Retro-Cope elimination of cyclic alkynes: reactivity trends and rational design of next-generation bioorthogonal reagents

The retro-Cope elimination reaction between dimethylhydroxylamine (DMHA) and various cyclic alkynes has been quantum chemically explored using DFT at ZORA-BP86/TZ2P. The purpose of this study is to understand the role of the following three unique activation modes on the overall reactivity, that is (i) additional cycloalkyne predistortion via fused cycles, (ii) exocyclic heteroatom substitution on the cycloalkyne, and (iii) endocyclic heteroatom substitution on the cycloalkyne. Trends in reactivity are analyzed and explained by using the activation strain model (ASM) of chemical reactivity. Based on our newly formulated design principles, we constructed a priori a suite of novel bioorthogonal reagents that are highly reactive towards the retro-Cope elimination reaction with DMHA. Our findings offer valuable insights into the design principles for highly reactive bioorthogonal reagents in chemical synthesis.


Introduction
Bioorthogonal chemistry has emerged as a powerful tool for studying and manipulating biological systems. 1 Bioorthogonal reactions are biocompatible and robust, go with fast reaction rate constants, and do not interfere or react with the native biological environment.Bioorthogonal reagents that meet these requirements enable the probing of biological processes by labeling and imaging target molecules, both in vitro and in vivo. 2 Common biorthogonal reactions are the tetrazine-based inverse electron demand Diels-Alder (IED-DA), 3 traceless Staudinger ligation reactions, 4 and 1,3-dipolar cycloadditions 5 such as copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC).Bertozzi and co-workers developed the strain-promoted azidealkyne cycloaddition reaction (SPAAC) as a selective biorthogonal chemical reaction. 6The eld continues to ourish with the development of several novel bioorthogonal reactions, including strain-promoted alkyne-nitrone cycloadditions (SPANC), 7 isonitrile-based [4 + 1] cycloadditions, 8 and photoactivated tetrazole ligations. 9ecently, Kang et al. presented the retro-Cope elimination reaction (hydroamination of cyclic cyclooctyne) between functionalized (cyclic) alkynes and N,N-dialkylhydroxylamines as a novel bioorthogonal reaction (Scheme 1a). 10 The calculated Gibbs free energy activation barrier at M06-2X/6-311G(2d,p)// M06-2X/6-31G (d,p) for the parent cyclooctyne was determined to be 18.9 kcal mol −1 , which is adequate for the reaction to proceed at room temperature.Experimentally, the retro-Cope elimination reaction between the non-substituted cyclooctyne (COT) and hydroxylamine in CD 3 CN at room temperature shows second-order rate constants of 3.25 × 10 −2 M −1 s −1 , an order of magnitude higher than the strain-promoted azide-alkyne cycloaddition (SPAAC) reaction with benzyl azide.10a,11 Notably, the retro-Cope elimination reaction is highly regioselective when the COT is substituted with electronegative heteroatoms at the propargylic position.Furthermore, Kang et al. showcased the retro-Cope elimination reaction in an in vitro study and demonstrated mutual orthogonality in conjunction with the inverse electron demand Diels Alder (IED-DA) reaction between tetrazine and strained alkenes.10a,12 In doing so, they nicely underscored the potential of this reaction to be applied in mutually orthogonal bioorthogonal chemistry.
Decorated cyclooctynes have emerged as functional bioorthogonal reagents in 1,3-dipolar cycloadditions.5e,13 Similarly, these cyclic alkynes show high reactivity and selectivity towards the retro-Cope elimination reaction.10a Kim and co-workers 10a reported only a minor reactivity enhancement aer the introduction of additional strain by three-membered ring fusion in bicyclo[6.1.0]nonyne(BCN), in contrast to a drastic two-order magnitude increase in the second-order rate constants observed for the SPAAC reaction reported by Dommerholt et al. 14 The authors described further enhanced reactivity upon adding electronegative substituents on the exocyclic propargylic position, achieving up to three orders of magnitude increase in the second-order rate constants (Scheme 2).16a Interestingly, upon the addition of electronegative substituents on the propargylic position, they found that the lowering of the activation barrier was not caused by a less favorable interaction term but, rather, driven by the lowering of the strain energy for both fragments.They further attribute this to a shi of the transition state towards the reactants in accordance with the Hammond postulate.
We have computationally investigated the concerted retro-Cope elimination reaction between dimethylhydroxylamine (DMHA) and cyclic alkynes at ZORA-BP86/TZ2P (Scheme 2).Three sets of cyclooctynes were studied.The rst set includes cyclic alkynes with increased predistortion due to the introduction of cyclic functionality (DIBO and BCN).The second and third sets consist of cycloalkynes modied at the exocyclic (HO-COT and DIFO) and endocyclic (N-COT, O-COT, and S-COT) propargylic position, respectively.The anti-pathways (dimethyl groups and propargylic substituent on opposite sides) and the syn-pathways (dimethyl groups and propargylic substituent on the same side) were investigated.To gain insight into the physical factors that control the reactivity, the activation strain model (ASM) 16 of reactivity in conjunction with the matching energy decomposition analysis (EDA) and quantitative Kohn-Sham molecular orbital (KS-MO) 17 theory analysis.Based on our found rational design principles, we constructed a priori a suite of novel bioorthogonal reagents that are highly reactive towards the retro-Cope elimination reaction with DMHA.

Computational details
All calculations were performed with the AMS2021 program (an example input le is provided in the ESI †). 18Aer a conformational search using Grimme's CREST 2. 12 (ref.19) using default settings in the gas phase, all geometries and energies were computed using the generalized gradient approximation (GGA) functional BP86, 20 and the MOs were expanded using a large uncontracted set of Slater-type orbitals (STO): TZ2P. 21Our benchmarks 22a,b and numerous DFT studies 22c-g support the use of this method to compute trends in reactivity for similar reactions.The trends in reactivity remain the same in implicit solvent (COSMO(acetonitrile)-BP86/TZ2P//BP86/TZ2P).Additionally, the trends were successfully reproduced with dispersion corrections (BP86-D3(BJ)/TZ2P//BP86/TZ2P), and at M06-2X/TZ2P//BP86/TZ2P, and DLPNO-CCSD(T)/def2-QZVPP//BP86/ TZ2P (Table S3 †).The zeroth order approximation (ZORA) accounted for the scalar relativistic effects. 23The accuracies of the t scheme (Zlm t) 24a and the integration grid (Becke grid) 24b were set to VERYGOOD.The convergence criteria for the SCF and geometry optimization procedures were set to 10 −5 hartree.Frequency calculations were performed to characterize the nature of stationary points where local minima had real frequencies while transition structures had a single imaginary frequency.The steepest descent path from the TS was calculated using the intrinsic reaction coordinate (IRC) method, 25 which follows the transition vector (the vibrational normal mode associated with the reaction and with a negative force constant) from the transition structure toward the reactants and product and was analyzed with the aid of the PyFrag 2019. 26All structures were visualized using CYLview. 27tivation strain model and energy decomposition analysis Quantitative analyses of the activation barriers associated with the studied reactions were obtained using the activation strain model (ASM) of reactivity. 16The PES, that is, DE(z), was decomposed into the strain energy, DE strain (z), and interaction energy, DE int (z) [eqn (1)].All energy terms were projected onto the length of the forming C/H bond, which undergoes a well-dened change during the reaction.Other reaction coordinates, such as the length of the C/N bond or C/C stretch, were shown to provide the same general conclusions. 28 The DE strain (z) is associated with the rigidity and the structural deformation of the reactants from their equilibrium structure to the geometry they adopt at the coordinate of z during the reaction.The DE int (z) is related to the electronic structure of the reactants and their spatial orientation and represents the mutual interactions between the deformed reactants.
To obtain a deeper insight into the physical mechanism behind DE int (z), we employed our canonical energy decomposition analysis (EDA), 17 which decomposes the DE int between the deformed reactants, within the framework of Kohn-Sham MO theory, into three physically meaningful terms [eqn (2)].
The electrostatic interaction, DV elstat (z), corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the deformed reactants.The Pauli repulsion, DE Pauli (z), comprises the Pauli-repulsive orbital interactions between closed-shell orbitals.The term DE oi (z) represents the stabilizing orbital interactions, such as charge transfer, namely, the interactions between the occupied orbitals of one reactant and the unoccupied orbitals of the other reactant, and polarization, that is, the occupied-unoccupied orbital mixing within one reactant due to the presence of the other reactant.

Voronoi deformation density analysis
The electron density distribution is analyzed using the Voronoi deformation density (VDD) method 29 for computing atomic charges.The VDD atomic charge on atom A (Q VDD A ) is computed as the (numerical) integral of the deformation density in the volume of the Voronoi cell of atom A (eqn (3)).The Voronoi cell of atom A is dened as the compartment of space bounded by the bond midplanes on and perpendicular to all bond axes between nucleus A and its neighboring nuclei.
Here, r(r) is the electron density of the molecule, and is the superposition of atomic densities r B of a ctitious promolecule without chemical interactions that is associated with the situation in which all atoms are neutral.The interpretation of the VDD charge Q VDD A is rather straightforward and transparent: instead of measuring the amount of charge associated with a particular atom A,

Cyclic alkynes
First, we discuss the effect of the bending of the alkyne, or alkyne predistortion, on the retro-Cope elimination reactivity by comparison of the linear 2-butyne and cyclooctyne (COT).The computed electronic activation energies (DE ‡ ) and reaction energies (DE rxn ) associated with the retro-Cope elimination reaction between these reactants and dimethylhydroxylamine (DMHA) are provided in Table 1.The electronic activation barrier is signicantly lowered from 15.8 kcal mol −1 to 4.6 kcal mol −1 (Table 1) going from 2-butyne to COT.
To identify the physical factors leading to the enhanced retro-Cope elimination reactivity of the strained alkynes relative to the linear 2-butyne, the activation strain model (ASM) of reactivity is applied (Fig. 1a).We nd that predistortion of the alkyne in COT serves to enhance retro-Cope elimination reactivity via (1) reducing the activation strain and (2) enhancing the overall interaction energy via more stabilizing orbital interactions.Kim et al. also observed a notable reduction in the activation strain of the retro-Cope elimination reaction with COT. 10 Relative to its linear counterpart, the strain in COT is reduced by approximately 10 kcal mol −1 at a consistent geometry, where the lengths of the C/H bond are 1.45 Å, and the slope of the strain in the alkyne fragment is smaller along the reaction coordinate.By partitioning the strain energy in terms of the two fragments (Fig. 1b), we conrm that the strain is lowered for the COT fragment, due to the alkyne predistortion in the COT reagent.To understand the origin of this effect, further analysis of both equilibrium geometry and consistent geometry (Fig. 1c  and d) reveals that the reaction of predistorted alkyne, COT, simply requires less bending of the alkyne to react with DMHA.
In addition, we show how predistortion of COT also acts to enhance the stabilizing interaction energy with DMHA (Fig. 1a).Using our EDA, we could pinpoint the enhanced interaction energy originates from signicantly more stabilizing orbital interactions (Fig. S3b †).The predistortion of the alkyne results in a stabilization of the LUMO and a slight destabilization of the HOMO. 30The lowering of the LUMO, is caused by the in-phase mixing of the s* and p* orbitals, resulting in a smaller p*-LUMO COT and HOMO DMHA energy gap.

Cyclic alkynes with additional predistortion
Next, we compare the reactivity of our parent COT with two popular bioorthogonal cyclic alkynes reagents in 1,3-dipolar cycloaddition reactions 5 dibenzocyclooctyne (DIBO) 31 and bicyclononyne (BCN) 14 that feature additional alkyne predistortion (:C-C-C) from the presence of fused carbocycles (154.7°and154.5°relative to 157.6°for COT in the optimized reactants (Fig. S1 †)).The computed electronic activation energies (DE ‡ ) and reaction energies (DE rxn ) associated with the retro-Cope elimination reaction between these reactants and dimethylhydroxylamine (DMHA) are shown in Table 2. Our calculations show that the activation barrier for the retro-Cope elimination reaction with DMHA decreases from 4.6 to 4.1 to 2.1 kcal mol −1 , as going from COT to DIBO to BCN.
The physical factors leading to the enhanced retro-Cope elimination reactivity of DIBO and BCN compared to COT are next analyzed using the ASM.In Fig. 2b, the ASM diagram shows that the retro-Cope elimination reaction of DIBO benets from signicantly less destabilizing strain energy (DE strain ), as compared to COT.The retro-Cope elimination reaction of BCN with DMHA also benets from less destabilizing strain but is paralleled by a more stabilizing interaction energy (DE int ), as compared to COT (Fig. 2b).Decomposition of the strain energies reveals that DIBO benets a reduced strain in both the DIBO and DMHA fragments, whereas the reduced strain for BCN at consistent geometry originates solely from the BCN fragment (Fig. 2d).Our structural analyses at the equilibrium geometry show that DIBO and BCN both have a more predistorted backbone than the parent COT (157.6°) in the equilibrium geometry, with internal C-C^C alkyne bond angles of 154.7°and 154.6°, respectively.This predistortion results in a structurally less distorted alkyne fragment at consistent geometry (Fig. 2d), and, consequently, reduced activation strain.For DIBO, the lowering of the activation strain is more pronounced because also the O/H bond breaking distance and compression of the H-O-N angle are less progressed, which causes the strain of the DMHA fragment to be shied to the right (Fig. 2a).As will be explained in more detail later on, this can be traced back to a more slanted reaction path, that is, the C/N bond is formed later than the C/H bond for DIBO (Dr = 0.76 Å, where Dr is the difference in length between the C/N and C/H bonds at the consistent geometry) than for COT (Dr = 0.67 Å).
Hamlin and coworkers have shown that, in addition to the reduction of the destabilizing strain, a more stabilizing interaction energy is at the root of the enhanced reactivity in 1,3dipolar cycloaddition between azides and strained alkynes (SPAAC). 30Energy decomposition analyses in conjunction with KS-MO analyses illustrated that the bending of alkynes has a profound effect on the frontier molecular orbitals (FMOs), i.e., the LUMO ðp * in-plane Þ is stabilized and the HOMO (p in-plane ) is slightly destabilized because of mixing with the adjacent s*and s-orbitals, respectively.Thus, a more bent alkyne has a lower LUMO alkyne , giving rise to a smaller HOMO DMHA -LUMO COT gap.Therefore, the reaction of BCN, which has a 3.0°s maller internal C-C^C angle at equilibrium geometry, goes with a smaller initial HOMO DMHA -LUMO BCN gap than the reaction of COT (Fig. 3).It must be noted that, with the exception of DIBO, the p * in-plane -LUMO-lowering along the reaction coordinate (the slope), relative to the energy at equilibrium geometry, is approximately equal (Fig. S4d †).As for BCN the Dr remains equal, this leads to a larger S 2 /D3 term, i.e., the more favorable HOMO DMHA -LUMO BCN interaction and, consequently, more stabilizing orbital interactions associated with the retro-Cope elimination reaction between BCN and DMHA.
Despite DIBO having a lower p * in-plane -LUMO energy than COT, the overall orbital interactions for the DIBO reaction are less stabilizing (Fig. 3).This can be rationalized by the reduced HOMO DMHA -LUMO DIBO orbital overlap brought about by the C/N bond formation distance in the reaction of DIBO (Dr = 0.76 Å) lagging substantially behind that of COT (Dr = 0.67 Å).This geometric effect also brings about considerably less destabilizing Pauli repulsion.At a double consistent geometry (Table S4 †), where Dr is equal to that of COT at consistent geometry (Dr = 0.67 Å), the Pauli repulsion exceeds the more stabilizing orbital and electrostatic interaction.This is due to the overlap of various lled in-plane orbitals of the DMHA fragment overlapping with the HOMO−4, HOMO−2 and, HOMO−1 of DIBO (Fig. S7 †).It is the buildup of this Pauli repulsion that is effectively absorbed into the reaction path causing the more slanted reaction path (higher Dr).As a result, the Pauli repulsion is lowered, and, concomitantly, the orbital overlaps between the two fragments are reduced, also decreasing the HOMO DMHA -LUMO DIBO overlap.Similar to the retro-Cope elimination reaction with linear alkynes with added steric bulk, 28 the Pauli lowering effect originates in more (not less) steric repulsion introduced by the fused aryls in DIBO.
We observe that the additional repulsive interaction occurs between the various in-plane orbitals of DMHA and the HOMO−1, HOMO−2, and HOMO−4 orbitals in DIBO.In contrast, the literature attributes this repulsive effect to "agpole" hydrogens.6d,32 At double consistent geometry, the occupied-occupied orbital overlaps that actually increase are not in the vicinity of the "agpole" hydrogen atoms.Instead, the three orbitals are combinations of the p in-plane -HOMO of COT and the p-HOMOs of the benzene substituents.The p in-plane -HOMO of COT is allowed to mix with the p-system benzene substituents due to the twisted nature of DIBO (Fig. S7 †).
Thus, although the introduction of fused benzenes causes a substantially smaller HOMO DMHA -LUMO DIBO gap (Fig. 3), the more stabilizing orbital interaction are hampered by lowered HOMO DMHA -LUMO DIBO overlaps, due to the C/N bond forming distance in DIBO lagging behind that of COT.The greater C/N bond forming distance can be traced back to the increased two-center four-electron Pauli repulsion, which is absorbed into the geometry of the reaction system by forcing it into a slanted reaction path.As a result, the overlap between the lled FMOs decreases, ultimately reducing Pauli repulsion, which outweighs the concurrent decrease in stabilizing orbital and electrostatic interactions.The smaller HOMO DMHA -LUMO DIBO gap in DIBO, together with the introduction of additional HOMO-LUMO interactions, limit the destabilization by the additional in-plane steric bulk between the two fragments.
Considering that orbital interactions play a key role in the enhanced reactivity of DIBO and BCN compared to COT, we performed an additional analysis on the key p*-LUMO in-plane that engages with the p-HOMO DHMA .We sought to determine the factors that lead to the observed lowering of the p*-LUMO in- plane orbital energies of DIBO and BCN relative to COT.To do so, we constrained COT in the equilibrium geometries of the respective substituted cyclic alkynes and reported the p-HOMO in-plane and p*-LUMO in-plane orbital energies in Fig. S4c.† The root of the p*-LUMO in-plane -lowering in the equilibrium geometry was further analyzed by decomposing the change in orbital energy, D3 MO , into substituent, D3 sub , and bending, D3 deform , contributions, which were dened as (Fig. S4a and b †): D3 MO,predist = 3 MO (COT constrained ) − 3 MO (COT eq ) (5) At the equilibrium geometry, the p*-LUMO in-plane -lowering of BCN is primarily caused by the additional bending of the alkyne enforced by the fused cyclopropane (0.14 eV (79%)) and only lowered by 0.04 eV (21%) because of the addition of the fused cyclopropane to the deformed cyclooctyne.In contrast, the p*-LUMO in-plane -lowering in DIBO primarily nds its origin in substituent effects instead of the additional bending of the alkyne.In equilibrium geometry, DIBO is stabilized by the bending of the alkyne enforced by the more rigid cyclic backbone by only 0.24 eV (23%), whereas the substitution by the dibenzo-substituents accounts for a stabilization of 0.78 eV (77%).
Table 2 Transition state structures for the retro-Cope elimination reactions, Dr in the transition state (in Å), electronic energies relative to reactants of the reactant complex DE RC (in kcal mol −1 ), transition state DE ‡ (in kcal mol −1 ), product DE rxn (in kcal mol −1 ), Gibbs free energies of activation DG ‡ (in kcal mol −1 ) and the second-order rate constants relative to COT, k rel , for retro-Cope elimination reactions of Additionally, the p*-LUMO in-plane orbital energies along the reaction coordinate associated with the retro-Cope elimination reaction are shown in Fig. S4d.† The orbital energy proles of the p*-LUMO in-plane orbitals look alike with similar steepness along the reaction coordinate and differ primarily in the p*-LUMO in-plane orbital energy in the equilibrium geometry.DIBO stands out in that the steepness is lower, i.e., the rigid DIBO is less affected by deformation of the alkyne along the reaction coordinate.This is likely due to the smaller angle deformation needed for consistent geometry (Fig. 2a), resulting from the more slanted reaction path (larger Dr).

Effect of exocyclic propargylic substitution
Next, we discuss the modulation of COT at the exocyclic propargylic position.We studied the effect of appending a hydroxy group (HO-COT) and diuoro group (DIFO) at the exocyclic propargylic position of COT.Cyclooctynes activated by exocyclic propargylic substitution prefer the anti-Markovnikov adduct (anti-pathway) over the Markovnikov adduct (syn-pathway) in the retro-Cope elimination reaction with DMHA (Tables S1 and  S2 †), as such, we focus on the retro-Cope elimination reaction along the anti-pathways.The relative electronic energies for the reactant complex (DE RC ), activation barriers (DE ‡ ), and the reaction energies (DE rxn ) for cyclooctynes substituted on the exocyclic propargylic position towards the retro-Cope elimination reaction along the anti-pathway are shown in Table 3. Replacing the exocyclic propargylic hydrogen with the more electronegative HO-COT and DIFO lowers the activation barrier from 4.6 to 2.3 and 0.2 kcal mol −1 , respectively.
Kang et al. suggested that the reaction does not benet from a more stabilizing interaction energy upon the addition of electronegative substituents but, rather, from a decrease in strain energy.10a Our analysis at the transition states also furnishes the same insight.However, performing our activation strain and energy decomposition analyses along the full reaction coordinate provides us with a more comprehensive picture of the factors dictating the reactivity.22a In Fig. 4a, the ASM diagram reveals that, at consistent geometry, the activation strain follows a trend opposite to the activation barriers.This would indicate, at odds with Kang et al. 10a that the strain is not responsible for observed rate enhancements, but instead it is the progressively more stabilizing interaction energy going from COT to HO-COT to DIFO that is key for the enhanced reactivity.Because the HO-COT and DIFO benet from more stabilizing interaction energy, the transition states shi to an early point on the reaction coordinate towards the reactants.This, in turn, causes the reactants to be less structurally deformed in their respective TSs.
Our energy decomposition analyses (EDA) (Fig. 4b) show that the more stabilizing DE int term associated with the retro-Cope elimination reactions of HO-COT and DIFO arises from To determine the origin of the enhanced orbital interactions, we quantied all donor-acceptor orbital interactions associated with the retro-Cope elimination reaction of COT, HO-COT, and DIFO at consistent geometry where C/H bond forming distance is 1.60 Å and conrmed the HOMO DMHA -LUMO X-COT interaction as the most important contributor (Fig. S8 †).Further KS-MO analyses reveal that the enhanced orbital interactions of HO-COT and DIFO compared to COT originate in their lowered LUMOs and a slightly more efficient orbital overlap.Especially the former brings about a larger orbital interaction term (fS 2 /D3 term) as the energy gap reduces from 3.5 to 2.8 to 2.4 eV going from COT to HO-COT to DIFO (Fig. 5).
The origin of the p*-LUMO in-plane -lowering in the equilibrium geometry was further analyzed by decomposing the change in orbital energy into, D3 p*-LUMO , into substituent, D3 sub , and bending, D3 bend , contributions.We conrmed that the LUMOlowering effect principally stems from the substituent effect and not the deformation of the alkyne (Fig. S4c †).

Effect of endocyclic propargylic substitution
Lastly, we analyzed the reactivity of a group of endocyclic heterocyclooctynes (Y-COT) toward the retro-Cope elimination reaction with DMHA.We substitute the endocyclic propargylic carbon with the nitrogen (N-COT), oxygen (O-COT), and sulfur (S-COT).Analogous to the cyclooctynes activated by exocyclic propargylic substitution (Tables S1 and S2 †), we nd that the cyclooctynes activated by endocyclic propargylic substitution prefer the anti-Markovnikov adduct (anti-pathway) over the Markovnikov adduct (syn-pathway) in the retro-Cope elimination reaction with DMHA (Tables S1 and S2 †).Therefore, we center our analysis on the retro-Cope elimination reaction along the anti-pathways.Table 4 presents the relative electronic energies for the reactant complex (DE RC ), activation barriers (DE ‡ ), and the reaction energies (DE rxn ) for Y-COT cyclooctynes towards the retro-Cope elimination reaction along the antipathway.Replacing the endocyclic propargylic carbon COT with the more electronegative N-COT and O-COT lowers the activation barrier from 4.6 kcal mol −1 to 2.9 and 1.1 kcal mol −1 , respectively.Incorporation of a sulfur heteroatom (S-COT) at the endocyclic propargylic position raises the activation barrier to 5.9 kcal mol −1 .
To gain a quantitative understanding of the physical factors that are at the root of the trends in reactivity, we again turned to ASM.In Fig. 6a, the activation strain diagram highlights that the reduction in activation barrier height from COT to N-COT to O-COT cyclooctyne is driven by an increasingly stabilizing DE int term.Despite observing a more favorable interaction energy for the S-COT cyclooctyne at consistent geometry, this is offset by the considerable increase in activation strain (Fig. S9 †).The  larger atomic radius of the sulfur relative to oxygen allows the alkyne to be less bent i.e., less predistorted, and consequently, a greater structural deformation of the D:(C-C^C) is necessary at consistent geometry (Table S6 †).Consequently, the reduced reactivity of S-COT towards the retro-Cope elimination reaction is attributed to the higher activation strain.
Our canonical EDA analyses (Fig. 6b) reveal that the more stabilizing DE oi is responsible for the progressively more stabilizing DE int term associated with the retro-Cope elimination reaction going from COT to N-COT to O-COT.The differences in the DV elstat curves are minimal, whereas the DE Pauli shows a reverse trend to that of DE int and is, thus, not responsible for the more stabilizing interaction energy.
As the more stabilizing orbital interactions were identied as a key factor that dictated the enhanced reactivity of Y-COT, we screened all orbital donor-acceptor interactions associated with the retro-Cope elimination reactions of COT, N-COT, and O-COT at consistent geometry where the length of the forming  C/H bond is 1.56 Å (Fig. S10 †).The HOMO DMHA -LUMO Y-COT interaction was conrmed as the most important contributor.
The KS-MO analyses at the consistent geometries reveal that it is the consistent lowering of the p*-LUMO alkyne of the Y-COT cyclooctyne that causes the more favorable orbital interactions between HOMO DMHA and LUMO Y-COT (Fig. 7).Because of the lowering of the p * in-plane -LUMO Y-COT ; the HOMO DMHA -LUMO Y- COT energy gap is reduced from D3 = 2.6 to 2.4 to 2.1 eV.The orbital overlap is minimally affected by substitution on the endocyclic propargylic position.As the changes in orbital overlaps remain limited, we can conclude that the enhanced orbital interactions of N-COT and O-COT in retro-Cope elimination reactions can directly be ascribed to the LUMO Y-COTlowering effect of the endocyclic propargylic substitution, which causes the smaller HOMO DMHA -LUMO Y-COT energy gaps.

Next-generation bioorthogonal reagents
Next, with our new design principles in hand, we sought to generate a suite of novel reagents that exhibit enhanced retro-Cope reactivity relative to current state-of-the-art reagents.Firstly, we propose the judicious combination of rigid cyclic substituents in tandem with both endo-and exocyclic heteroatoms.Based on this, we present 3,3-diuoro-BCN (DF-BCN) and a cyclooctyne annulated with single aryl substituent combined with diuoro and oxide substituents on the exo-and endocyclic propargylic position, respectively (DF-O-MOBO).Based on our computations, we predict a that the reactivity is further enhanced (relative to COT) by DDE ‡ = 6.1 and 5.2 with k rel values of 2.6 × 10 3 and 5.2 × 10 2 , respectively.Fusion of aryl groups on the carbons 5 and 6 of the cyclooctyne with diuorosubstituents on the exocyclic propargylic position (DF-p-MOBO) furnished a reagent with a remarkable k rel value of 4.7 × 10 4 .32b Additionally, substitution by chloro (DCl-BCN, DF-p-MOBO) and triuoromethyl (DCF 3 -BCN, DCF 3 -p-MOBO) substituents enhanced the k rel values up to four orders of magnitude.

Conclusions
Our theoretical study reveals that the retro-Cope elimination reaction between dimethylhydroxylamine (DMHA) and cyclic alkynes can be accelerated by judicious functionalization of the alkyne.We explored three distinct activation modes, (i) additional predistortion of the alkyne by fused cycles and decorating the cycloalkyne with (ii) exocyclic heteroatom substituents, and (iii) endocyclic heteroatom substitution on the cycloalkyne.Our design principles and judicious combination of these activation modes were used to rationally design a suite of novel bioorthogonal reagents that feature second-order rate constants that outperform all other current reagents in these retro-Cope elimination reactions.
Our activation strain and Kohn-Sham molecular orbital analyses identied the enhanced retro-Cope elimination reactivity upon predistortion of the alkyne (linear to cyclic) arises from a reduction in activation strain and a strengthening of stabilizing orbital interactions.Predistortion of the alkyne via cyclization induces a stabilization of the propyne p*-LUMO alkyne , which results in a smaller, more favorable HOMO DMHA -LUMO alkyne gap and thus more stabilizing inverse electron demand (IED) orbital interactions.Appending the COT with fused cycles imparts additional predistortion of the alkyne, leading to even less activation strain and even more stabilizing IED orbital interactions.Decorating COT with exo-and endocyclic heteroatom substituents also stabilizes the p*-LUMO alkyne , and consequently further enhances the stabilizing IED orbital interactions.
A secondary effect is observed in the case of DIBO, a dibenzoannulated cyclooctyne, which exhibits a more pronounced decrease in the activation strain that occurs at the consistent geometry, that is, a consistent point along the reaction coordinate (r(C/H)), relative to BCN (bicyclononyne).This can be related to the more slanted reaction path, where the formation of the C/N bond lags behind that of the C/H bond because of the following: Due to the twisted nature of DIBO, the p in-plane -HOMO of COT mixes in with the p-system of the benzene substituents, heightening the steric Pauli repulsion.The strong repulsive interaction is absorbed by adapting the reaction system to a more slanted reaction path.As a consequence, the overlaps are reduced, thereby lowering both the repulsive Pauli repulsion and the favorable orbital interactions.Notably, because of this more slanted reaction path, both reactants are less distorted at consistent geometry, causing a more pronounced decrease in the activation strain.
Our rational design principles allowed us to construct a priori a suite of novel bioorthogonal reagents that are highly reactive towards the retro-Cope elimination reaction with DMHA.Based on the judicious substitution of the parent COT, our novel reagents exhibit reactivities that are two to four orders of magnitude greater than COT.
Scheme 1 (a) The retro-Cope elimination reactions between cyclic alkynes or alkenes and hydroxylamines.(b)Effects of modifying cyclic octynes on the reactivity in the retro-Cope elimination reaction with diethylhydroxylamine. 10a a The second-order rate constants were determined for a 1 : 1 ratio of the reactants in CD 3 CN at room temperature using NMR spectroscopy. 1 b The relative second-order rate constants (k rel ) were calculated relative to the parent cyclooctyne, COT (k rel = k/k COT ).

Fig. 1
Fig. 1 (a) Activation strain model and (b) decomposition of strain energies for the retro-Cope elimination reactions of 2-butyne and COT with DMHA.Transition states are indicated by dots.The energy terms along the IRC are projected on the length of the newly forming C/H bond and the vertical dotted line indicates the point at which the length of the C/H bond is 1.45 Å. (c) Structural information (in Å and deg.) associated with the retro-Cope elimination reactions of propyne and COT with DMHA along anti-pathways and (d) changes in key angles and bond distances from equilibrium geometries to consistent geometries where the lengths of the C/H bond are 1.45 Å.All were computed at ZORA-BP86/TZ2P.

Fig. 2
Fig. 2 (a) Activation strain diagram, (b) energy decomposition analyses and (c) decomposition of strain energies for the retro-Cope elimination reactions of cyclooctyne (COT), dibenzocyclooctyne (DIBO), and bicyclononyne (BCN) with dimethylhydroxylamine (DMHA) along the antipathways.Transition states are indicated by dots.The energy terms along the IRC are projected on the length of the newly forming C/H bond and the vertical dotted line indicates the point at which the length of the C/H bond is 1.50 Å.(d) Structural information and (e) geometrical changes (in Å and deg.) for the retro-Cope elimination reactions of COT, DIBO, and BCN with DMHA along the anti-pathways at equilibrium geometries and consistent geometries where the lengths of the C/H bond are 1.50 Å.

Fig. 3 a
Fig. 3 Schematic diagrams with LUMO energies, energy gaps D3, overlaps S, and values of S 2 /D3 term associated with the key donoracceptor interaction between HOMO DHMA jLUMO alkyne along with the retro-Cope elimination reactions between cyclooctyne (COT), DIBO and BCN with DMHA.All were computed at the consistent geometries where the length of the C/H bond is 1.50 Å at ZORA-BP86/TZ2P.

Fig. 4
Fig. 4 (a) Activation strain and (b) energy decomposition analyses for the retro-Cope elimination reactions of COT, HO-COT, and DIFO with DHMA along anti-pathways.Transition states are indicated by dots.The energy terms along the IRC are projected on the length of the newly forming C/H bond and the vertical dotted line indicates the point at which the length of C/H bond is 1.60 Å. Computed at ZORA-BP86/TZ2P.

Fig. 5
Fig. 5 Schematic diagrams with LUMO energies, energy gaps D3, overlaps S, and values of 10 3 × S 2 /D3 term associated with the key donor-acceptor interaction between HOMO DHMA -LUMO X-COT along with the retro-Cope elimination reactions between COT, HO-COT, and DIFO with DMHA.All were computed at the consistent geometries where the length of the C/H bond is 1.60 Å at ZORA-BP86/TZ2P.

Table 4 a
Transition state structures for the retro-Cope elimination reactions, Dr in the transition state (in Å), electronic energies relative to reactants of the reactant complex DE RC (in kcal mol −1 ), transition state DE ‡ (in kcal mol −1 ), product DE rxn (in kcal mol −1 ), Gibbs free energies of activation DG ‡ (in kcal mol −1 ) and the second-order rate constants relative to COT, k rel , for retro-Cope elimination reactions of Y-COT with DMHA along anti-pathways a Computed at ZORA-BP86/TZ2P.b Dr is the difference in length between the forming C/N and C/H bonds at the transition state.cThe relative second-order rate constants (k rel ) were calculated relative to COT (k/k COT ).Only the anti-pathway was considered.

Fig. 6
Fig. 6 (a) Activation strain diagram and (b) energy decomposition analyses for the retro-Cope elimination reactions of the COT, N-COT, and O-COT with DHMA along anti-pathways.Transition states are indicated by dots.The energy terms along the IRC are projected on the length of the newly forming C/H bond and the vertical dotted line indicates the point at which the length of C/H bond is 1.56 Å. Computed at ZORA-BP86/ TZ2P.

Fig. 7
Fig. 7 (a) Schematic orbital-interaction diagrams with energy gaps D3, overlaps S, values of 10 3 × S 2 /D3 of the individual HOMO DHMA and LUMO alkyne interactions associated with the retro-Cope elimination reactions between DMHA and the original cyclooctyne COT, N-COT and O-COT.All were computed at the consistent geometries where the length of the C/H bond is 1.56 Å at ZORA-BP86/TZ2P.

Table 1
Transition state structures for the retro-Cope elimination reactions, Dr in the transition state (in Å), electronic energies relative to reactants of the reactant complex DE RC (in kcal mol −1 ), transition state DE ‡ (in kcal mol −1 ), product DE rxn (in kcal mol −1 ), Gibbs free energies of activation DG ‡ (in kcal mol −1 ) and the second-order rate constants relative to COT, k rel , for retro-Cope elimination reactions of 2-butyne and COT with DMHA a c 1.2 × 10 −8 1.0 a Computed at ZORA-BP86/TZ2P.bDr is the difference in length between the forming C/N and C/H bonds at the transition state.cTherelative second-order rate constants (k rel ) were calculated relative to the COT (k/k COT ).
COT, DIBO, and BCN with DMHA a