The Copper‐Catalyzed Azide–Alkyne Cycloaddition Reaction: Why Two Is Faster than One

Abstract

The copper‐catalyzed azide–alkyne cycloaddition (CuAAC) reaction is a foundational transformation in synthetic chemistry, owing to its high efficiency and selectivity. In this work, state‐of‐the‐art quantum chemical methods are applied to elucidate the preference for the dinuclear CuAAC mechanism, involving two copper centers, over the mononuclear analog, involving one copper center. Activation strain and Kohn–Sham molecular orbital analyses reveal that the enhanced reactivity of the dinuclear CuAAC mechanism arises not from alleviation of strain in the copper acetylide upon formation of the six‐membered metallacycle, as previously proposed, but rather from reduced steric Pauli repulsion between the copper acetylide and the azide. These results provide mechanistic insight into the origin of dinuclear catalysis in the CuAAC reaction.

Quantum chemical analyses uncover that the copper‐catalyzed azide–alkyne cycloaddition favors the dinuclear catalyst mechanism over the mononuclear analog due to reduced steric Pauli repulsion between the copper acetylide and the azide, rather than relief of strain in the six‐membered metallacycle.

1. Introduction

The copper‐catalyzed azide–alkyne cycloaddition (CuAAC) reaction, a pillar of click chemistry, has revolutionized synthetic methodologies across chemical and biological sciences.^{[ 1} , ² , ³ , ⁴ , ⁵ , ⁶ , ⁷ , ⁸ , ^{9 ]} First introduced by Sharpless and Meldal in 2002,^{[ 10} , ¹¹ , ^{12 ]} the CuAAC reaction enables the regioselective formation of 1,2,3‐triazoles via the copper(I)‐catalyzed coupling of an azide with an alkyne (Scheme  1 ). The reaction proceeds efficiently in aqueous or mixed solvents at room temperature without the need for harsh reagents. The efficiency and orthogonality of the CuAAC reaction facilitate its application in biological or polymeric systems, leading to widespread use in drug discovery,^{[ 13} , ¹⁴ , ¹⁵ , ¹⁶ , ^{17 ]} biomolecule labeling,^{[ 18} , ¹⁹ , ²⁰ , ^{21 ]} polymer chemistry,^{[ 22} , ²³ , ²⁴ , ²⁵ , ²⁶ , ^{27 ]} and materials science.^{[ 28} , ²⁹ , ³⁰ , ^{31 ]}

Scheme 1.

The copper‐catalyzed azide–alkyne cycloaddition (CuAAC) reaction.

A detailed insight into the catalytic mechanism of the CuAAC reaction is essential for understanding its extraordinary performance. The first proposed CuAAC mechanism, by Fokin and Sharpless, involves a mononuclear copper catalyst (Scheme  2 , left).^{[ 11} , ^{32 ]} This mechanism begins with the formation of σ‐copper(I) acetylide,^{[ 33} , ^{34 ]} followed by the coordination of the azide via its alkylated nitrogen to the copper center. Next, the first C—N bond is formed, generating a strained six‐membered copper metallacycle and formally oxidizing the copper center from +1 to +3. Subsequent reductive ring contraction forms a five‐membered copper triazolide,^{[ 35} , ^{36 ]} reducing the copper center back to +1. In the absence of other proton sources, the copper triazolide abstracts a proton from an additional alkyne to complete the triazole formation, while regenerating the σ‐copper(I) acetylide to close the catalytic cycle.

Scheme 2.

CuAAC reaction following the mononuclear copper catalyst mechanism^{[ 11} , ^{32 ]} (left) and dinuclear copper catalyst mechanism^{[ 4} , ^{36 ]} (right).

Subsequent mechanistic studies suggested the involvement of two copper(I) catalysts, leading to the proposal of a dinuclear catalytic mechanism (Scheme 2, right).^{[ 4} , ^{36 ]} In this mechanism, a second copper(I) catalyst binds to the π‐system of the σ‐copper(I) acetylide, forming a σ,π‐dicopper(I) acetylide species. The following steps mirror those in the mononuclear mechanism: azide coordination, formation of the six‐membered dinuclear copper metallacycle, reductive ring contraction to yield a dicopper triazolide, and triazole release. Kinetic experiments and theoretical studies have demonstrated that the presence of a second copper(I) catalyst lowers the reaction barrier,^{[ 37} , ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ^{44 ]} accelerating the reaction by nearly two orders of magnitude compared to the mononuclear mechanism.^{[ 45 ]} This rate enhancement is often attributed to stabilization of the σ‐copper(I) acetylide and additional stabilization of the transition state (TS) and intermediate during the formation of the six‐membered dinuclear copper metallacycle.^{[ 41} , ⁴² , ⁴³ , ^{44 ]} Additionally, Straub proposed that the formation of the mononuclear copper metallacycle is unfavorable due to the buildup of ring strain.^{[ 42 ]} The sp‐hybridized acetylide carbon favors a linear Cu=C=C fragment, which needs to be bent in the mononuclear copper metallacycle, increasing the strain in this fragment. In contrast, in the dinuclear catalytic mechanism, migration of the second copper(I) catalyst to the acetylide carbon atom induces sp² hybridization of this carbon atom. The resulting Cu—C=C fragment is more prone to bending, which decreases the associated strain in this fragment upon metallacycle formation. Despite these qualitative proposals, it remains unclear whether these rationales fully explain the rate enhancement observed for the dinuclear copper catalyst mechanism.

In this work, we perform a detailed quantum chemical study to elucidate the origin of the rate enhancement observed for the dinuclear CuAAC mechanism relative to the mononuclear mechanism. We investigate the CuAAC reaction, following both the mononuclear and dinuclear catalyst mechanisms, between propyne and methylazide catalyzed by copper(I)–1,3‐dimethylimidazol‐2‐ylidene ([Cu(I)–NHC]⁺) in tetrahydrofuran (THF) (Scheme 1), employing relativistic, dispersion‐corrected density functional theory (DFT) at COSMO(THF)‐ZORA‐BLYP‐D3(BJ)/TZ2P.^{[ 46} , ⁴⁷ , ⁴⁸ , ⁴⁹ , ⁵⁰ , ⁵¹ , ⁵² , ⁵³ , ⁵⁴ , ⁵⁵ , ⁵⁶ , ⁵⁷ , ⁵⁸ , ⁵⁹ , ^{60 ]} N‐heterocyclic carbene (NHC) ligands, such as the 1,3‐dimethylimidazol‐2‐ylidene ligand used in this work, have unique properties, which render them efficient catalysts for the CuAAC reactions.^{[ 35} , ³⁶ , ⁴⁵ , ⁶¹ , ⁶² , ^{63 ]} The activation strain model (ASM),^{[ 64} , ⁶⁵ , ^{66 ]} Kohn–Sham molecular orbital (KS‐MO),^{[ 67} , ^{68 ]} and the matching canonical energy decomposition analysis (EDA)^{[ 69} , ^{70 ]} are applied to quantitatively identify the physical factors responsible for the observed rate enhancement.

2. Results and Discussion

The Gibbs free energy reaction profiles and key TS structures for the mononuclear and dinuclear CuAAC reactions are shown in Figure  1 . Note that all stationary point structures are provided in Figure S1, Supporting Information. In agreement with previously proposed mechanisms,^{[ 4} , ¹¹ , ³² , ^{36 ]} we find that both CuAAC reactions proceed via a stepwise mechanism. Following the Gibbs free energy reaction profile, the azide coordinates through its methylated nitrogen to the σ‐copper(I) of the σ‐copper acetylide (mononuclear catalyst) or the σ,π‐dicopper(I) acetylide (dinuclear catalyst), forming a reactant complex (RC) of 7.1 kcal mol⁻¹ and 3.6 kcal mol⁻¹, respectively. Next, the first C—N bond forms via a ring‐closure TS1, resulting in the formation of the six‐membered copper metallacycle. This is the rate‐determining step for both mechanisms. The calculated barriers reveal that the mononuclear mechanism proceeds with a high barrier of 19.6 kcal mol⁻¹, whereas the dinuclear mechanism exhibits a significantly lower barrier of 12.9 kcal mol⁻¹. This difference accounts for the experimentally observed acceleration of the dinuclear CuAAC reaction.^{[ 37} , ³⁸ , ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ , ⁴⁴ , ^{45 ]} The reductive ring contraction leads to the formation of the second C—N bond and yields the five‐membered (di)copper triazolide product complex (PC) with a Gibbs free energy of −30.9 kcal mol⁻¹ and −34.4 kcal mol⁻¹ for the mononuclear and dinuclear reactions, respectively.^{[ 35} , ^{45 ]} Finally, the triazole is released, which regenerates the σ‐copper acetylide for the mononuclear catalyst and the σ,π‐dicopper(I) acetylide for the dinuclear catalyst. Thus, it is the formation of the metallacycle, and differences therein, that determine the observed rate enhancement of the dinuclear CuAAC compared to the analogous mononuclear reaction. Note that in the subsequent quantum chemical analyses, we focus on the electronic energy reaction profiles, as it is the leading energetic term and reproduces the trend in reactivity shown in the Gibbs free energy reaction profiles (Figure S2, Supporting Information).

Figure 1.

a) Gibbs free energy reaction profiles (in kcal mol⁻¹) and b) transition state (TS) structures of rate‐determining step with key geometrical data (in Å and °) of the mononuclear and dinuclear CuAAC reaction, computed at COSMO(THF)‐ZORA‐BLYP‐D3(BJ)/TZ2P.

Next, we examine the physical factors leading to the enhanced reactivity of the dinuclear CuAAC relative to the mononuclear analog, by subjecting the reaction step involving the formation of the metallacycle to more detailed quantum chemical analyses. To do so, we apply the ASM,^{[ 64} , ⁶⁵ , ^{66 ]} which decomposes the total electronic energy of the solute (ΔE _solute) into the strain (ΔE _strain) that results from deforming the reactants and the interaction (ΔE _int) between the deformed reactants (Figure  2a).^{[ 71 ]} We find that along the entire potential energy surface the CuAAC reaction involving the dinuclear catalyst engages in a more stabilizing interaction energy than the mononuclear catalyst. The strain energy, on the other hand, is nearly identical along the mononuclear and dinuclear copper catalyst pathways. This makes, in contrast to the current rationale,^{[ 41} , ⁴² , ⁴³ , ^{44 ]} the associated deformations in the interacting fragments not responsible for the mechanistic preference for the dinuclear catalyst pathway.

Figure 2.

a) Activation strain analyses, b) strain decomposition analyses, and c) energy decomposition analyses (in kcal mol⁻¹) of the mononuclear and dinuclear CuAAC, where the TSs are indicated with a dot and the energies along the IRC are projected onto the newly forming C···N bond distance, computed at ZORA‐BLYP‐D3(BJ)/TZ2P//COSMO(THF)‐ZORA‐BLYP‐D3(BJ)/TZ2P.

To understand why the total strain energies along the mono‐ and dinuclear mechanisms are similar, we further decompose the strain energies into the individual contributions from the interacting fragments (Figure 2b), that is, the azide (ΔE _strain,azide) and the (di)copper acetylide (ΔE _{strain,Cu‐acet}). As expected from the smaller N—N—N angle in the mononuclear TS and Int (Figure 1b and S1, Supporting Information), the azide following the mononuclear mechanism experiences a larger strain than in the dinuclear mechanism, that is, a more destabilizing ΔE _strain,azide. Interestingly, this is offset by a larger energetic penalty for deforming the dicopper(I) acetylide during the dinuclear mechanism, as illustrated by the fact that the ΔE _{strain,Cu‐acet} of the dicopper acetylide is more destabilizing along the dinuclear pathway than the corresponding copper(I) acetylide in the mononuclear pathway. At first glance, this appears to contradict the prevailing rationale that the dicopper acetylide should bend more easily to form the metallacycle and hence should proceed with a low strain.^{[ 42 ]} However, this rationale neglects that the formation of the dinuclear metallacycle requires migration of [Cu²(I)–NHC]⁺ (in red) to the acetylide carbon, which effectively weakens the interaction between the [Cu²(I)–NHC]⁺ and the [Cu¹(I)–NHC]–acetylide (Figure  3 ). Specifically, this interaction weakens by 3.4 kcal mol⁻¹, from −75.3 kcal mol⁻¹ in the σ,π‐dicopper acetylide (R) to the six‐membered dinuclear metallacycle (Int). Loosing this stabilizing interaction effectively counteracts the gain from easier bending and explains why the ΔE _{strain,Cu‐acet} is larger for the dinuclear mechanism compared to the mononuclear mechanism, thereby rationalizing the observed trend in overall strain energy.

Figure 3.

Strength of the interaction (in kcal mol⁻¹) between [Cu²(I)–NHC]⁺ (in red) and the [Cu¹(I)–NHC]–acetylide (in green) in the equilibrium geometry of σ,π‐dicopper(I) acetylide (R), the geometry it obtains in the ring‐closure TS1 and the six‐membered dinuclear copper metallacycle (Int), computed at ZORA‐BLYP‐D3(BJ)/TZ2P//COSMO(THF)‐ZORA‐BLYP‐D3(BJ)/TZ2P. The strength of the interaction, in square brackets, is computed by: ΔE _int = E(overall system)–E([Cu²(I)–NHC]⁺)–E([Cu¹(I)–NHC]–acetylide).

To determine the origin of the more stabilizing interaction energy of the mechanism involving the dinuclear compared to the mononuclear catalyst and hence the origin of the rate enhancement, we decompose the interaction energy using the EDA.^{[ 69} , ^{70 ]} This analysis method decomposes the ΔE _int into four energy terms that are associated with the following physical factors: quasiclassical electrostatic interaction (ΔV _elstat), Pauli repulsion (ΔE _Pauli) between closed‐shell orbitals on both reactants which is responsible for steric repulsion, stabilizing orbital interactions (ΔE _oi) that account, among others, for highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) interactions and polarization, and dispersion interactions (ΔE _disp). To our surprise, we find that it is the reduced steric repulsion that causes the dinuclear catalyst to have a more stabilizing interaction energy than the mononuclear analog (Figure 2c). In the TS region, the Pauli repulsion between the azide and dicopper acetylide (dinuclear mechanism) is less destabilizing than that between the azide and the copper acetylide (mononuclear mechanism), resulting in a lower reaction barrier for the former compared to the latter. The electrostatic, dispersion, and orbital interactions, on the other hand, are identical or, for the latter, even less stabilizing for the dinuclear compared to the mononuclear pathway. However, at early stages of the reaction, that is, in the RC region, the electrostatic interaction for the dinuclear catalyst is more stabilizing than for the mononuclear catalyst, due to the shorter distance between the methylated nitrogen of the azide and the σ‐bonded copper(I) catalyst (Figure S1, Supporting Information). Nevertheless, none of the stabilizing energy terms are responsible for the observed trend in interaction energy.

The origin of the less destabilizing Pauli repulsion for the dinuclear compared to the mononuclear catalyst upon formation of the metallacycle is further studied by performing a KS‐MO analysis, because the Pauli repulsion is proportional to the overlap of occupied orbitals on both fragments (ΔE _Pauli ∝ S ²).^{[ 67} , ^{68 ]} The key occupied fragment orbitals of the azide, mononuclear, and dinuclear catalyst that engage in the repulsive closed‐shell–closed‐shell orbital overlaps are quantified at consistent, TS‐like geometries taken from the intrinsic reaction coordinate (IRC) with a newly forming C···N bond distance of 1.94 Å (Figure  4 and Table S1, Supporting Information). For the azide, the most important fragment orbitals are its HOMO–6 and HOMO–7, which both exhibit large orbital amplitude on the terminal and methylated nitrogen atoms (Figure 4b). The participating fragment orbitals on the mononuclear and dinuclear catalysts are the HOMO–1 and HOMO, respectively, which both have predominant π‐orbital character on the copper acetylide (Figure 4b). The repulsive orbital overlap is large for the mononuclear catalyst (S = 0.11 and 0.14) and becomes smaller and hence less destabilizing for the dinuclear catalyst (S = 0.08 and 0.11).^{[ 72 ]} This reduced repulsive orbital overlap arises directly from the binding of the second [Cu(I)–NHC]⁺ to the acetylide. Due to its Lewis acidic nature, the second [Cu(I)–NHC]⁺ binds to the acetylide via a strong donor–acceptor interaction (Figure S5, Supporting Information) and hence polarizes the occupied π orbital density of the acetylide toward the second [Cu(I)–NHC]⁺ and away from the incoming azide. This polarizing effect can be seen in the shape of the participating fragment orbitals on the mononuclear and dinuclear catalyst (Figure 4b). In addition, this occupied fragment orbital size reduction can be quantified by inspecting the MO‐coefficients of the carbon 2p_z atomic orbitals on these occupied fragment orbitals, which reduce in magnitude from 0.35 and 0.45 for the mononuclear catalyst to 0.13 and 0.27 for the dinuclear catalyst. Thus, this smaller orbital lobe at the external face of the dinuclear catalyst, pointing toward the incoming azide, leads to a relatively small repulsive orbital overlap with the azide and hence a reduced Pauli repulsion compared to the mononuclear catalyst.

Figure 4.

a) Schematic molecular orbital (MO) diagram and the key closed‐shell–closed‐shell orbital overlaps between the mononuclear and dinuclear catalyst and the azide; b) most important occupied fragment orbitals of the azide, mononuclear and dinuclear catalyst (isovalue = 0.03 Bohr^−3/2), where the MO‐coefficients of the carbon 2p_z atomic orbitals on the copper acetylide, contributing to the occupied orbitals are shown. Computed on consistent, TS‐like geometries taken from the IRC with a newly forming C···N bond distance of 1.94 Å at ZORA‐BLYP‐D3(BJ)/TZ2P//COSMO(THF)‐ZORA‐BLYP‐D3(BJ)/TZ2P.

3. Conclusions

In this work, we have quantum chemically elucidated the origin of the experimentally and theoretically observed preference for the dinuclear CuAAC reaction mechanism over its mononuclear counterpart. By investigating the CuAAC reaction between propyne and methylazide catalyzed by copper(I)–1,3‐dimethylimidazol‐2‐ylidene ([Cu(I)–NHC]⁺), we show that this preference for the dinuclear mechanism arises not from alleviation of strain in the copper(I) acetylide upon forming the six‐membered metallacycle, but from a reduction in destabilizing steric Pauli repulsion between the copper(I) acetylide and the azide.

Our analysis, based on the ASM and KS‐MO theory, reveals that, following the dinuclear mechanism, coordination of a second [Cu(I)–NHC]⁺ catalyst to the copper(I) acetylide induces polarization of the π‐orbital density away from the copper acetylide. This polarization, driven by strong donor–acceptor interactions between the second [Cu(I)–NHC]⁺ catalyst and the copper(I) acetylide, minimizes the repulsive orbital overlap with the approaching azide, thereby lowering the activation barrier for the dinuclear catalyst mechanism.

The alleviation of strain in the copper(I) acetylide upon forming the six‐membered metallacycle following the dinuclear catalyst mechanism is not the reason behind the observed rate enhancement. In fact, the strain associated with deforming the dicopper(I) acetylide (dinuclear mechanism) is larger than for the copper(I) acetylide (mononuclear mechanism). This originates not from the bending flexibility of the dicopper acetylide itself, but from the loss of stabilizing Cu–acetylide interactions upon migration of the second [Cu(I)–NHC]⁺ to the acetylide carbon during metallacycle formation. These insights provide a detailed mechanistic rationale for the observed preference for the dinuclear CuAAC.

4. Theoretical Methods

4.1. Computational Details

All calculations are performed using the Amsterdam Density Functional module of the AMS software package.^{[ 46} , ⁴⁷ , ^{48 ]} The generalized gradient approximation (GGA) functional BLYP is used for the optimizations of all stationary points.^{[ 49} , ^{50 ]} The DFT‐D3(BJ) method developed by Grimme and coworkers,^{[ 51} , ^{52 ]} which contains the damping function proposed by Becke and Johnson,^{[ 53 ]} is used to describe nonlocal dispersion interactions. Relativistic effects were considered using the zeroth‐order regular approximation (ZORA).^{[ 54} , ^{55 ]} The molecular orbitals (MOs) are expanded using a large, uncontracted set of Slater‐type orbitals (STOs) containing diffuse functions. The utilized basis set, denoted TZ2P, is of triple‐ζ quality and has been augmented with two sets of polarization functions.^{[ 56 ]} This level is referred to as ZORA‐BLYP‐D3(BJ)/TZ2P and has been widely tested with several ab initio reference benchmarks up until the coupled cluster CCSD(T) and CCSDT(Q).^{[ 73} , ⁷⁴ , ⁷⁵ , ⁷⁶ , ^{77 ]} The accuracies of the fit schemes and integration grid (Becke grid) were set to VERYGOOD.^{[ 78} , ^{79 ]} Implicit THF solvation was approximated using the conductor‐like screening model (COSMO).^{[ 57} , ⁵⁸ , ⁵⁹ , ^{60 ]} Stationary points were verified through frequency analyses with zero imaginary frequencies for equilibrium geometries and one imaginary frequency for TSs, indicating a first‐order saddle point.^{[ 80 ]} The normal mode associated with the imaginary frequency of a TS was examined to ensure that its character corresponded to the appropriate reaction coordinate of interest. Potential energy surfaces were obtained by using the intrinsic reaction coordinate method,^{[ 81 ]} and were further analyzed by using the PyFrag 2019 program.^{[ 82} , ^{83 ]} Geometries were visualized with CYLview.^{[ 84 ]}

4.2. Activation Strain Model and Energy Decomposition Analysis

The ASM of chemical reactivity^{[ 64} , ⁶⁵ , ^{66 ]} is a fragment‐based approach based on the idea that the energy of a reacting system, that is, the potential energy surface, is described with respect to, and understood in terms of, the characteristics of the original reactants, which are the σ‐copper acetylide (mononuclear catalyst) or the σ,π‐dicopper(I) acetylide (dinuclear catalyst) and the azide. It considers their rigidity and the extent to which the reactants must deform during the reaction, plus their capability to interact as the reaction proceeds. First, to account for the role of solvation, the potential energy surface in solution, ΔE _solution(ζ), is decomposed into the energy of the solute, ΔE _solute(ζ), that is, the reaction system in the gas phase with solution‐phase geometry, and the solvation energy, ΔE _solvation,^{[ 85} , ^{86 ]} along the IRC, which is projected onto a reaction coordinate ζ that is critically involved in the reaction [Equation 1].

$$\Delta E_{\text{solution}}(\zeta )=\Delta E_{\text{solute}}(\zeta )+\Delta E_{\text{solvation}}(\zeta )$$ (1)

Next, we decompose the energy of the solute, ΔE _solute(ζ), into the strain and interaction energy, ΔE _strain(ζ) and ΔE _int(ζ), respectively [Equation 2].

$$\Delta E_{\text{solute}}(\zeta )=\Delta E_{\text{strain}}(\zeta )+\Delta E_{\text{int}}(\zeta )$$ (2)

In this equation, the strain energy, ΔE _strain(ζ), is the penalty that needs to be paid to deform the reactants from their equilibrium structure to the geometry they adopt during the reaction at point ζ of the reaction coordinate. On the other hand, the interaction energy, ΔE _int(ζ), accounts for all the mutual interactions that occur between the deformed fragments along the reaction coordinate.

The strain energy is further decomposed into the individual contributions from the interacting fragments [Equation 3]

$$\Delta E_{\text{strain}}(\zeta )=\Delta E_{\text{strain,azide}}(\zeta )+\Delta E_{\text{strain},\text{Cu‐acet}}(\zeta )$$ (3)

Here, ΔE _strain,azide(ζ) is the energy required for deforming the azide and ΔE _{strain,Cu‐acet}(ζ) is the energy needed to deform the (di)copper acetylide.

The interaction energy between the deformed reactants is further analyzed by means of our canonical EDA scheme.^{[ 69} , ^{70 ]} The EDA decomposes the ΔE _int(ζ) into the following four physically meaningful energy terms [Equation 4]

$$\Delta E_{\text{int}}(\zeta )=\Delta V_{\text{elstat}}(\zeta )+\Delta E_{\text{Pauli}}(\zeta )+\Delta E_{\text{oi}}(\zeta )+\Delta E_{\text{disp}}(\zeta )$$ (4)

Herein, ΔV _elstat(ζ) is the quasiclassical electrostatic interaction between the unperturbed charge distributions of the (deformed) reactants. The Pauli repulsion, ΔE _Pauli(ζ), comprises the destabilizing interaction between occupied closed‐shell orbitals of both fragments due to Pauli's exclusion principle. The orbital interactions, ΔE _oi(ζ), account, amongst others, for HOMO–LUMO interactions and polarization within reactants. Nonlocal dispersion interactions, ΔE _disp, are described using the aforementioned D3(BJ) correction.^{[ 51} , ⁵² , ^{53 ]}

Conflict of Interest

The author declares no conflict of interest.

Supporting information

Supplementary Material

Vermeeren Pascal, ChemPhysChem. 2026, 0, e202500771. 10.1002/cphc.202500771

Data Availability Statement

The data that supports the findings of this study are available within the article and its supporting material.