 4.50 eV. This indicates that the SA5-CASSCF(12,11)/cc-pVDZ method overestimates the S₀ → S₁ vertical excitation energy by 0.43 eV compared to EOM-CCSD/cc-pVDZ results. Additionally, it overestimates the S₀ → S₁ vertical excitation energy relative to CAM-B3LYP-GD3BJ/cc-pVDZ and ωB97X-D/cc-pVDZ by 0.79 and 0.78, respectively. The discrepancies observed in the SA5-CASSCF(12,11)/cc-pVDZ calculation and single-reference methods arise from the omission of dynamical correlation in the former, which the CASPT2 method corrects. For the CASPT2 correction, the calculation was performed as SA5-CASPT2(12,11)/cc-pVDZ//SA5-CASSCF(12,11)/cc-pVDZ; the S₀ → S₁ vertical excitation energy was 3.90 eV. This value is 0.17 eV lower than the EOM-CCSD/cc-pVDZ results and 0.19 eV and 0.18 eV higher than those predicted by CAM-B3LYP-D3(BJ)/cc-pVDZ and ωB97X-D/cc-pVDZ, respectively. The differences in vertical excitation energies among TD-DFT, EOM-CCSD, and CASPT2 arise because single-reference methods lack the static electronic correlation needed for multiconfigurational descriptions, which CASPT2 includes. This missing static correlation becomes more evident in states with multiconfigurational electronic character (i.e., bd-S₀; see Fig. S1 for further discussion), underscoring the importance of using the CASSCF and CASPT2 methods for our photochemical study. The CASSCF and CASPT2 methods classify the S₀ → S₁ excitation as an n_N → π_NN* transition; this nature of the transition aligns with the TD-DFT and EOM-CCSD results. Table 1 summarizes these findings.

Table 1 Benchmarked TD-DFT and CASSCF vertical excitation energies

Method	State	Energy (eV)	Wavelength (nm)	Oscillator strength	Nature
CAM-B3LYP-D3(BJ)/cc-pVDZ	S1	3.71	334	0.003	nN → πNN*
	S2	4.24	292	0.000	πNN → 2pB
	S3	6.31	196	0.000	nN → πNN*
ωB97X-D/cc-pVDZ	S1	3.72	333	0.003	nN → πNN*
	S2	4.29	289	0.000	πNN → 2pB
	S3	6.29	197	0.000	nN → πNN*
EOM-CCSD/cc-pVDZ	S1	4.07	305	0.004	nN → πNN*
	S2	4.47	277	0.000	πNN → 2pB
	S3	6.58	188	0.000	nN → πNN*
SA5-CASSCF(12,11)/cc-pVDZ	S1	4.50	276	0.010	nN → πNN*
	S2	4.67	265	0.000	πNN → 2pB
	S3	6.82	182	0.000	nN → πNN*
SA5-CASPT2(12,11)/cc-pVDZ//SA5-CASSCF(12,11)/cc-pVDZ	S1	3.90	318		nN → πNN*
	S2	4.32	287		πNN → 2pB
	S3	5.57	223		nN → πNN*

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After comparing the orbital transitions, vertical excitation energies, and oscillator strengths across CASSCF(12,11), CASPT2(12,11), TD-DFT, and EOM-CCSD methods, we determined that calculations using CAS(12,11), as illustrated in Fig. S1, effectively capture the vertical excitation energies of bd at equilibrium (i.e., bd-S₀). Consequently, we employed SA5-CASSCF(12,11)/cc-pVDZ for all the following calculations.

Predicted absorption spectra and S₁ minimum energy path

To confirm bd has an accessible S₀ to S₁ excitation, we calculate its absorption spectrum. We generated 500 Wigner-sampled non-equilibrium geometries based on the ground state frequencies of bd (Fig. 3a) and calculated the vertical excitation energies [S₀ → S_n (n = 0–4)] for each structure using MS-CASPT2(12,11)/cc-pVDZ//CAS(12,11)/cc-pVDZ. We consolidate the results of the 500 vertical excitation calculations into the computed spectra shown in Fig. 3b.

Fig. 3 (a) The top view (top) and side view (bottom) overlay of 500 non-equilibrium structures from the Wigner ensemble of bd. (b) The predicted absorption spectrum was obtained by averaging the 500 vertical-excitation energy calculations. The absorption intensity is normalized to the peak with the highest oscillator strength, S₁. All calculations utilized the MS-CASPT2(12,11)/cc-pVDZ//CASSCF(12,11)/cc-pVDZ method.

The calculated spectrum exhibits three prominent peaks at 325 nm, 308 nm, and 200 nm, along with a minor peak at 188 nm. The red peak at 325 nm corresponds to the S₀ → S₁ (n_N → π_NN*) transition and is the most intense, despite being spectroscopically forbidden. The blue peak, centered at 308 nm, corresponds to an S₀ → S₂ (n_N → 2p_B) transition; this peak has the second-highest intensity and significant overlap with the S₀ → S₁ (n_N → π_NN*) peak. The purple peak at 200 nm corresponds to the S₀ → S₄ (n_N → 2p_B) transition; it has the lowest intensity of the three major peaks. The green peak at 188 nm corresponds to the S₀ → S₃ (n_N → π_NN*) transition. Its intensity is minimal compared to the other peaks [i.e., S₀ → S_n (n = 1, 2, and 4)]; it significantly overlaps with the S₀ → S₄ peak. Like S₀ → S₁, the S₀ → S₃ transition is also spectroscopically forbidden (i.e., n_N → π_NN*). The variation in intensity between the S₀ → S₁ and S₀ → S₃ peaks arises from the different n_N orbitals involved in the electronic transitions (i.e., out-of-phase and in-phase n_N orbitals, respectively). The out-of-phase n_N orbital in the S₀ → S₁ transition shows greater overlap with the π_NN* orbital compared to the in-phase n_N orbital in the S₀ → S₃ excitation (See SI Fig. S3). This leads to the S₀ → S₁ being the bright state, while the S₀ → S₃ peak has the lowest intensity of all the peaks. The S₀ → S₁ (n_N → π_NN*) and S₀ → S₂ (n_N → 2p_B) transitions are accessible via a 254 nm ultraviolet light source. In contrast, the S₀ → S₃ (n_N → π_NN*) and S₀ → S₄ (n_N → 2p_B) transitions are inaccessible because the required excitation energy exceeds the energy of the photon source. The overlap and accessibility of S₀ → S₁ (n_N → π_NN*) and S₀ → S₂ (n_N → 2p_B) peaks suggest a role in the photodenitrogenation of bd. We will focus on these excitations and their photochemistry.

We then focused on elucidating the photodenitrogenation mechanism. Since the S₁ state is the accessible bright state, we calculated the minimum energy path (MEP) to find the steepest descent along the S₁ surface, starting from the Franck–Condon point of bd-S₀. We hypothesized that the diazo double bond (π_NN) will elongate along the S₁-MEP due to n_N → π_NN* excitation. Fig. 4 shows the S₁-MEP, ground state geometry (bd-S₀), final MEP geometry (bd-MEP-8), and the S₁ minimum (bd-S₁).

Fig. 4 (a) The calculated SA5-CASPT2(12,11)/cc-pVDZ minimum energy path of bd along the S₁ surface. (b) The out-of-plane angle θ_B quantifies boron pyramidalization. The plane is defined by C₈–B₃–C₁₁ (shown in red), with an orthogonal vector from this plane and the carbon of the methyl group defining the measured angle, θ_BP (highlighted in green). (c) The ground state structure, optimized with SA5-CASSCF(12,11)/cc-pVDZ, bd-S₀. (d) The final step of the MEP, bd-MEP-8, and (e) the optimized S₁ structure, bd-S₁. The corresponding diazo double bond length (π_NN) and boron pyramidalization (θ_BP) values are shown below each structure.

Fig. 4 demonstrates the MEP along the S₁ surface and the energies corresponding to the S₀–S₄ states; it includes 8 geometries [bd-MEP-X (X = 1–8)]. We observe that in the initial two steps of the S₁-MEP (i.e., bd-MEP-1 and bd-MEP-2), the S₁ surface is energetically close to the S₂ surface; the S₂–S₁ energy gaps are 0.46 eV and 0.21 eV, respectively. The small S₂–S₁ energy gaps in bd-MEP-1 and bd-MEP-2 suggest a rapid crossing between the S₁ and S₂ surfaces immediately outside the Franck–Condon point. The S₁-MEP converges to a structure, bd-MEP-8, 3.83 eV above bd-S₀. At bd-MEP-8, the S₁–S₀ energy gap is 2.23 eV; this large gap indicates there is no significant coupling between the S₁ and S₀ surfaces (i.e., no S₁/S₀ crossing). Therefore, the steepest descent on the S₁ surface leads toward a radiative decay channel rather than the proposed photodenitrogenation. The two geometries, bd-S₀ and bd-MEP-8, shown in Fig. 4c and d have π_NN bond lengths of 1.26 Å and 1.18 Å, respectively, reflecting a decrease of 0.08 Å from the Franck–Condon geometry to bd-MEP-8. Instead of the expected elongation of the π_NN bond, we saw boron undergo a conformational change, shifting from a planar conformation in bd-S₀ (Fig. 4d) to a pyramidalized conformation in bd-MEP-8 (Fig. 4e). These structures—bd-S₀ and bd-MEP-8—demonstrate that boron pyramidalization outcompetes the elongation of the π_NN bond along the S₁-MEP. We attribute boron pyramidalization to an increase in electron occupancy in the 2p_B orbital, along the S₁-MEP, despite the initial n_N → π_NN* excitation.

To measure the extent of boron pyramidalization, we defined an out-of-plane angle, θ_BP, where a planar boron (unoccupied 2p_B orbital) has a θ_BP of 90°, and an ideally pyramidalized boron (occupied 2p_B orbital) has a θ_BP outside of 75°–105° (Fig. 4b). bd-S₀ and bd-MEP-8 show θ_BP values of 89° and 69°, respectively. The 20° decrease in θ_BP from bd-S₀ to bd-MEP-8 indicates a full pyramidalization of the boron along the S₁-MEP. This boron pyramidalization occurs alongside the previously observed 0.08 Å reduction in the π_NN bond length. The concurrent shortening of the π_NN bond and boron pyramidalization along the S₁ MEP suggests that the 2p_B orbital is gaining electron occupancy along the steepest S₁ path. This is supported by the notable overlap of the S₀ → S₁ (n_N → π_NN*) and S₀ → S₂ (n_N → 2p_B) peaks observed in the absorption spectra (Fig. 3b), suggesting that the S₀ → S₂ (n_N → 2p_B) transition is energetically accessible. These findings are in line with a charge transfer between the π_NN* and 2p_B orbitals.

Due to the large S₁/S₀ energy gap at bd-MEP-8, we optimized an S₁ minimum, bd-S₁, using the last step of the MEP as an initial guess. bd-S₁ has a π_NN of 1.18 Å and θ_BP of 69°; it is 3.61 eV above the bd-S₀. These values show decreases of 0.08 Å and 20° for π_NN and θ_BP, respectively, from bd-S₀ to bd-S₁. These measurements indicate that the boron in bd-S₁ is pyramidalized relative to bd-S₀. bd-S₁ and bd-MEP-8 shared π_NN and θ_BP values (1.18 Å and 69°, respectively) and had similar energies (3.83 eV and 3.61 eV, respectively), indicating that these structures occupy similar regions of the potential energy surface. At bd-S₁, a 2.26 eV S₁/S₀ energy gap confirms a nonradiative decay channel via the S₁ MEP, contradicting the hypothesis of nonradiative photodenitrogenation to 5. Although the S₁-MEP offers detailed insight along the steepest S₁-path, it neglects essential dynamical effects required to study the excited-state mechanism of bd.

We accounted for the missing dynamical effects by running quantum-mechanical nonadiabatic molecular dynamics (QM-NAMD) simulations using our open-source Python Rapid Artificial Intelligence Ab Initio Molecular Dynamics (PyRAI²MD) software.^22,23 We generated 700 initial conditions for production trajectories using Wigner sampling based on bd-S₀ frequencies. The fewest-switches surface-hopping (FSSH) algorithm captured nonadiabatic transitions over 1 ps with analytical nonadiabatic coupling vectors. A trajectory was considered complete if denitrogenation and an S₁/S₀ hop occurred, or if it reached 1 ps. The maximum energy drift allowed for these trajectories was 0.05 a.u.; 261 trajectories met this criterion. After 1 ps, 244 (94%) trajectories were on S₀ surface, and 16 (6%) remained on the S₁ state. Of those passing through an S₁/S₀ hop, 218 underwent denitrogenation to 5 (73) or a diradical, 6 (145). The remaining 26 either stayed as reactants (13) or formed diazoborete, 7 (13) (Scheme 2).

Scheme 2 Product distribution of productive trajectories within our ensemble. The observed products include (a) borirane (5), (b) diradical (6), and (c) diazoborete (7). Below each structure are the number of trajectories leading to each product and their percentages (i.e., quantum yields).

To investigate the photodenitrogenation mechanism, we monitored the two breaking CN bonds (σ_CN) throughout our ensemble of trajectories. We propose that denitrogenation may proceed through two possible mechanistic pathways: either both CN bonds break simultaneously (concerted), or one CN bond breaks first, followed shortly by the other (stepwise). We hypothesize that bd undergoes stepwise denitrogenation due to increased flexibility from n_N → π_NN* excitation, enabling π_NN rotation (i.e., partial cis-to-trans isomerization) and σ_CN bond cleavage. We plotted the two σ_CN bond lengths from 244 trajectories ending in the ground state in Fig. 5. Additionally, two arbitrary profiles are shown as dashed lines, representing the ideal stepwise (red) and concerted (gray) denitrogenation pathways within this trajectory map.

Fig. 5 Trajectory map of the photodenitrogenation reaction of bd. Each line represents a single trajectory, with black dots marking S₁/S₀ hopping points. We tracked the two CN bonds (σ_CN) that must break for photodenitrogenation during the NAMD simulations. To illustrate an ideal stepwise denitrogenation mechanism, we drew an arbitrary bilinear profile with red dashed lines indicating ±0.1 Å around the optimized C–N distance (1.54 Å) in the S₀ state. A trajectory would follow this bilinear profile, with one CN bond elongating while the other stays within the red boundaries. Once the first CN bond breaks, the second CN bond then elongates and breaks as well. To depict an ideal concerted denitrogenation mechanism, we included an arbitrary 1 : 1 line, indicating that both CN bonds elongate simultaneously until denitrogenation occurs.

In Fig. 5, both concerted and stepwise mechanisms are present, indicating that neither pathway dominates; instead, both are readily accessible for the denitrogenation reaction of bd. To clearly classify the denitrogenation mechanism in the ensemble of trajectories, we used the literature definition of dynamically stepwise or dynamically concerted mechanism, as reported by Yang et al.⁹⁰ We determined that of the 244 trajectories that terminate in the S₀ state, 218 undergo denitrogenation. 60 (28%) followed a dynamically stepwise mechanism, while 158 (72%) followed a dynamically concerted mechanism. Thus, denitrogenation of bd is mainly driven by the dynamically concerted mechanism.

Having established that the dynamically concerted mechanism (72%) outcompetes the dynamically stepwise mechanism (28%), we now examine the consistent boron pyramidalization in static (bd-S₁ and bd-MEP-8) and dynamic (QM-NAMD) calculations. The pyramidilized boron in these geometries indicates that the 2p_B orbital acquires additional electron occupancy along the S₁ surface from the π_NN* (i.e., a charge transfer). We hypothesize that trajectories will adopt one of two geometries (i.e., boron pyramidalization or partial cis-to-trans π_NN isomerization) on the S₁ surface, and those adopting boron pyramidalization will not denitrogenate.

To measure the extent of boron pyramidalization and partial cis-to-trans π_NN isomerization in the denitrogenation mechanism within our trajectory ensemble, we used the geometrical parameters and thresholds presented in Fig. 6: θ_BP and θ_CNNC.

Fig. 6 (a) The out-of-plane angle θ_BP is defined as the angle between the methyl-boron and the normal vector (green) to the plane formed by the atoms highlighted in red. We defined a planar boron with θ_BP values of 75°–105°; otherwise, we classified the boron as pyramidilized. (b) The dihedral angle, θ_CNNC, is defined by the C–N–N–C (orange); we classify the cis-π_NN as having θ_CNNC values from −25° to 25°, while other configurations are considered partial trans-π_NN.

Based on the geometrical descriptions shown in Fig. 6, we observed that 177 trajectories (82%) exhibit boron pyramidalization, while 182 (83%) undergo a partial cis-to-trans π_NN isomerization. Out of 218 trajectories that underwent denitrogenation, 120 trajectories included both geometries, 37 only experienced boron pyramidalization, and 59 only experienced partial π_NN isomerization. These statistics show that bd can undergo denitrogenation via either the boron pyramidalization or the partial π_NN isomerization pathway; however, the major pathway includes both.

Out of 120 trajectories that experience both geometries, 12 initially undergo partial π_NN isomerization, while 108 first experience boron pyramidalization. The π_NN isomerization and boron pyramidalization conformations are linked to the electronic occupancy of the π_NN* orbital and the 2p_B orbital, respectively. The frequent occurrence of both geometries is associated with the near degeneracy between the S₁ and S₂ surfaces in the Franck–Condon region, which correspond to the n_N → π_NN* and n_N → 2p_B transitions, respectively. Furthermore, the favorable spatial overlap between the π_NN* and 2p_B orbitals facilitates charge transfer, thereby enabling the adoption of the associated conformations (i.e., partial π_NN isomerization and boron pyramidalization). Statistically, the photodenitrogenation process begins with boron pyramidalization, followed by partial π_NN isomerization, and ends with denitrogenation. We identified a trajectory that proceeds through partial π_NN isomerization and boron pyramidalization during denitrogenation, characterized by the angles θ_CNNC and θ_BP, respectively. Fig. 7 provides a detailed analysis of this trajectory.

Fig. 7 Snapshots of a representative trajectory that undergoes the denitrogenation on the S₁ surface via the mechanistic pathway that includes boron pyramidalization and partial cis-to-trans π_NN isomerization.

Fig. 7 shows snapshots of a trajectory undergoing denitrogenation via the dominant pathway that involves the partial π_NN isomerization and boron pyramidalization. At 0 fs, θ_BP is 82°, and θ_CNNC is 10°. At 50 fs, θ_BP is 139°, and θ_CNNC is −5°. By 400 fs, θ_BP and θ_CNNC are 140° and 1°, respectively. At 500, θ_BP is 46°, and θ_CNNC is −16°. At 650 fs, θ_BP is 124°, and θ_CNNC is −21°. By 858.5 fs, θ_BP is 71°, and θ_CNNC is 57°. At 900 fs, θ_BP is 114°, and θ_CNNC is −8°. Between 0 fs and 50 fs, θ_BP and θ_CNNC increased by 57° and 15°, respectively. The rapid rise in θ_BP (57°) with a small decrease in θ_CNNC (15°) suggests the 2p_B orbital gains electron occupancy, driving the mechanism, rather than the π_NN* orbital. In the next 350 fs (50 fs to 400 fs), θ_BP and θ_CNNC increased by 1° and 6°, respectively, demonstrating that the geometry remains unchanged. We attribute this persistent geometry to the close resemblance between the 50 fs geometry and bd-S₁. From 400 fs to 500 fs, θ_BP decreased by 94°, and θ_CNNC increased by 17°. The decrease in θ_BP from 140° to 46° indicates that the trajectory rehybridizes boron from sp² to sp³, in the opposite direction to the initial pyramidalization. By 650 fs, θ_BP increased by 78°, and θ_CNNC decreased by 5°. Like the previous 100 fs window, the changes in θ_BP and θ_CNNC for the 500 fs to 650 fs period suggest that the sp³ boron has inverted, while the π_NN bond remains in the cis-configuration. The fluctuation in the θ_BP indicates prolonged occupation of the 2p_B orbital, whereas minimal changes in θ_CNNC suggest that the π_NN* orbital remains empty during this period. Within the 650 fs to 858.5 fs time window, the θ_BP decreased by 53°, and θ_CNNC increased by 78°; at the 858.5 fs geometry, the trajectory underwent an S₁/S₀ hop. The lower θ_BP value (71°) is 4° below our planar boron threshold (75°), while the higher θ_CNNC (57°) indicates a partial cis-to-trans π_NN isomerization. These geometric changes show that the 2p_B orbital is essentially empty, while the π_NN* orbital is occupied. 41.5 fs (i.e., at 900 fs) after the S₁/S₀ hop, the trajectory denitrogenates towards the 1,3-diyl. This trajectory shows the mechanistic pathway involving boron pyramidalization and partial π_NN isomerization. Boron pyramidalization occurs first, followed by partial π_NN isomerization, which leads to denitrogenation. Minor denitrogenation pathways are explored in Fig. S4 and S5.

Minor pathways

After analyzing the mechanisms for the major product, we investigate the pathway to the minor product, diazoborete (7). We identified a trajectory bypassing denitrogenation, leading to 7. To compare with earlier figures, we measured θ_BP and θ_CNNC along this trajectory. Thirteen trajectories (6%) showed this rearrangement. Fig. 8 examines a representative trajectory in detail.

Fig. 8 Snapshots of a representative trajectory that does not involve denitrogenation on the S₁ surface; instead, it involves an insertion-like reaction that results in BN bond formation and BC bond cleavage, producing diazoborete (7).

Fig. 8 provides snapshots of the representative trajectory. θ_BP and θ_CNNC are reported to facilitate direct comparison with previous figures (Fig. 7 and Fig. S4 and S5). At 0 fs, θ_BP measures 90° while θ_CNNC is −10°. By 50 fs, θ_BP is 83°, whereas θ_CNNC measures −54°. At 100 fs, θ_BP is 84°, with θ_CNNC equal to −35°. By 130 fs, θ_BP reaches 96°, and θ_CNNC is −70°. At 150 fs, θ_BP measures 93°, while θ_CNNC is at −92°. Finally, at 200 fs, θ_BP measures 53°, and θ_CNNC is −150°. Between 0 fs and 50 fs, θ_BP drops by 7°, and θ_CNNC decreases by 44°. This suggests that the 2p_B orbital remains unoccupied during this period, while the π_NN* orbital gains electron occupancy. In the following 50 fs (50 fs to 100 fs), θ_BP and θ_CNNC increased by 1° and decreased by 19°, respectively, indicating a prolonged occupancy of the π_NN* orbital. From 100 fs to 130 fs, there is a 12° increase in θ_BP and a 35° decrease in θ_CNNC. Although the θ_BP increase is significant, boron remains in a planar conformation, not pyramidalizing per our geometric thresholds. At the 130 fs geometry, the trajectory undergoes an S₁/S₀ hop. Between 130 fs and 150 fs, the θ_BP decreases by 3°, while θ_CNNC decreases by 22°. Due to partial π_NN isomerization, the n_N orbital aligns with the 2p_B orbital, leading to BN bond formation and BC bond cleavage; this rearrangement results in 7. Between 150 fs and 200 fs, the θ_BP drops by 40°, and θ_CNNC decreases by 58°. At this stage, the reference plane for θ_BP and the dihedral θ_CNNC have increased conformational freedom due to the rearrangement, rendering both measurements geometrically meaningless. This structure remains in the ground state and undergoes further rearrangements, as shown in Fig. S3.

Conclusion

This study provides an enumeration of the mechanistic pathways for the photochemical denitrogenation of 1-methylborodiazene (bd) towards base-free 1-methylborirane (5). We employed static multiconfigurational quantum-mechanical computations, combined with quantum–mechanical nonadiabatic molecular dynamics (QM-NAMD). The static MEP calculation showed a pyramidalizing (bd-MEP-8) on the S₁-surface and optimized bd-MEP-8 to an S₁-minimum. Static calculations indicate that the S₁-MEP leads to radiative decay instead of photochemical denitrogenation. Static calculations, therefore, omit dynamical effects. As such, we used our open-source software, PyRAI²MD, to perform QM-NAMD simulations. Our QM-NAMD trajectories show that the denitrogenation reaction mainly follows a dynamically concerted mechanism (72%), involving two key geometries: partial π_NN isomerization and boron pyramidalization. Of 218 trajectories, 120 (55%) involved both, 37 (17%) had only boron pyramidalization, and 59 (27%) only partial cis-to-trans π_NN isomerization. As such, we concluded that denitrogenation can occur through either the boron pyramidalization pathway or the partial π_NN isomerization path, but the dominant pathway involves both geometries. We attribute the high prevalence of these geometries to the near-degeneracy between S₂- and S₁-states near the Franck–Condon region. The S₀ → S₁(n_N → π_NN*) and S₀ → S₂(n_N → 2p_B) transitions cause bd to undergo conformational changes, such as partial π_NN isomerization or boron pyramidalization, thereby facilitating denitrogenation. Most trajectories (71%) experience denitrogenation on the S₀ surface, while a smaller portion (29%) fully denitrogenates on the S₁ surface. We predicted quantum yields of 21% for 5 and 67% for 6.

Computational methods

Single reference methods

All density functional electronic structure methods (i.e., DFT and TD-DFT) used Gaussian 16.B01.⁹¹ We used DFT to optimize the initial ground-state global minimum of bd using the PBE0/cc-pVDZ method. We used time-dependent density functional theory (TD-DFT) to calculate the vertical excitation energies of bd using the CAM-B3LYP-GD3(BJ) and ωB97X-D functionals with the cc-pVDZ basis set. We used Gaussian 16.B01⁹¹ to run the equation of motion coupled-cluster single doubles (EOM-CCSD) with the cc-pVDZ basis set.

Multiconfigurational methods

We employed the state-average complete active space self-consistent field (SA-CASSCF) method, as implemented in OpenMolcas 19.11.⁹² This approach uses the format SA(N)-CASSCF(m,n), where N denotes the number of singlet states averaged in the calculation, while m and n denote the number of electrons and orbitals in the active space. Implementing the CASSCF method poses challenges, including appropriate active space selection and the inherent computational expense. The size of the active space is intrinsically connected to computational cost, scaling O(C(2n,m)) where n is the number of orbitals and m is the number of electrons.⁹³ To the best of our knowledge, the current maximum active space size in contemporary computing hardware is 18 electrons distributed across 18 orbitals in OpenMolcas⁹² and NWChem.^94,95

Quantum mechanical nonadiabatic molecular dynamics

To incorporate the missing dynamical effects from previous static calculations—such as vertical excitation energies, computed absorption spectra, and the minimum energy path—we performed quantum mechanical nonadiabatic molecular dynamics (QM-NAMD) simulations. We generated 700 initial conditions for production trajectories using Wigner sampling based on bd-S₀ frequencies. All computations were performed using OpenMolcas 19.11⁹² through our open-source software, PyRAI²MD.^22,23 Trajectory propagation employed our SA5-CASSCF(12,11)/cc-pVDZ electronic-structure method with the Verlet algorithm, using a 0.5 fs time step. The fewest-switches surface-hopping (FSSH) algorithm tracked nonadiabatic transitions over 1 ps, utilizing analytical nonadiabatic coupling vectors. All trajectories were launched from the S₁ surface; a trajectory was deemed complete if denitrogenation and an S₁/S₀ hop occurred, or if it reached 1 ps. Trajectories that had a maximal energy drift exceeding 0.05 a.u. were eliminated from the analysis. In total, 261 trajectories satisfied these criteria.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The ML-photodynamics simulation code is open-sourced and released at: https://github.com/mlcclab/PyRAI2MD-hiam. The complete quantum mechanical data and initial conditions can be found at: https://doi.org/10.6084/m9.figshare.29294228.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d6cp00519e.

Acknowledgements

The National Science Foundation Center under NSF-CHE-2144556 supported this work. We appreciate the assistance from the Northeastern Research Computing Team and the computing resources provided by the Massachusetts Life Science Center grant (G00006360). We dedicate this manuscript to Professor David Yarkony, who contributed 47 years to advancing theoretical chemistry and was very supportive of our research.

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