Exploring the Mechanism of the Intramolecular Diels–Alder Reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one Using Bonding Evolution Theory

In the present work, the bond breaking/forming events along the intramolecular Diels–Alder (IMDA) reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one have been revealed within bonding evolution theory (BET) at the density functional theory level, using the M05-2X functional with the cc-pVTZ basis set. Prior to achieving this task, the energy profiles and stationary points at the potential energy surface (PES) have been characterized. The analysis of the results finds that this rearrangement can proceed along three alternative reaction pathways (a–c). Paths a and b involve two steps, while path c is a one-step process. The first step in path b is kinetically favored, and leads to the formation of an intermediate step, Int-b. Further evolution from Int-b leads mainly to 3-b1. However, 2 is the thermodynamically preferred product and is obtained at high temperatures, in agreement with the experimental observations. Regarding the BET analysis along path b, the breaking/forming process is described by four structural stability domains (SSDs) during the first step, which can be summarized as follows: (1) the breaking of the C–O bond with the transfer of its population to the lone pair (V(O)), (2) the reorganization of the electron density with the creation of two V(C) basins, and (3) the formation of a new C–C single bond via the merger of the two previous V(C) basins. Finally, the conversion of Int-b (via TS2-b1) occurs via the reorganization of the electron density during the first stage (the creation of different pseudoradical centers on the carbon atoms as a result of the depopulation of the C–C double bond involved in the formation of new single bonds), while the last stage corresponds to the non-concerted formation of the two new C–C bonds via the disappearance of the population of the four pseudoradical centers formed in the previous stage. On the other hand, along path a, the first step displays three SSDs, associated with the depopulation of the V(C2,C3) and V(C6,C7) basins, the appearance of the new monosynaptic basins V(C2) and V(C7), and finally the merging of these new monosynaptic basins through the creation of the C2–C7 single bond. The second step is described by a series of five SSDs, that account for the reorganization of the electron density within Int-a via the creation of four pseudoradical centers on the C12, C13, C3 and C6 carbon atoms. The last two SSDs deal with the formation of two C-C bonds via the merging of the monosynaptic basins formed in the previous domains.


Introduction
Intramolecular cyclic rearrangements refer to the reaction of a single molecule where two atoms or sites react to form a new cyclic product.Among them, the intramolecular Diels-Alder (IMDA) reaction is widely used for the stereoselective synthesis of complex molecules containing fused and/or bridged 6-membered rings, which appear in many natural products or pharmaceuticals [1][2][3].IMDA reactions are faster, cleaner and more selective than intermolecular reactions [4].In the seminal review on IMDA reactions, Brieger and Bennett [3], based on the results by Kitahara et al. [5], reported on the IMDA reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one, 1 to 2 (path a), although other products, 3b-1 and 3b-2, and 4c-1 and 4c-2, can be also formed via path b and path c, respectively (see Scheme 1).
One of the ultimate goals of chemistry is to understand how chemical bonds break/form throughout the progress of a chemical reaction, which in turn implies the ability to disclose the underlying mechanism at an atomic scale.In his seminal works on quantum theory of atoms in molecules (QTAIM) [6][7][8], Richard Bader has demonstrated that topological analysis of the electron density, ρ(r), as a quantum chemically accessible scalar field, condenses the chemically relevant information obtained from quantum calculations into an observable computed from it, such as electron density.Later, Popelier introduced the concept of quantum chemical topology (QCT) [9,10] to embrace QTAIM, bonding evolution theory (BET) and non-covalent interaction analysis (NCI), as appropriate tools to analyze the topology of the electron density ρ(r), by means of real-space partitioning of the molecular space by using functions of the electronic density and/or its derivatives [11][12][13].Within the BET framework, the evolution of the topology of the ELF along a chosen reaction path (e.g., the intrinsic reaction coordinate, connecting the reactants to the products) is characterized in terms of Thom's elementary catastrophes.BET has a
One of the ultimate goals of chemistry is to understand how chemical bonds break/form throughout the progress of a chemical reaction, which in turn implies the ability to disclose the underlying mechanism at an atomic scale.In his seminal works on quantum theory of atoms in molecules (QTAIM) [6][7][8], Richard Bader has demonstrated that topological analysis of the electron density, ρ(r), as a quantum chemically accessible scalar field, condenses the chemically relevant information obtained from quantum calculations into an observable computed from it, such as electron density.Later, Popelier introduced the concept of quantum chemical topology (QCT) [9,10] to embrace QTAIM, bonding evolution theory (BET) and non-covalent interaction analysis (NCI), as appropriate tools to analyze the topology of the electron density ρ(r), by means of real-space partitioning of the molecular space by using functions of the electronic density and/or its derivatives [11][12][13].Within the BET framework, the evolution of the topology of the ELF along a chosen reaction path (e.g., the intrinsic reaction coordinate, connecting the reactants to the products) is characterized in terms of Thom's elementary catastrophes.BET has a demonstrated capability that not only distinguishes between fundamental changes to ρ(r) electron density throughout a chemical reaction, but also stablishes where and how the chemical bonds are broken throughout the reaction progress [11,[14][15][16][17][18][19][20][21][22][23].These processes become naturally associated with specific stability domains (SSDs) separated by catastrophe bifurcations [14,16,[24][25][26][27].
In view of the scope of the IMDA reaction, computational studies on its mechanism are important in the areas of theoretical and synthetic organic chemistry.However, few computational/theoretical studies applying BET to the corresponding mechanisms have been published to date [28,29].Herein, we report on a theoretical study, based on BET, to disclose the nature of the reaction mechanisms for the three possible reactive channels for the transformation of 1 (Scheme 1).Specifically, the answers to the following questions are the main goals of the present work: (1) where and how do electron density changes occur during the reaction, (2) how can electron density rearrangement track events in the bond breaking/forming process, and (3) how should the electronic reorganization along the chemical reaction path be deciphered?Or, in other words, what types of catastrophes and SSDs appear throughout each reaction pathway during BET analysis?
In view of the scope of the IMDA reaction, computational studies on its mechanism are important in the areas of theoretical and synthetic organic chemistry.However, few computational/theoretical studies applying BET to the corresponding mechanisms have been published to date [28,29].Herein, we report on a theoretical study, based on BET, to disclose the nature of the reaction mechanisms for the three possible reactive channels for the transformation of 1 (Scheme 1).Specifically, the answers to the following questions are the main goals of the present work: (1) where and how do electron density changes occur during the reaction, (2) how can electron density rearrangement track events in the bond breaking/forming process, and (3) how should the electronic reorganization along the chemical reaction path be deciphered?Or, in other words, what types of catastrophes and SSDs appear throughout each reaction pathway during BET analysis?

Thermodynamic and Geometrical Aspects
The IMDA reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one (1) can proceed, as explained, along three reaction paths (a, b and c) and leads to the formation of 6-(allyloxy)bicycle [4.2.0]octa-2,4-dien-7-one and (4Z,6Z)-3-allylcyclooctane-4,6-dien-1,2-dione, named as intermediates Int-a and Int-b, respectively, together with the final products, namely 2, 3-b1, 3-b2, 4-c1 and 4-c2 (see Scheme 2).The reaction mechanism along path a is divided into two steps, the first leads to Inta, while the second step corresponds to the Diels-Alder process.The first step corresponding to the tautomerization of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one and leading to the formation of Int-a overcomes an activation free Gibbs energy of 56.6 kcal/mol with The reaction mechanism along path a is divided into two steps, the first leads to Int-a, while the second step corresponds to the Diels-Alder process.The first step corresponding to the tautomerization of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one and leading to the formation of Int-a overcomes an activation free Gibbs energy of 56.6 kcal/mol with a reaction Gibbs free energy of 13.3 kcal/mol (see Figure 1 and Table 1).The transformation of Int-a to 2 presents an activation Gibbs free energy of 12.0 kcal/mol and a reaction Gibbs free energy of 40.1 kcal/mol.Path b starts with a [3,3] sigmatropic rearrangement of 1 leading to Int-b, followed by its conversion into 3-b1 and 3-b2.This [3,3] sigmatropic rearrangement needs to overcome an activation barrier of 31.3 kcal/mol and has a reaction energy of −5.6 kcal/mol.During the second step, Int-b can perform two alternative Diels-Alder processes through the transition state TS2-b1 (with a barrier of 46.1 kcal/mol) or TS2-b2 (with a barrier of 64.0 kcal/mol) to form two cycloadducts, 3-b1 and 3-b2, having a reaction Gibbs free energy of −10.1 and 31.2 kcal/mol, respectively, by considering Int-b as a reference.Thus, 3-b1 is more thermodynamically stable than 3-b2, since its formation energy is 41.3 kcal/mol lower (see Figure 1).Finally, the last path, path c corresponds to a direct Diels-Alder reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one via the activation Gibbs free barrier of 63.9 (TS1-c1) and 70.0 kcal/mol (TS1-c2) leading to the formation of cycloadducts, 4-c1 and 4-c2, that takes place with a reaction energy of 0.7 and 20.6 kcal/mol, respectively.As can be seen, our results confirm 2 as the thermodynamically preferred product at high temperatures, as experimentally detected [5], while 3-b1 is the main product in kinetically controlled conditions.a reaction Gibbs free energy of 13.3 kcal/mol (see Figure 1 and Table 1).The transformation of Int-a to 2 presents an activation Gibbs free energy of 12.0 kcal/mol and a reaction Gibbs free energy of 40.1 kcal/mol.Path b starts with a [3,3] sigmatropic rearrangement of 1 leading to Int-b, followed by its conversion into 3-b1 and 3-b2.This [3,3] sigmatropic rearrangement needs to overcome an activation barrier of 31.3 kcal/mol and has a reaction energy of −5.6 kcal/mol.During the second step, Int-b can perform two alternative Diels-Alder processes through the transition state TS2-b1 (with a barrier of 46.1 kcal/mol) or TS2-b2 (with a barrier of 64.0 kcal/mol) to form two cycloadducts, 3-b1 and 3-b2, having a reaction Gibbs free energy of −10.1 and 31.2 kcal/mol, respectively, by considering Int-b as a reference.Thus, 3-b1 is more thermodynamically stable than 3-b2, since its formation energy is 41.3 kcal/mol lower (see Figure 1).Finally, the last path, path c corresponds to a direct Diels-Alder reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one via the activation Gibbs free barrier of 63.9 (TS1-c1) and 70.0 kcal/mol (TS1-c2) leading to the formation of cycloadducts, 4-c1 and 4-c2, that takes place with a reaction energy of 0.7 and 20.6 kcal/mol, respectively.As can be seen, our results confirm 2 as the thermodynamically preferred product at high temperatures, as experimentally detected [5], while 3-b1 is the main product in kinetically controlled conditions.Table 1.M05-2X/cc-pVTZ relative electronic energies, ∆E (in kcal mol −1 ); enthalpies, ∆H (in kcal•mol −1 ); entropies, ∆S (in cal mol −1 K −1 ); and Gibbs free energies, ∆G (in kcal mol −1 ), for the species involved in the intramolecular Diels-Alder reaction in diphenyl ether.All values are given with respect to those of the reactant (1), see Table S1 for the absolute values.

QTAIM Analysis of the Transition State Structures
Before performing the analysis of bond forming/breaking processes, an AIM study on each transition state is required.Figure 3 displays the presence of bond critical points (BCPs), while Table S2 contains the value of each topological parameter.According to Table S2, each TS structure presents a small value (ca.0.12 a.u. or less) on the Laplacian density at the different BCPs, corresponding to a type of non-covalent or closed-shell

QTAIM Analysis of the Transition State Structures
Before performing the analysis of bond forming/breaking processes, an AIM study on each transition state is required.Figure 3 displays the presence of bond critical points (BCPs), while Table S2 contains the value of each topological parameter.According to Table S2, each TS structure presents a small value (ca.0.12 a.u. or less) on the Laplacian density at the different BCPs, corresponding to a type of non-covalent or closed-shell (ionic) interactions.Moreover, the positive value of the Laplacian density confirms the initial stage in the formation of various new single bonds (see Section 2.3).In addition to the topological parameters discussed above, the other BCP parameters were used to characterize the chemical bond properties of the TS structures for the IMDA reaction.However, with respect to the total energy density H(r), all the values are negative (Table S2), which at first glance might suggest significant electron sharing.The highest magnitude values obtained (−0.02 a.u.for O … C at TS1-b, −0.032 and −0.022 a.u.for O … C and O … C at TS2-b2, respectively) reflect a higher degree of covalence in these interactions.Likewise, in order to measure the π character of the bond, ellipticity descriptors have been admitted.Thus, the C … C bond of TS2-b1 exhibits a higher ellipticity (0.638 a.u.) than all the others, suggesting that it is more involved in a hyper conjugative interaction than in the case of the other TSs and corresponds to a greater instability of this bond [30].Furthermore, since some covalence is evidenced by the ratio |V(r)|/G(r), which is always greater than 1 at the BCP, the emerging C-C and C-O bonds seem to be triggered more easily in all the TS series (ratio close to 1.5) (Table S2).Thereafter, the QTAIM analysis shows that along the TS series, passing from path a to path c, the covalent character of all the bonds are reinforced, since the values of the ratio |λ1|/λ3 increase (values close to 0.35) (Table S2).

BET Analysis along Different Reaction Paths
As we have shown in Section 2.1, the IMDA reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one occurs along three reaction paths.Therefore, a BET study is carried out to gain deep insight into the corresponding bond breaking/forming processes.

BET Analysis within Path a First
Step: Tautomerization Process Yielding Int1-a Analysis of the results presented in Figure 4 and Table S3 reveals that three structural stability domains (SSDs) are required to describe the formation of the C2-C7 bond.The first domain, SSD-I (d(C2-C7) = 2.606 Å) displays the electron population of the key atoms involved in the bond formation: the disynaptic V(C2,C3), V(C4,C5) and V(C6,C7) basins, In addition to the topological parameters discussed above, the other BCP parameters were used to characterize the chemical bond properties of the TS structures for the IMDA reaction.However, with respect to the total energy density H(r), all the values are negative (Table S2), which at first glance might suggest significant electron sharing.The highest magnitude values obtained (−0.02 a.u.for O 10 . . .C 11 at TS1-b, −0.032 and −0.022 a.u.for O 10 . . .C 12 and O 9 . . .C 11 at TS2-b2, respectively) reflect a higher degree of covalence in these interactions.Likewise, in order to measure the π character of the bond, ellipticity descriptors have been admitted.Thus, the C 4 . . .C 12 bond of TS2-b1 exhibits a higher ellipticity (0.638 a.u.) than all the others, suggesting that it is more involved in a hyper conjugative interaction than in the case of the other TSs and corresponds to a greater instability of this bond [30].Furthermore, since some covalence is evidenced by the ratio |V(r)|/G(r), which is always greater than 1 at the BCP, the emerging C-C and C-O bonds seem to be triggered more easily in all the TS series (ratio close to 1.5) (Table S2).Thereafter, the QTAIM analysis shows that along the TS series, passing from path a to path c, the covalent character of all the bonds are reinforced, since the values of the ratio |λ1|/λ3 increase (values close to 0.35) (Table S2).

BET Analysis along Different Reaction Paths
As we have shown in Section 2.1, the IMDA reaction of (2E,4Z,6Z)-2(allyloxy)cycloocta-2,4,6-trien-1-one occurs along three reaction paths.Therefore, a BET study is carried out to gain deep insight into the corresponding bond breaking/forming processes.

BET Analysis within Path a First Step: Tautomerization Process Yielding Int1-a
Analysis of the results presented in Figure 4 and Table S3 reveals that three structural stability domains (SSDs) are required to describe the formation of the C2-C7 bond.The first domain, SSD-I (d(C2-C7) = 2.606 Å) displays the electron population of the key atoms involved in the bond formation: the disynaptic V(C2,C3), V(C4,C5) and V(C6,C7) basins, which illustrate the C2-C3, C4-C5 and C6-C7 double bonds, and hold an electron population of 3.63, 3.42 and 3.48e, respectively, at the beginning of the domain.In addition, two other disynaptic basins V(C3,C4) and V(C5,C6) with a population of 2.12e at the beginning, symbolize the single C3-C4 and C5-C6 bonds, respectively.At the end of this domain, some electron fluctuations are recorded with a decrease in the population of 0.67, 0.57 and 0.60e for the V(C2,C3), V(C4,C5) and V(C6,C7) basins, respectively.In fact, these drops in basin population are mainly transferred to the V(C3,C4) (+0.87e) and V(C5,C6) (+0.63e) basins.
At the beginning of the second domain, SSD-II (d(C2-C7) = 2.067 Å), the electron population of the V(C3,C4) and V(C5,C6) basins continue to increase, while the population of the V(C2,C3), V(C4,C5) and V(C6,C7) basins decrease.This continuous decrease in the populations of the V(C2,C3) and V(C6,C7) basins comes from the appearance of two new monosynaptic basins (V(C2) and V(C7), see Figure 5) on the C2 and C7 carbon atoms, with an electron population of 0.31 ad 0.26, respectively.These monosynaptic basins are the precursors [31,32] for the formation of a new C-C single bond.
The new single C-C bond appears at the beginning of the last domain, SSD-III (d(C2-C7) = 1.859Å), from the merger of two former V(C2) and V(C7) basins formed at the SSD-II domain.The electron population starts from 1.44e, before reaching a value of 1.92e at the end of the domain (d(C2-C7) = 1.569Å).At the beginning of the second domain, SSD-II (d(C2-C7) = 2.067 Å), the electron population of the V(C3,C4) and V(C5,C6) basins continue to increase, while the population of the V(C2,C3), V(C4,C5) and V(C6,C7) basins decrease.This continuous decrease in the populations of the V(C2,C3) and V(C6,C7) basins comes from the appearance of two new monosynaptic basins (V(C2) and V(C7), see Figure 5) on the C2 and C7 carbon atoms, with an electron population of 0.31 ad 0.26, respectively.These monosynaptic basins are the precursors [31,32] for the formation of a new C-C single bond.
The new single C-C bond appears at the beginning of the last domain, SSD-III (d(C2-C7) = 1.859Å), from the merger of two former V(C2) and V(C7) basins formed at the SSD-II domain.The electron population starts from 1.44e, before reaching a value of 1.92e at the end of the domain (d(C2-C7) = 1.569Å).
Extending from −15.72 to 6.74 amu 1/2 Bohr, the topological changes occur along the IRC path at the following reaction coordinates: −0.48 and −1.76 amu 1/2 Bohr, allowing for the calculation of the value of synchronicity (S y ) and absolute synchronicity (S abs y ), which are equal to 0.94 and 0.91, respectively.According to these values, the topological changes take place with 91% of synchronous character [33,34].Extending from −15.72 to 6.74 amu 1/2 Bohr, the topological changes occur along the IRC path at the following reaction coordinates: −0.48 and −1.76 amu 1/2 Bohr, allowing for the calculation of the value of synchronicity ( ) and absolute synchronicity ( ), which are equal to 0.94 and 0.91, respectively.According to these values, the topological changes take place with 91% of synchronous character [33,34].

Second
Step: Diels-Alder Reaction of the Intermediate Int-a Yielding to 2 The BET analysis of the Diels-Alder reaction of the intermediate Int-a yielding to 2 is described by five SSDs (see Figures 6 and S1).The first domain, SSD-I (d(C3-C12) = 3.235 Å and d(C6-C13) = 3.655 Å), represents the electron population of different atoms of the intermediate Int-a, required for the formation of the new C3-C12 and C6-C13 single bonds (see Table S4).The transition from SSD-I to II (d(C3-C12) = 2.208 Å and d(C6-C13) = 2.184 Å) deals with the creation of two-fold catastrophes on the C12 and C13 carbon atoms.In fact, these two-fold catastrophes correspond to the creation of monosynaptic basins, whose electron population of 0.21 and 0.25e come from the reduction in the V(C12,C13) basin population.The electron populations of the V(C12) and V(C13) basins slightly increase at the beginning of the third domain, SSD-III (d(C3-C12) = 2.166 Å and d(C6-C13) = 2.137 Å), while we note a high decrease in the electron population of the V(C3,C4) and V(C5,C6) basins.These electron drops illustrate the appearance of another two new monosynaptic basins (V(C3) and V(C6)) integrating an electron population of 0.29 and 0.26 e, respectively.
At the beginning of SSD-IV (d(C3-C12) = 1.997Å and d(C6-C13) = 1.954Å), the population of the V(C3) and V(C12) basins continues to grow, while that of the V(C6) and V(C13) basins has completely disappeared.The new V(C6,C13) basin collects its population of 1.20e from the former population of V(C6) and V(C13) (0.51 and 0.56e, respectively, at the end of the last domain).Finally, at the beginning of the last domain SSD-V (d(C3-C12) = 1.911Å and d(C6-C13) = 1.863Å), the formation of the second C3-C12 single bond, associated with the appearance of a cusp catastrophe, begins when the formation of the former C3-C4 single bond has reached 77% of its population.This last cusp catastrophe corresponds to the creation of the V(C3-C12) disynaptic basin with a population of 1.28e, which symbolizes the formation of the new C3-C12 single bond.
With the values of the reaction coordinates (0.30, 0.60, 1.79 and 2.40 amu 1/2 Bohr) for the different topological changes along this pathway, we have calculated the values of  (0.93) and  (0.88).Therefore, these bond formation processes take place with 88% of The BET analysis of the Diels-Alder reaction of the intermediate Int-a yielding to 2 is described by five SSDs (see Figure 6 and Figure S1).The first domain, SSD-I (d(C3-C12) = 3.235 Å and d(C6-C13) = 3.655 Å), represents the electron population of different atoms of the intermediate Int-a, required for the formation of the new C3-C12 and C6-C13 single bonds (see Table S4).The transition from SSD-I to II (d(C3-C12) = 2.208 Å and d(C6-C13) = 2.184 Å) deals with the creation of two-fold catastrophes on the C12 and C13 carbon atoms.In fact, these two-fold catastrophes correspond to the creation of monosynaptic basins, whose electron population of 0.21 and 0.25e come from the reduction in the V(C12,C13) basin population.The electron populations of the V(C12) and V(C13) basins slightly increase at the beginning of the third domain, SSD-III (d(C3-C12) = 2.166 Å and d(C6-C13) = 2.137 Å), while we note a high decrease in the electron population of the V(C3,C4) and V(C5,C6) basins.These electron drops illustrate the appearance of another two new monosynaptic basins (V(C3) and V(C6)) integrating an electron population of 0.29 and 0.26 e, respectively.
At the beginning of SSD-IV (d(C3-C12) = 1.997Å and d(C6-C13) = 1.954Å), the population of the V(C3) and V(C12) basins continues to grow, while that of the V(C6) and V(C13) basins has completely disappeared.The new V(C6,C13) basin collects its population of 1.20e from the former population of V(C6) and V(C13) (0.51 and 0.56e, respectively, at the end of the last domain).Finally, at the beginning of the last domain SSD-V (d(C3-C12) = 1.911Å and d(C6-C13) = 1.863Å), the formation of the second C3-C12 single bond, associated with the appearance of a cusp catastrophe, begins when the formation of the former C3-C4 single bond has reached 77% of its population.This last cusp catastrophe corresponds to the creation of the V(C3-C12) disynaptic basin with a population of 1.28e, which symbolizes the formation of the new C3-C12 single bond.
With the values of the reaction coordinates (0.30, 0.60, 1.79 and 2.40 amu 1/2 Bohr) for the different topological changes along this pathway, we have calculated the values of S y (0.93) and S abs y (0.88).Therefore, these bond formation processes take place with 88% of synchronous character.According to BET analysis, the second and third domains along the TS2-b2 path involve the presence of the two disynaptic V(O10,C12) and V(O9,C11) basins, which illustrate the formation of new O10-C12 and O9-C11 single bonds.In fact, at the end of the first domain, the population of the V(O9) and V(O10) basins record a slight increase of 0.51 and 0.61e, respectively.At the same time, the population of the V(C1,O9) and V(C2,O10) basins are strongly depopulated (0.72 and 0.88e), as well as V(C11,C12), which loses 1.22e, in favor of the V(C1,C2) basin, which has recorded an increase of 1.60e, as well as the monosynaptic V(O9) and V(O10) basins (whose populations increase by 0.51 and 0.61e, as already mentioned).The next two final steps describe the formation of the O10-C12 (SSD-II) and O9-C11 (SSD-III) bonds with the population of 0.64 and 0.79e, coming from the reduction of the main lone pairs on O10 and O9, which have lost a population of 0.54 and 0.75e, respectively (see Figures 9 and S4, as well as Table S7).Their populations reach up to 1.21 or 1.22e at the end of the last domain, while the population of the V(C1,C2) basin is worth 4.00e, and symbolize the total transformation of the C1-C2 single bond into a double bound.
The corresponding values of    along the two paths are equal to 0.95 and 0.97, and these latter values predict that the topological changes along the TS2-b2 pathway are slightly more synchronous compared to the changes in the TS2-b1 pathway.According to BET analysis, the second and third domains along the TS2-b2 path involve the presence of the two disynaptic V(O10,C12) and V(O9,C11) basins, which illustrate the formation of new O10-C12 and O9-C11 single bonds.In fact, at the end of the first domain, the population of the V(O9) and V(O10) basins record a slight increase of 0.51 and 0.61e, respectively.At the same time, the population of the V(C1,O9) and V(C2,O10) basins are strongly depopulated (0.72 and 0.88e), as well as V(C11,C12), which loses 1.22e, in favor of the V(C1,C2) basin, which has recorded an increase of 1.60e, as well as the monosynaptic V(O9) and V(O10) basins (whose populations increase by 0.51 and 0.61e, as already mentioned).The next two final steps describe the formation of the O10-C12 (SSD-II) and O9-C11 (SSD-III) bonds with the population of 0.64 and 0.79e, coming from the reduction of the main lone pairs on O10 and O9, which have lost a population of 0.54 and 0.75e, respectively (see Figures 9 and S4, as well as Table S7).Their populations reach up to 1.21 or 1.22e at the end of the last domain, while the population of the V(C1,C2) basin is worth 4.00e, and symbolize the total transformation of the C1-C2 single bond into a double bound.The corresponding values of S abs y along the two paths are equal to 0.95 and 0.97, and these latter values predict that the topological changes along the TS2-b2 pathway are slightly more synchronous compared to the changes in the TS2-b1 pathway.

BET Analysis within Path c
The Diels-Alder reaction of 1 yielding to products 4-c1 and 4-c2 via the transition states TS1-c1 and TS1-c2 takes place within five SSDs, as displayed in Figures 10 and 11,

Figure 2
displays the geometrical structures of the different transition states (TSs) during each reaction pathway.The key distances of the new forming bonds are indicated.Along the reaction path a, they are equal to 2.143 Å at TS1-a, and 2.240 and 2.229 Å at TS2-a.Concerning path b, they correspond to 1.942 (C-O) and 2.116 (C-C) Å at TS1-b, 2.180 (C-C) and 2.170 (C-C) Å at TS2-b1, and 1.938 (C-O) and 1.875 (C-O) Å at TS2-b2.Finally, the length of the two new forming C-C bonds are equal to 2.271 and 2.309 Å at TS1-c1, and 2.345 and 1.992 Å at TS1-c2.

Figure 2 18 Figure 1 .
Figure 2 displays the geometrical structures of the different transition states (TSs) during each reaction pathway.The key distances of the new forming bonds are indicated.Along the reaction path a, they are equal to 2.143 Å at TS1-a, and 2.240 and 2.229 Å at TS2-a.Concerning path b, they correspond to 1.942 (C-O) and 2.116 (C-C) Å at TS1-b, 2.180 (C-C) and 2.170 (C-C) Å at TS2-b1, and 1.938 (C-O) and 1.875 (C-O) Å at TS2-b2.Finally, the length of the two new forming C-C bonds are equal to 2.271 and 2.309 Å at TS1-c1, and 2.345 and 1.992 Å at TS1-c2.

Figure 2 .
Figure 2. M05-2X/cc-pVTZ optimized geometries for the TSs associated with the intramolecular Diels-Alder reaction.Distances are given in Å.The numbers in red indicate different atoms (carbons and oxygen) involved in the formation of new bonds, according to Scheme 2.

Figure 2 .
Figure 2. M05-2X/cc-pVTZ optimized geometries for the TSs associated with the intramolecular Diels-Alder reaction.Distances are given in Å.The numbers in red indicate different atoms (carbons and oxygen) involved in the formation of new bonds, according to Scheme 2.

Molecules 2023 ,
28, x FOR PEER REVIEW 6 of 18 (ionic) interactions.Moreover, the positive value of the Laplacian density confirms the initial stage in the formation of various new single bonds (see Section 2.3).

Figure 3 .
Figure 3. AIM representation of TSs, with a violet ellipse used to highlight the bond critical point (BCP) of new forming or old breaking bonds.The numbers in red indicate different atoms (carbon and oxygen) involved in the formation of new bonds, according to Scheme 2.

Figure 3 .
Figure 3. AIM representation of TSs, with a violet ellipse used to highlight the bond critical point (BCP) of new forming or old breaking bonds.The numbers in red indicate different atoms (carbon and oxygen) involved in the formation of new bonds, according to Scheme 2.

Figure 4 .
Figure 4. Population evolution (in e) of selected basins along the IRC associated with TS1-a.
er of electro ns N um b er of electro ns

Figure 4 .
Figure 4. Population evolution (in e) of selected basins along the IRC associated with TS1-a.

Figure 5 .
Figure 5. ELF basin isosurface of chosen points representing the SSDs along the IRC associated with TS1-a.See Figure 4 for the color labeling of the basins.

Figure 5 .
Figure 5. ELF basin isosurface of chosen points representing the SSDs along the IRC associated with TS1-a.See Figure 4 for the color labeling of the basins.Second Step: Diels-Alder Reaction of the Intermediate Int-a Yielding to 2

Figure 8 .
Figure 8. ELF basin isosurface of chosen points representing the SSDs along the IRC associated with TS2-b1.See Figure S3 for the color labeling of the basins.

Figure 8 .
Figure 8. ELF basin isosurface of chosen points representing the SSDs along the IRC associated with TS2-b1.See Figure S3 for the color labeling of the basins.

Molecules 2023 ,Figure 9 .
Figure 9. ELF basin isosurface of chosen points representing the SSDs along the IRC associated wi TS2-b2.See Figure S4 for the color labeling of the basins.2.3.3.BET Analysis within Path c The Diels-Alder reaction of 1 yielding to products 4-c1 and 4-c2 via the transitio states TS1-c1 and TS1-c2 takes place within five SSDs, as displayed in Figures 10 and 1 while the electron populations of the key basins engaged in the formation of two new C C bonds are given in Tables S8 and S9 and their evolution throughout the processes a illustrated in Figures S5 and S6.Along the TS1-c1 reaction path, the second domain (d(C4 C12) = 2.274 Å and d(C7-C13) = 2.233 Å) deals with the depopulation of the ma V(C12,C13) basin via the creation of the V(C13) monosynaptic basin, which integrates population of 0.23e, while the third domain (d(C4-C12) = 2.239 Å and d(C7-C13) = 2.19 Å) depicts the depopulation of the V(C4,C5) basin due to the appearance of the new V(C basin.Like the V(C13) basin, the V(C4) basin with a population of 0.30e, represents th pseudoradical center on the C4 atom, and is required for the formation of the new sing

Figure 9 .
Figure 9. ELF basin isosurface of chosen points representing the SSDs along the IRC associated with TS2-b2.See Figure S4 for the color labeling of the basins.