Factors Controlling the Diels–Alder Reactivity of Hetero‐1,3‐Butadienes

Abstract We have quantum chemically explored the Diels–Alder reactivities of a systematic series of hetero‐1,3‐butadienes with ethylene by using density functional theory at the BP86/TZ2P level. Activation strain analyses provided physical insight into the factors controlling the relative cycloaddition reactivity of aza‐ and oxa‐1,3‐butadienes. We find that dienes with a terminal heteroatom, such as 2‐propen‐1‐imine (NCCC) or acrolein (OCCC), are less reactive than the archetypal 1,3‐butadiene (CCCC), primarily owing to weaker orbital interactions between the more electronegative heteroatoms with ethylene. Thus, the addition of a second heteroatom at the other terminal position (NCCN and OCCO) further reduces the reactivity. However, the introduction of a nitrogen atom in the backbone (CNCC) leads to enhanced reactivity, owing to less Pauli repulsion resulting from polarization of the diene HOMO in CNCC towards the nitrogen atom and away from the terminal carbon atom. The Diels–Alder reactions of ethenyl‐diazene (NNCC) and 1,3‐diaza‐butadiene (NCNC), which contain heteroatoms at both the terminal and backbone positions, are much more reactive due to less activation strain compared to CCCC.

One can differentiate between different subtypes of hetero-Diels-Alder reactions. The most common classification is based on the hetero element present in the substrates. Introduction of nitrogen into the diene or dienophile leads to aza-Diels-Alder cycloadditions. These reactions are commonly used in total synthesis for the formation of nitrogen containing heterocyclic scaffolds. Notable examples employing aza-Diels-Alder reactionsa sakey step include, among many others, [5] the synthesis of streptonigrone by Boger and co-workers, [6] ipalbidine by Danishefsky andc o-workers, [7] (+ +)-reserpine by Jacobsen and co-workers, [8] and phyllanthine by Weinreb and co-workers [9] (Figure 1).
Another important aza-Diels-Alder cycloadditioni st he reaction between 1,2,4,5-tetrazines and electron rich dienophiles. In 1964, Sauer reported on the reaction of tetrazines with dienophiles. [10] This bioorthogonal cycloaddition proceeds through an inverse electron demand Diels-Alder reaction, followed by ac ycloreversion under the loss of nitrogen, and was independently introduced by Fox and co-workers [11] and Weissleder and co-workers [12] in 2008. This ligationi so ften used in time-critical applications, [13] due to the exceptionally high possible secondorder rate constantso fu pt o3 ,300,000 m À1 s À1 . [14] Due to the range of possible dienophiles, this bioorthogonal reactionc an be appliedi nv arious applications. While trans-cyclooctenes are used for high reactivity,c yclopropenes [15] can be used for metabolic incorporation, [16] due to their smaller size. Introduction We have quantum chemically explored the Diels-Alder reactivities of as ystematic series of hetero-1,3-butadienes with ethylene by using density functional theory at the BP86/TZ2P level. Activation strain analyses providedp hysical insight into the factors controlling the relative cycloaddition reactivity of azaand oxa-1,3-butadienes.W ef ind that dienesw ith at erminal heteroatom, such as 2-propen-1-imine (NCCC) or acrolein (OCCC),a re less reactive than the archetypal 1,3-butadiene (CCCC), primarily owing to weaker orbital interactions between the more electronegative heteroatoms with ethylene. Thus, the addition of as econd heteroatom at the other terminalp osition (NCCN and OCCO)f urtherr educes the reactivity.H owever,t he introduction of an itrogen atom in the backbone (CNCC)l eads to enhanced reactivity,o wing to less Pauli repulsion resulting from polarization of the diene HOMO in CNCC towards the nitrogena tom and away from the terminal carbon atom. The Diels-Alder reactions of ethenyl-diazene (NNCC) and 1,3-diazabutadiene (NCNC), which contain heteroatoms at both the terminal and backbone positions, are much more reactive due to less activation strain compared to CCCC.
of ac arbamate in allylic position to the double bond of a trans-cyclooctenea llows for "click-to-release" reactions, [17] openingu pt he possibility for targeted drug delivery. [18] The use of vinylboronic acids [19] can lead to high selectivityt owards 2-pyridyl [20] or 2-hydroxyphenyl [21] substituted1 ,2,4,5-tetrazines, as recently shown by Bonger and co-workers. Other bioorthogonal ligationsb ased on aza-Diels-Alder reactions include the 1,2,4-triazinel igation introduced by Prescher and co-workers [22] and av ariant of the Kondrat'eva reaction introduced by Jouanno et al. (Figure 1). [23] Another subtypeo fh etero-Diels-Alder reactions are oxo-Diels-Alder cycloadditions. In these [4+ +2] cycloadditions,c arbonyl compounds are used as dienophiles or 1,3-dienes. [4,24] Due to the low reactivity of such reaction partners in predominantly inverse electron demand Diels-Alder reactions Lewis acid catalysis, [25] cinchona alkaloid-derived amine catalysis, [26] or N-heterocyclic carbene organocatalysis [27] is often used. This also opens the possibility of enantioselective Diels-Alder cycloadditions forming pyran derivatives. [28] Reactivities of aza-and oxo-hetero-Diels-Alder cycloadditions are found within aw ide range, from unreactive to very highly reactive as observed in tetrazine ligation reactions [14] or the Diels-Alder reactions of superelectrophiles, which show good yields with the quite unreactive ethylene at reasonably low pressure and at room temperature. [29] However,w hile the kinetics of several examples of such hetero-Diels-Alder reactions have been the subject of experimental and theoretical studies, [30] to the besto fo ur knowledgeo nly one study on the influenceo fs inglen itrogen or oxygen atoms within the 1,3diene on the kineticso fD iels-Alder cycloadditionsh as been conducted. Houk and co-workers have investigated the reactivity of cyclic and acyclic1 -a nd 2-azadienes in Diels-Alder reac-tions with ethylene. [31] They could showthat the activation barrier height correlates very well with distortion energies at the transition state obtained from the distortion/interaction analysis (activation strain model) developedb yB ickelhaupt and Houk. [32] They also noted that the position of the transition state is shifted along the reactionc oordinate for different systems. However, comparing interaction and strain energiesf or different systemsa tt heir respective transition state can lead to skewed conclusions, as for cycloadditions both the interaction and strain energy often increases along the reaction coordinate. [32,33] This means that for reactions following Hammond's postulate, systems with lower barriers of activation,a nd therefore earlier transition states, should have lowered strain energies at the transition state associated with them. Hence, these reactions often seem to be strain-controlled, even when the interaction energy is the key causal factor. Therefore, the activation strain analysis should be performed at either ac onsistent point of the reaction coordinate or,e ven better,a long the entire reactionc oordinate. This approach has been successfully used in the past to provide quantitative insight into cycloadditionss uch as 1,3-dipolar cycloadditions, [34] [3 + 2] cycloadditions [35] and Diels-Alder reactions. [33b, 36] We therefore aimed for an in-depths ystematic investigation on the factors controlling the reactivity of oxo-and aza-heterodienes( Scheme 1) in Diels-Alder cycloadditions using the activation strain model in combinationwith aquantitative molecular orbital (MO) theory and associated canonicale nergy decomposition scheme. This allows for aq uantitative analysis of different factors influencing the reactivity,s uch as strain energy,P auli repulsion, orbital interactions and electrostatic interactions.

ComputationalDetails
All calculations were carried out in ADF.2017 [37] using the BP86 [38] functional in combination with the TZ2P [39] basis set. This exchange and correlation functional has been proven to adequately reproduce relative trends in activation energies and reaction energies for various cycloadditions. [40] Vibrational frequency calculations were performed to verify energy minima and transition states. [41] Local minima had zero imaginary frequencies, while transition states had asingle imaginary frequency.The intrinsic reaction coordinate (IRC) method was used to follow the imaginary eigenvector towards both the reactant complex and the cycloadduct. All relative energies are with respect to the s-cis conformation of the diene. Optimized structures were illustrated using CYLview. [42] Quantitative analyses of the activation barriers associated with the studied Diels-Alder reactions are obtained by means of the activation strain model (ASM), which involves decomposing the potential energy surface DE(z)a long the reaction coordinate z into the strain DE strain (z)a ssociated with the structural deformation of the reactants from their equilibrium geometry and the interaction DE int (z)b etween the deformed reactants. [32,43] The DE strain (z)i sd etermined by the rigidity of the reactants and by the extent to which they must deform in order to achieve the geometry of the transition state. The DE int (z)i su sually stabilizing and is related to the electronic structure of the reactants and how they are mutually oriented over the course of the reaction [Eq. (1)]: DEðzÞ¼DE strain ðzÞþDE int ðzÞð 1Þ Ad eeperu nderstandingo ft he interactione nergyc an be obtained usinga ne nergyd ecompositiona nalysis( EDA), in whicht he DE int (z) between the deformed reactants is decomposed, within the conceptual framework provided by the Kohn-Sham molecular orbital (KS-MO) model, into three physically meaningful terms [Eq. (2)]: [44] DE int ðzÞ¼DV elstat ðzÞþDE Pauli ðzÞþDE oi ðzÞð 2Þ The DV elstat (z)t erm corresponds to the classical electrostatic interaction between unperturbed charge distributions 1 A (r) + 1 B (r)o f the deformed fragments Aa nd Ba nd is usually attractive. The Pauli repulsion DE Pauli (z)c omprises the destabilizing interactions between occupied orbitals and is responsible for any steric repulsion. The orbital interaction DE oi (z)a ccounts for charge transfer (interaction between occupied orbitals on one fragment with unoccupied orbitals of the other fragment) and polarization (empty-occupied orbital mixing on one fragment due to the presence of another fragment).
In activation strain diagrams and associated EDA plots in this study,t he IRC is projected onto the average distance of two newly forming bonds. The resulting reaction coordinate z undergoes a well-defined change in the course of the reaction from the reactant complex to the transition state and cycloadducts. The analyses along the reaction coordinate were performed with the aid of the PyFrag program. [45] 2. Results and Discussion  lower barrier energiesa nd are more exothermict han the reaction of CCCC.T he cases outlined above are in line with the Hammond's postulate. However, TS-NCNC has as horter average bond formingd istance and ther eactioni sl ess exothermic than TS-CCCC,b ut also has al ower barrier than TS-CCCC. TS-CNNC has al onger average bond forming distance than TS-CCCC,b ut the barrier is much higher, and the reaction is much less exothermic comparedt oTS-CCCC.T op rovide ar ationale for the differences in activation barriers for theseD iels-Alder reactions, we undertook ac ombined activation strain and energy decomposition analysis study.T he results are summarized below in three sections (2.1-2.3).

Diels-Alder Cycloadditions of CCCC, NCCC,NCCN, OCCC,and OCCO
The activation strain diagram for the Diels-Alder reactions between e and CCCC, NCCC, NCCN, OCCC,a nd OCCO is shown in Figure 3a.T he terminal atoms of these dienes are systematically varied from carbon to nitrogen to oxygen. To be able to comparet he different systems, energies will be compared at a consistentpoint along the reaction coordinate with an average bond forming distance of 2.10 ,s ince this point is close, in both energy and position, to all TSs. CCCC is the most reactive diene of thesef ive dienes. Reactivity decreases upon substitution of at erminal carbon atom with an itrogen or oxygen atom and decreases furtherw hen both terminal carbon atoms are substituted.T he differences in reactivity are mainly caused by as maller p-orbital of the FMOs on the terminal atoms of the dienes with increasing electronegativity of the terminal atoms. [40a, 46] For this reason the oxa-dienes are less reactive than their respective aza-dienes.
The total energiesa tt he consistentg eometry (Figure 3a)a s well as the heights of the activation barriers of the reactions ( Figure 2) of dienes NCCC, NCCN, OCCC,a nd OCCO are larger than those of CCCC.I na ddition, the total energies at the consistent geometry are larger fort he oxa-butadienes (OCCC and OCCO)t han for the aza-butadienes (NCCC and NCCN). We find that DE int follows the trend of DE:i ti sm ore stabilizing for systems with al ower DE and ac orrelation is found between DE and DE int at the consistent geometry (Figure 3b). DE strain increasesw ith decreasing DE. Therefore, DE int governs the differences in DE between the systems. This conclusion is consistent with our previous findings for cycloalkene 36a] and aza-1,3-dipolar cycloadditions. [40a] The differences between the systemsw ill be furtherd iscussed by the comparison of one set of dienes (CCCC, NCCC,a nd OCCC)b ased on the ASM, EDA, andF rontier Molecular Orbital (FMO) analyses. Analyses of the two other sets of dienes (CCCC, NCCC, NCCN and CCCC, OCCC, OCCO)p rovided similar results and can be found in the Supporting Information.
The ASM and EDA diagrams for the Diels-Alder reactions of CCCC (black), NCCC (blue), and OCCC (red) with e are shown in Figure 4a and Figure 4b,r espectively.A tt he consistent geometry, DE strain decreases going from CCCC to NCCC to OCCC due to the decreased number of terminal hydrogens in the hetero-butadienes, which need to be bent away during the reaction. However,t his decrease in DE strain does not yield al ower DE for the Diels-Alder reactions of these hetero-butadienes: DE int plays ad ecisive role and governs the trends in DE. Decomposition of DE int shows that DE int is controlled by DE oi and less so by DV elstat ,w hile DE Pauli follows at rend opposite that of DE int (Figure 4b).
The differences in DE oi are caused by the decrease in the size of the lobe of the FMO diene and LUMO diene on the terminal atom,a si tc hanges from Ct oNto O, due to the more compact natureo ft he 2p orbital of the nitrogen and oxygen atom, and by ad ecreaseo ft he energy levels of both the occupied FMO and LUMO of the diene. [40a, 46] The overlap ande nergy gaps between the FMO diene -LUMO e and the LUMO diene -HOMO e (for the normal and inverse electron demando rbitali nteraction, respectively)a re shown in Figure 5a and 5b. DE oi is most stabilizing for CCCC,a nd becomes weaker going to NCCC and OCCC.T his destabilization is reflectedi nt he FMO diene -LUMO e and LUMO diene -HOMO e gaps and the overlap betweent heseo rbitals. For the normal electron demando rbitali nteraction, the orbitale nergy gap and the overlap between the FMO diene and LUMO e are smallest (3.1eV) and largest( 0.28) respectively for CCCC,w hile they are largest( 5.3 eV) and smallest( 0.19) for OCCC.T he HOMO-1 of OCCC reacts with LUMO e insteado ft he HOMO,d ue to the fact that the HOMO has become al one pair MO. For the inverse electron demand orbital interaction, the orbitale nergy gap for CCCC is larger than for OCCC (3.4 and 2.8 eV respectively), but the overlapi sm uch larger for CCCC than for OCCC (0.25 and 0.18 respectively), thus also yielding a more stabilizing DE oi in case of CCCC.

Diels-Alder Cycloadditions of CCCC, CNCC,and CNNC
Next, we investigatedt he Diels-Alder reactions between CCCC, CNCC,a nd CNNC with e.I ntroducing nitrogen atoms in the backbone of butadiene raises the strain energy along the reaction coordinate, yielding the highest barrier for CNNC.T he  The reaction of CNNC with e has the highest barrier due to the large deformation of the dienei nt he transition state with respectt ot he ground state. In order to react with ethylene, the dienes must adopt an s-cis conformation where the dihedral angle of the backbone is < 108.F or CNNC,t he dihedral angle in the ground state is 95.68.T his has been attributed, very recently by Wiberg, Rablen, and Baraban, to the repulsion between the nitrogen lone pairs. [47] Interestingly,t he dihedral angle decreases to 55.5 and 30.78 for CNCC and CCCC,r espectively.C ompared to the CÀCÀCa ngle of CCCC (125.98), the smaller C-N-C angle of CNCC (120.48)l eads to al arger dihedral angle of CNCC in order to reduce the repulsion between the terminal hydrogens on opposite ends (FigureS5). [47] Therefore DE strain is the largestf or CNNC (which has therefore the highest barrier) and decreases with ad ecreasing amounto fn itrogen atoms ( Figure S5 and Figure 6a). Although DE strain is larger for CNCC than for CCCC,t he barrier heightf or CNCC is lower,d ue to am ore stabilizing DE int along the entire reactionc oordinate. The lower DE int is caused by al ower DE Pauli ,w hile DE oi and DV elstat are very similar along the reactionc oordinate (Figure 6b).
To rationalize the differences in the DE Pauli between the Diels-Alder reactions of CNCC and CCCC,w eq uantified the most significant interactions between filled orbitals [48] of the dienes and e (Figure 7a)a taconsistent geometry with an average C···C bond formingd istance of 2.30 (which is close,  To understand why the DE oi is so similarf or the reactions of CCCC and CNCC,a nF MO analysis was performed (Figure 8). It turns out that the normal demando rbitali nteraction is more favorable for CCCC,w hile the inverse demando rbital interaction is more favorable for CNCC.T hese two interactions effectively offset each other,r esulting in av ery similar DE oi for the two reactions. In the normale lectron demando rbital interaction, the energy gap and orbital overlap between the HO-MO diene and LUMO e are more favorable, i.e.,s maller and larger, respectively for CCCC (3.9 eV and 0.23 compared to 4.2 eV and 0.19 for CNCC). In the inverse electron demand orbitali nteraction, the energy gap and orbitalo verlap are more favorable, i.e.,s maller and larger,r espectively for CNCC (3.4 eV and0 .20 versus 4.0 eV and 0.19 for CCCC), thus yielding av ery similar DE oi .T he differencei nt he overlap in the normald emando rbital interaction can be explained by inspecting the HOMOs of CCCC and CNCC (Figure 7b). Compared to the HOMO of CCCC,t he HOMO of CNCC has ar educed amplitude on one of the terminal carbon atoms, thus yielding as maller overlap between the HOMO diene and LUMO e .T he LUMOs of both dienes are more similar on the terminal carbon atoms (Figure 7b), resulting in av ery similar overlap for the inverse demand orbital interaction.

Diels-Alder Cycloadditions of CNCC, NCNC, and NNCC
The Diels-Alder reactions of CNCC, NCNC,a nd NNCC were compared. These dienes all contain as ingle nitrogen atom in the backbone, but the number and position of the nitrogen atom in the terminal sites is varied. The Diels-Alder reaction of CNCC with e has ah igher barrier compared to NCNC and NNCC causedb yt he more destabilizing DE strain .T his is the result of having to benda way more terminalh ydrogen atoms in the case of the terminal =CH 2 compared to =NH, as previously discussed in Section2.1. DE int is more stabilizing for CNCC than for both NNCC and NCNC,b ut is unable to compensatef or the high DE strain (Figure 9a). The Diels-Alder reaction of NNCC has the lowest reactionb arriero ft he three dienes,due to the more stabilizing DE oi compared to NCNC.
The lower barrier for NNCC compared to NCNC is determined by DE int ,s ince DE strain for these reactions follows the opposite trend of the DE. The decomposition of DE int (Figure 9b) shows that DE oi is the sole factor determining the heighto f DE int .T ou nderstand the differencei nDE oi ,a nF MO analysis was performed for both the normala nd inverse electron demando rbitali nteractions at ac onsistent geometry with an average C···X bond forming distance of 2.30 ,w hich has been chosen since it is close, in both energy and position, to all TSs ( Figure 10). The more stabilizing DE oi for NNCC is due to smaller FMO gaps between thei nteractingo rbitals in both the normala nd inverse demand orbitali nteractions (5.3 and 2.9 eV respectively for NNCC compared to 6.0 and 3.4 eV for NCNC) and to al arger FMO diene -LUMO e overlap for NNCC (0.17 versus 0.11f or NCNC). The decreased orbitalo verlap for NCNC in the normald emand orbital interaction is due the presence of the nitrogen atom directly adjacent to the terminalc arbona tom. This adjacent nitrogen atom effectively reduces the electron density on the terminal carbon atom, resulting in as maller lobe of the FMO diene on the carbon atom and al ess efficient overlap between the FMO diene and the LUMO e .T he LUMOs of NNCC and NCNC are very similar in shape and size, resulting in the same overlap (0.16) between the LUMO diene and the HOMO e at aconsistent formingb ond length (see Figure S6).

Conclusions
The replacement of carbon atoms by heteroatoms in 1,3-butadiene (CCCC) dramatically influences the Diels-Alder reactivity of these dienes with ethylene. Dienes with at erminal heteroatom (NCCC and OCCC)a re less reactive than CCCC and replacemento ft he other terminal carbon atom by nitrogen or oxygen furtherd ecreases the reactivity.R eplacing one of the carbon atoms in the backbone by nitrogen (CNCC)e nhances the reactivity compared to CCCC.T he replacement of two carbon atoms, one at the terminal position and one in the backbone( NNCC and NCNC), yields even more reactive systems.
For dienes in whicho ne or two terminal carbon atoms are replaced by heteroatoms, the Diels-Alderr eaction rate is decreased.T he reasoni st he combination of am ore contracted and lower energyp -orbital on the heteroatom in the highest occupied p-type orbital of the diene, which weakens the stabilizing donor-acceptor orbital overlapa nd interaction with the ethylene LUMO. This factor dominates ac ounteracting influence of the activation strain, which generally decreases as the number of terminal elementÀHb onds that have to bend away becomes smaller. However,i ntroduction of an itrogen atom in the backbone (CNCC)f urnishes am ore reactive diene compared to CCCC,primarily due to aless destabilizing Pauli repulsion. This effect was traced back to the polarized nature of the  HOMO of CNCC towards the nitrogen atom and away from the terminal carbon atom. Consequently,t he four electron-two center overlap between the HOMO of CNCC and HOMO of e is reduced.
The reactivity of hetero-1,3-butadienes with ethylene turns out to be ad elicate interplay between the overlap of bond forming orbitals, the energy levels of those orbitals, and the overlap of filled orbitals on both substrates. We envision dienes containing nitrogen atoms in the backbone (2-azadienes)t ob em ore reactive than their all-carbon counterparts, while addition of heteroatoms on the bond forming positions (1-azadienes) to result in lessr eactive dienes,w hich is consistent with previouss tudies. [31] However,t he combinationo fn itrogen atoms in one of the bond forming positions and in one of the backbone positionsy ields the most reactive diene. We believe these insights to be valuable in the design of Diels-Alder reactions in the future.