A Molecular Electron Density Theory Study of the Polar Diels-Alder Reaction of Naphtoquinone:Cr(CO)3 Complex with Cyclic Dienes

Abstract The role of the Cr(CO)3 coordination to the aromatic ring of naphtoquinone (NQ) in the polar Diels-Alder (P-DA) reactions with cyclic dienes, cyclopentadiene (Cp), cyclohexadiene (Ch), and 1-methoxy-cyclohexadiene (ChOMe), has been studied within Molecular Electron Density Theory (MEDT). Electron Localization Function (ELF) of the NQ:Cr(CO)3 complex indicates that Cr(CO)3 does not cause any remarkable change in the electronic structure of NQ. While the NQ:Cr(CO)3 complex is categorized as a strong electrophile, the cyclic dienes are categorized as strong nucleophiles, suggesting P-DA reactions. Formation of the NQ:Cr(CO)3 complex reduces the activation energy by only 0.7 kcal·mol−1. While Ch shows a lower reactivity than Cp, ChOMe presents the highest reactivity of this series of cyclic dienes. Analysis of the activation Gibbs free energies of the P-DA reaction with Cp indicates that the reaction is completely endo and anti stereoselective. The present MEDT study shows that the Cr(CO)3 complex has no effective catalytic activity in the P-DA reactions of NQ with cyclic dienes, but only permits the reaction to take place experimentally with a total endo and anti facial stereoselectivity, yielding a single cycloadduct.


Introduction
The Diels-Alder (DA) reaction between a conjugated diene and an ethylene to yield a cyclohexene, reported for the first time by Diels and Alder in 1928, 1 is one of the most significant organic reactions from a synthetic as well as a theoretical point of view. 2,3owever, not all DA reactions take place easily in the laboratory.For instance, the DA reaction between butadiene 1 and ethylene 2, which is presented in all textbooks as the prototype DA reaction, does not easily take place in the laboratory; only after 17 hours at 165 C and 900 atmospheres, it gives a 78% yield (see Scheme 1). 4 After an extensive theoretical study of experimental DA reactions, the polar Diels-Alder (P-DA) mechanism was proposed in 2009. 5A good correlation between the activation energies and the global electron density transfer 6 (GEDT) for the DA reactions of cyclopentadiene (Cp) 4 with a series of twelve substituted ethylenes of increased electrophilic character was found. 5That study allowed the classification of DA reactions in non-polar DA (N-DA) reactions, with GEDT < 0.1 e, which do not take place easily experimentally, and P-DA reactions, with GEDT !0.1 e.Thus, the N-DA reaction of Cp 4 with ethylene 2 presented a high activation energy of 19.9 kcalÁmol À1 . 5The use of electron-withdrawing (EW) substituents, such as -CN, -CHO or -NO 2 , accelerated the P-DA reactions.In addition, the use of Lewis acids (LAs) favored the P-DA reactions by notably increasing the polar character of the reaction. 5,7In this sense, the analysis of the electrophilicity 8 x and nucleophilicity 9 N indices defined within the conceptual DFT 10 , 11 (CDFT) have become a powerful tool to predict the polar character of DA reactions, and therefore their feasibility. 12ransition metal complexation is attractive in organic synthesis because it changes the chemical behavior of organic molecules, allowing transformations that are not possible in free substrates.In this sense, Cr(CO) 3 arene complexes are widely used in organic synthesis. 13The EW effect of the Cr(CO) 3 unit allows efficient nucleophilic attacks, stabilizing negative charges.In addition, the Cr(CO) 3 moiety exerts great facial control so it can be used as an auxiliary that can easily be removed. 13n 2005, D€ otz et al. experimentally reported the DA reactions between a Cr(CO) 3 complex with natphoquinone (NQ) 5 and a series of cyclic dienes in good to excellent yield (see Scheme 2). 14X-ray analyses revealed that these DA reactions take place with a complete endo stereoselectivity, while the presence of Cr(CO) 3 in the NQ:Cr(CO) 3 complex 6 exhibited a complete anti directory role.The reaction conditions indicated that the reactivity of these cyclic dienes increases in the order 1-metoxy-cyclohexadiene (ChOMe) 8 > Cp 4 > cyclohexadiene (Ch) 7 (see Scheme 2).
Very recently, the role of the coordination of the Cr(CO) 3 complex to the aromatic ring of styrene in complex 12 in the N-DA reaction with Cp 4 has been studied within the Molecular Electron Density Theory 15 (MEDT) (see Scheme 3). 16That study revealed that formation of the styrene:Cr(CO) 3 complex 12 decreases the unfavorable activation energy of this N-DA reaction by only 2.1 kcalÁmol À1 .This N-DA reaction was found endo stereoselective, while the presence of the Cr(CO) 3 complex causes a complete anti facial selectivity.
Herein an MEDT study of the P-DA reactions of NQ:Cr(CO) 3 complex 6 with cyclic dienes 4, 7, 8, experimentally studied by D€ otz et al. 14 (see Scheme 2), is performed using DFT calculations at the xB97X-D/6-311G(d,p) computational level in order to elucidate how the coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 modifies the reactivity of this electrophilic ethylene derivative participating in P-DA reactions, as well as the different experimentally observed reactivity of these cyclic dienes.

Computational methods
DFT calculations were performed using the xB97X-D functional, 17 which includes long-range exchange (denoted by X) correction as well as the semiclassical London-dispersion correction (indicated by suffix D).The standard 6-311 G(d,p) basis set was used, 18 which includes d-type polarization for second row elements and p-type polarization functions for hydrogen atoms.The Berny method was used in optimizations. 19,20Only one imaginary frequency characterized all studied TSs.The intrinsic reaction coordinate (IRC) paths 21 were carried out to find the unique connection given between the TSs and the minimum stationary points. 22,23Solvent effects of benzene were considered by full optimization of the gas phase structures at the same computational level using the polarizable continuum model 24,25 (PCM) in the framework of the self-consistent reaction field [26][27][28] (SCRF).Values of xB97X-D/6-311G(d,p) enthalpies, entropies and Gibbs free energies in benzene were calculated with standard statistical thermodynamics at 20 C and 1 atm, 18 by PCM frequency calculations at the solvent optimized structures.
The GEDT 6 values were estimated by Natural Population Analysis 29,30 (NPA), using the equation GEDT(f) ¼ X q2f q, where q are the atoms of one of the two frameworks (f) at the TSs.CDFT reactivity indices, 10,11 computed at the B3LYP/6-31G(d) level, were calculated through the equations given in reference. 11All calculations were carried out with the Gaussian 16 suite of programs. 31he topology of the electron localization function 32 (ELF) of the xB97X-D/6-311G(d,p) monodeterminantal wavefunctions was carried out using the TopMod 33 package with a cubical grid of step size of 0.1 Bohr.The GaussView program 34 was used to visualize molecular geometries of all the systems as well as the position of the ELF basin attractors.

Results and discussion
The present MEDT study has been divided into five sections: i) first, an ELF topological analysis of the electronic structures of NQ 5, NQ:Cr(CO) 3 complex 6, and cyclic dienes 4, 7, 8 is performed; ii) next, the reactivity of the reagents is analyzed by using the CDFT reactivity indices; iii) then, the reaction paths associated with the P-DA reactions of NQ 5 with Cp 4, in the absence and in the presence of the Cr(CO) 3 complex, are studied; iv) the reaction paths associated with the P-DA reactions of NQ 5 with Ch 7 and ChOMe 8, in the absence and in the presence of the Cr(CO) 3 complex, are investigated; and finally, v) in the last section, the catalytic effect of the Cr(CO) 3 complex in the P-DA reaction of NQ:Cr(CO) 3 complex 6 with Cp 4 is evaluated.
3.1.ELF analysis of the electronic structures of NQ 5, NQ:Cr(CO) 3 complex 6 and cyclic dienes 4, 7, 8 The topological analysis of the ELF 32 permits a quantitative characterization of the electronic structure of molecules. 35Consequently, in order to understand the changes in the electron density distribution in NQ 5 with the coordination to the Cr(CO) 3 complex, a topological analysis the ELF of NQ 5 and the NQ:Cr(CO) 3 complex 6 was first carried out.The ELF basin attractor positions and the most relevant valence basin populations of these species and cyclic dienes 4, 7, 8 are shown in Figure 1.ELF analysis of NQ 5 shows the presence of a pair of disynaptic basins, V(C5,C6) and V'(C5,C6), integrating a total of 3.31e, a V(C6,C7) disynaptic basin, integrating 2.23 e, a V(C7,O) disynaptic basin, integrating 2.36 e, and a pair of monosynaptic basins, V(O) and V'(O), integrating 2.60 and 2.62 e, respectively.While the V(C5,C6) and V'(C5,C6) disynaptic basins are associated with a depopulated C5 À C6 double bond, the V(C7,O) disynaptic basin is related to a very depopulated carbonyl C À O bond.The two V(O) and V'(O) monosynaptic basins are associated with the non-bonding electron density of the carbonyl oxygen.
ELF analysis of the quinone framework of the NQ:Cr(CO) 3 complex 6 shows a great similitude to that of NQ 5. Minimal changes in the populations of the valence basins are observed.The C5 À C6 partial double bond is characterized by the presence a pair of disynaptic basins, V(C5,C6) and V'(C5,C6), integrating a total of 3.30 e.Consequently, coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 does not cause any remarkable change at the ethylenic C5 À C6 bonding region of NQ:Cr(CO) 3 complex 6.
The C1 ¼ C2 À C3 ¼ C4 bonding regions of Cp 4 and Ch 7 are characterized by the presence of a pair of disynaptic basins, V(C1,C2) and V'(C1,C2), integrating a total of ca.3.40 e, and one V(C2,C3) disynaptic basin, integrating ca.2.20 e.The C3 À C4 bonding region is similar to the C1 À C2 one.The introduction of a methoxy -OCH 3 group at the C1 carbon of Ch 7 practically does not modify the electronic structure of the diene system of 8.Only the population of C1 À C2 bonding region has increased by 0.20 e.

Conceptual DFT analysis of the reagents
The reactivity indices defined within CDFT 10,11 have shown to be powerful tools to understand the reactivity in polar reactions. 12The CDFT indices were calculated at the B3LYP/6-31G(d) computational level since it was used to establish the electrophilicity and nucleophilicity scales. 11he global reactivity indices, namely, the electronic chemical potential l, chemical hardness g, electrophilicity x and nucleophilicity N indices, of NQ 5, NQ:Cr(CO) 3 complex 6 and cyclic dienes 4, 7, 8 are shown in Table 1.
The electronic chemical potential 36 l of cyclic dienes 4, 7, 8, l > À3.03 (4) eV, are significantly higher than those of NQ 5, l ¼ À5.17 eV, and the NQ:Cr(CO) 3 complex 6, l ¼ À4.84 eV, indicating that the corresponding DA reactions will have polar character, being classified as forward electron density flux (FEDF) reactions. 37he chemical hardness 36 g of NQ 5 is 4.00 eV, which decreases by more than one unit in the NQ:Cr(CO) 3 complex 6, 2.59 eV.These results suggest that the resulting complex with Cr(CO) 3 is a much softer species than the individual compound.
The electrophilicity 8 x and nucleophilicity 9 N indices of NQ 5 are 3.34 and 1.95 eV, respectively, being classified as a strong electrophile and a marginal nucleophile within the electrophilicity and nucleophilicity scales. 11Consequently, NQ 5 will only participate as a strong electrophile in P-DA reactions.Coordination of the Cr(CO) 3 complex to NQ 5 increases the electrophilicity x and the nucleophilicity N indices of the NQ:Cr(CO) 3 complex 6 to 4.52 and 2.99 eV, respectively.Now, the NQ:Cr(CO) 3 complex 6 is classified as a superelectrophile 12 and on the borderline of strong nucleophiles.
The electrophilicity x and nucleophilicity N indices of cyclic dienes Cp 4 and Ch 7 are 0.83 (4) and 0.89 (7) eV, and 3.36 (4) and 3.53 (7) eV, respectively, being classified on the borderline between marginal and moderate electrophiles, and as strong nucleophiles.Inclusion of the electron-releasing (ER) methoxy group in Ch 7 decreases the electrophilicity x index of ChOMe 8 to 0.73 eV and increases its nucleophilic N index to 4.01 eV.Now, 8 is classified as a supernucleophile. 12onsequently, the present CDFT analysis indicates that pairing a superelectrophile such as NQ:Cr(CO) 3 complex 6 with strong to supernucleophiles such as Cp 4, Ch 7, and ChOMe 8, will lead to favorable P-DA reactions.

Study of the P-DA reactions of NQ 5 with Cp 4 in the absence and in the presence of the Cr(CO) 3 complex
In order to understand the role of the Cr(CO) 3 complexation to the aromatic ring of NQ 5 in the P-DA reaction with Cp 4, the P-DA reactions of NQ 5 with Cp 4, in the absence and in the presence of the Cr(CO) 3 complex, were studied (see Scheme 4).For these P-DA reactions, two endo/exo stereoisomeric reaction paths associated with the two approach modes of Cp 4 to the C5 À C6 double bond of NQ 5 were considered.On the other hand, the presence of the Cr(CO) 3 complex coordinated to the aromatic ring of 5 causes the presence of two additional stereoisomeric approach modes of Cp 4 with respect to the two faces of the C5 À C6 double bond of the NQ:Cr(CO) 3 complex 6, labeled anti and syn; these stereoisomeric reaction paths were also considered.Analysis of the stationary points associated with these P-DA reactions indicates that they take place through a one-step mechanism.The xB97X-D/6-311G(d,p) gas phase relative energies are given in Table 2, while the absolute electronic energies are given in Table S1 in the Supporting Information.Some appealing conclusions can be drawn from the relative energies given in Table 2: i) the gas phase activation energy associated with the P-DA reaction of NQ 5 with Cp 4 has a relatively low value, 8.5 (TS-I-n) kcalÁmol À1 , as a consequence of the polar character of this DA reaction, 5 which is exothermic by À28.3 (CA-I-n) kcalÁmol À1 .Note that the N-DA reaction of styrene 14 with Cp 4 has an activation energy of 15.9 kcalÁmol À1 ; 16 ii) this P-DA reaction is highly endo stereoselective as TS-I-x is located 2.5 kcalÁmol À1 above TS-I-n; iii) coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 decreases the activation energy of the P-DA reaction to 7.8 (TS-I-Cr-na) kcalÁmol À1 , and slightly decreases the endo stereoselectivity as TS-I-Cr-xa is located 2.4 kcalÁmol À1 above TS-I-Cr-na; iv) the presence of the Cr(CO) 3 complex coordinated to the aromatic ring of NQ 5 causes some hindrance along the syn approach mode of Cp 4 to the C5 À C6 double bond of the NQ:Cr(CO) 3 complex 6, making TS-I-Cr-ns to be located 1.2 kcalÁmol À1 above TS-I-Cr-na.Consequently, in gas phase, the P-DA reaction of NQ 5 with Cp 4 is somewhat anti selective in the presence of Cr(CO) 3 ; and finally, v) the low decrease in the activation energy of the P-DA reaction of the NQ:Cr(CO) 3 complex 6 with respect to that of NQ 5, 0.7 kcalÁmol À1 , shows the marginal catalytic role of the Cr(CO) 3 complex in this P-DA reaction (see later).This decrease is even lower than that observed in the N-DA reaction between styrene:Cr(CO) 3 complex 12 and Cp 4, 2.1 kcalÁmol À1 . 16nti facial selectivity can be easily explained by the hindrance caused by the presence of the Cr(CO) 3 complex to the approach of Cp 4 along the syn face.Endo stereoselectivity is more difficult to explain as it is determined by a combination of well-known factors, such as solvent effects, steric interactions, hydrogen bonds (HBs), electrostatic forces, and others. 38In P-DA reactions it has been proposed that the favorable electronic interactions appearing in the endo zwitterionic TSs, which increase with the polar character of the cycloaddition reaction, are responsible for the endo stereoselectivity. 39,40nclusion of solvent effects of benzene in the optimizations of the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Cp 4 does not practically modify the relative energies, as a consequence of the very low polar character of benzene (see Table 2 and Table S1 in the Supporting Information).In benzene, the endo stereoselectivity of the P-DA reaction of the NQ:Cr(CO) 3 complex 6 slightly increases, with TS-I-Cr-xa being 2.8 kcalÁmol À1 above TS-I-Crna, while the anti facial selectivity notably increases with TS-I-Cr-ns being 2.1 kcalÁmol À1 above TS-I-Cr-na.
The thermodynamic data of the P-DA reaction of the NQ:Cr(CO) 3 complex 6 with Cp 4 were subsequently analyzed.Relative enthalpies, entropies, and Gibbs free energies, computed at 20 C in benzene, are given in Table 3, while the absolute values are given in Table S2 in the Supporting Information.Addition of the thermal corrections to the electronic energies in benzene increases the relative enthalpies of the P-DA reaction of the NQ:Cr(CO) 3 complex 6 by between 1.2 and 3.7 kcalÁmol À1 (see Tables 2 and 3).The activation enthalpies associated with the TSs are only increased by less than 1.4 kcalÁmol À1 .Inclusion of entropies to enthalpies increases the relative Gibbs free energies by between 13.7 and 16.0 kcalÁmol À1 due to the unfavorable activation entropies associated with this bimolecular reaction, which are found in the range À46.9 and À54.7 calÁmol À1 ÁK À1 .The activation Gibbs free energy associated with this P-DA reaction via TS-I-Cr-na rises to 22.2 kcalÁmol À1 ; formation of CA-I-Cr-na remains exergonic by À11.5 kcalÁmol À1 .Considering the activation Gibb free energies, the P-DA reaction of the NQ:Cr(CO) 3 complex 6 with Cp 4 is completely endo stereo and anti facial selective, with TS-I-Cr-xa and TS-I-Cr-ns being 2.8 and 3.3 kcalÁmol À1 , respectively, above TS-I-Cr-na, in complete agreement with the experimental results. 14he geometries of the TSs involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Cp 4 are given in Figure 2. Except for the anti TS-I-Cr-na and TS-I-Cr-xa, which show some asynchronicity, the other four TSs correspond to synchronous C À C single bond formation processes.At the six TSs, the distances between the two pairs of interacting carbons are found in the short range of 2.18 À 2.24 Å.As the C À C single bond formation takes place in the short range of 1.9 À 2.0 Å, 6 these distances indicate that formation of the new C À C single bond has not begun yet at any TS.The endo TSs are slightly more advanced than the exo ones.
The geometrical data shown in Figure 2 indicate that coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 does not substantially modify the geometries of the four TSs.On the other hand, the inclusion of solvent effects of benzene in the geometrical optimizations neither modifies the gas phase geometries noticeably (see Figure 2).
The analysis of GEDT 6 at the TSs permits to establish the polar character of these DA reactions.GEDT values lower than 0.05 e correspond to non-polar processes, while values higher than 0.20 e correspond to polar processes.GEDT values at the six TSs are given in Table 4.The high GEDT value found at the most favorable endo TS-I-n of the DA reaction between NQ 5 and Cp 4, 0.21 e, permits its classification as a polar reaction. 5This P-DA reaction, in which the electron density at the TS-I-n fluxes from the diene to the ethylene, is classified as FEDF, 37 in agreement with the previous CDFT analysis.Coordination of the Cr(CO) 3 complex to NQ 5 slightly increases the GEDT at TS-I-Cr-na to 0.23 e.The GEDT at TS-I-Cr-na is only 0.02e higher than that at TS-I-n, in clear agreement with the low acceleration found in the P-DA reaction of the NQ:Cr(CO) 3 complex 6.
Finally, an ELF 32 comparative study of the electronic structures of the more favorable endo TS-I-n and endo/anti TS-I-Cr-na involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Cp 4 was performed in order to analyze the electronic changes caused by the coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5.The positions of the ELF basin attractors of TS-I-n and TS-I-Cr-na, together with the populations of the more relevant ELF valence basins involved in these P-DA reactions, are shown in Figure 3.
A comparison of the ELF basin attractors and populations of the more relevant valence basins of endo TS-I-n and endo/anti TS-I-Cr-na shows a complete similitude between them.The two TSs show the depopulation of the C1 À C2 and C3 À C4 bonding regions, by a total of ca.0.90 e, and the C5 À C6 one, by ca.0.53 e, with respect to those in NQ 5 and Cp 4. Note that at the reagents, these C À C bonding regions are characterized by the presence of two V(Cx,Cy) and V'(Cx,Cy) disynaptic basins (see Figure 1).The most relevant features of the ELF of the two endo TSs is the creation of two new monosynaptic basins, V(C5) and V(C6), with populations of 0.22 e.The electron density of these monosynaptic basins, which will be required for the subsequent formation of the new C À C single bond, 6 comes mainly from the depopulation of the C5 À C6 bonding regions.the Cr(CO) 3 complex, were further studied (see Scheme 5).For these P-DA reactions, only the two endo/exo stereoisomeric reaction paths associated with the more favorable anti approach modes of Ch 7 and ChOMe 8 to the C5 À C6 double bond of NQ 5 were considered.Analysis of the stationary points associated with these P-DA reactions indicates that they take place through a one-step mechanism.The xB97X-D/6-311G(d,p) gas phase relative energies are given in Table 5, while the absolute electronic energies are given in Table S3 in the Supporting Information.Some appealing conclusions can be drawn from the relative energies given in Table 5: i) the activation energy of the P-DA reaction between NQ 5 and Ch 7, 12.0 (TS-II-n) kcalÁmol À1 , is 3.5 kcalÁmol À1 higher than that with Cp 4; ii) coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 decreases the activation energy of the reaction involving Ch 7 by only 0.7 kcalÁmol À1 ; iii) the activation energy of the P-DA reaction between the NQ:Cr(CO) 3 complex 6 and Ch 7, 11.3 kcalÁmol À1 (TS-II-Cr-na), is also 3.5 kcalÁmol À1 higher than that with Cp 4; iv) the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Ch 7 are completely endo selective as TS-II-x and TS-II-Cr-xa are located 3.1 and 2.8 kcalÁmol À1 above TS-II-n and TS-II-Cr-na; vi) the inclusion of the ER -OCH 3 group on the C1 carbon of Ch 7 substantially reduces the activation energy of the P-DA reaction of NQ 5 with ChOMe 8 to 4.5 (TS-III-n) kcalÁmol À1 ; vii) coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 decreases the activation energy of the P-DA reaction involving ChOMe 8 by 1.6 kcalÁmol À1 ; viii) the two P-DA reactions of ChOMe 8 are endo selective as TS-III-x and TS-III-Cr-xa are located 3.3 and 3.0 kcalÁmol À1 above TS-III-n and TS-III-Cr-na; x) the strong exothermic character of these P-DA reactions, higher than À31.6 (CA-III-x) kcalÁmol À1 , makes them irreversible.Consequently, the reaction products are obtained by a kinetic control.The activation energies of the P-DA reactions of NQ:Cr(CO) 3 complex 6 with Cp 4, Ch 7 and ChOMe 8 decrease in the order 11.3 (TS-II-Cr-na) > 7.8 (TS-I-Cr-na) > 2.9 (TS-III-Cr-na) kcalÁmol À1 , in reasonable agreement with the experimental reaction conditions (see Scheme 2). 14nterestingly, the inclusion of the ER -OCH 3 group on the C1 carbon of Ch 7 causes a more effective acceleration in these P-DA reactions than the coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5.
On the other hand, it is also worth noting that the P-DA reaction of NQ:Cr(CO) 3 complex 6 with Cp 4 via TS-I-Cr-na presents lower activation energy, 7.8 kcalÁmol À1 , than that with Ch 7 via TS-II-Cr-na, 11.3 kcalÁmol À1 (see Tables 2 and 5), despite Ch 7, N ¼ 3.53 eV, is slightly more nucleophilic than Cp 4, N ¼ 3.36 eV (see Table 1).In P-DA reactions, the GEDT taking place at the TSs has a decisive role in activation energies. 41However, there may be other structural factors that may influence the activation energy.In the case of the P-DA reaction involving the fivemembered Cp 4, the loss of the ring-strain taking place on going to TS-I-Cr-na can be an additional factor reducing the activation energy with respect to that of six-membered Ch 7 via TS-II-Cr-na.In fact, the activation energy associated with the unfavorable N-DA reaction between butadiene 1 and ethylene 2 (see Scheme 1), 24.8 kcalÁmol À1 , is reduced by 3.8 kcalÁmol À1 in the N-DA reaction between Cp 4 and ethylene 2, 21.0 kcal/mol.Note that this energy difference is similar to that found in the P-DA reactions of NQ 5 with Ch 7 and Cp 4, 3.5 kcal/mol (see Tables 2 and 5).
The geometries of the TSs involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Ch 7 and ChOMe 8 are given in Figure 4. Similar to the P-DA reaction of NQ 5 with Cp 4, the P-DA reaction with Ch 7 presents a synchronous C À C single bond formation, which is only slightly disrupted by the formation of the NQ:Cr(CO) 3 complex 6.More drastic changes are observed in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with ChOMe 8. Despite the symmetry of NQ 5 and 6, the presence of the ER -OCH 3 group on the C1 carbon of Ch 7 breaks the symmetry of these cyclic dienes, thus yielding highly asynchronous C À C single bond formation processes through asynchronous TSs in which the formation of the C4 À C5 single bond is more advanced that the C1 À C6 one.Thus, the C À C distances at the more favorable endo TSs are 2.213 (C4 À C5) and 2.264 (C1 À C6) Å at TS-II-Cr-na and 1.963 (C4 À C5) and 2.705 (C1 À C6) Å at TS-III-Cr-na.Again, formation of the NQ:Cr(CO) 3 complex 6 does not produce remarkable changes in the TSs geometries, other than increasing the asynchronicity almost imperceptibly.
GEDT values at the eight TSs are given in Table 6.The GEDT values found at the TSs involving Ch 7 are similar to those found in the P-DA reactions with Cp 4. A drastic change is observed in the TSs associated with the P-DA reactions of ChOMe 8, which show a high GEDT, higher than 0.33 e (TS-III-x).Again, coordination of the Cr(CO) 3 complex to NQ 5 slightly increases the GEDT at the more favorable endo TSs by only 0.02-0.03e.The GEDT at the endo TSs is slightly higher than at the exo TSs as a consequence of the slightly more advanced character of the former.The significantly higher GEDT found at the TSs of the P-DA reactions of ChOMe 8 with respect to that found at the TSs of the P-DA reactions of Cp 4 and Ch 7, which is a consequence of the strong electrophilic character of NQ 5 and the NQ:Cr(CO) 3 complex 6 as well as of the supernucleophilic character of ChOMe 8 (see Table 1), accounts for the higher feasibility of the experimental reaction of cyclic diene 8 (see Scheme 2).benzoquinone oxygens of 15 increased notably the electrophilicity x index of the corresponding BQ:BF 3 complex 16 to 4.94 eV (see Scheme 6 and Table 1).This behavior reduced the activation energy of the corresponding P-DA reaction by 8.6 kcalÁmol À1 .In order to evaluate the catalytic effect with the formation of the NQ:Cr(CO) 3 complex 6, the endo reaction path associated with the BF 3 LA catalyzed P-DA reaction of NQ 5 with Cp 4 was furthermore investigated (see Scheme 7).The thermodynamic data associated with this BF 3 LA catalyzed P-DA reaction are given in Table S5 in the Supporting Information.
The activation Gibbs free energy associated with the P-DA reaction of NQ:BF 3 complex 19 with Cp 4, via TS-I-BF 3 -n, is 13.1 kcalÁmol À1 , the reaction being exergonic by À13.0 kcalÁmol À1 .Consequently, the activation Gibbs free energy associated with the BF 3 LA catalyzed P-DA reaction of NQ 5 with Cp 4 is reduced by 12.4 kcalÁmol À1 with respect to that associated with the non-catalyzed P-DA reaction (see Table S4 in the Supporting Information).This strong reduction in the activation Gibbs free energy is mainly a consequence of the strong electrophilic character of NQ:BF 3 complex 19, x ¼ 4.91 eV, which is classified as a superelectrophile 12 (see Table 1).
Taking into account that these P-DA reactions take place through favorable kinetic control, the Eyring-Polanyi equation 43 (1) was used to estimate the catalytic effect of the Cr(CO) 3 complex.
From this equation, the relative reaction rate constants k rel of the reactions in the absence and in the presence of the Cr(CO) 3 and BF 3 species can be obtained as: were DDG ‡ is the relative activation Gibbs free energies of the TSs associated with the non-catalyzed and promoted reactions, R the gas ideal constant, and T the reaction temperature.
Considering the activation Gibbs free energies associated with the non-catalyzed P-DA reaction via TS-I-n, 23.3 kcalÁmol À1 , those of the P-DA reactions in the presence of Cr(CO) 3 via TS-I-Crna, 22.2 kcalÁmol À1 , and BF 3 via TS-I-BF 3 -n, 13.1 kcalÁmol À1 , and the reaction temperature, 293.15 K, the following relative rate constants can be estimated: k rel ¼ 6.4 for the reaction involving Cr(CO) 3 , and k rel ¼ 3.0x10 7 for the BF 3 LA catalyzed reaction.Consequently, the BF 3 LA catalyst accelerates the P-DA reaction of NQ 5 with Cp 4 4.7x10 6 times more than that promoted by the Cr(CO) 3 complex.Consequently, formation of the NQ:Cr(CO) 3 complex 6 has no catalytic effect when compared with LA catalyzed P-DA reactions involving BF 3 for instance. 7

Conclusions
The role of the Cr(CO) 3 coordination to the aromatic ring of NQ 5 in the P-DA reactions with cyclic dienes, Cp 4, Ch 7, and ChOMe 8, experimentally reported by D€ otz et al., 14 has been studied within MEDT by using DFT calculations at the xB97X-D/6-311G(d,p) computational level.
ELF topological analysis of the electron density at the ground state of NQ 5 and the corresponding NQ:Cr(CO) 3 complex 6 indicates that formation of the latter does not cause any remarkable change in the electronic structure of NQ 5. On the other hand, the three cyclic dienes show a similar electronic structure to that of butadiene 1.
The P-DA reaction of NQ 5 with Cp 4 is endo stereoselective and has a low activation energy, 8.5 kcalÁmol À1 , as a consequence of the polar character of the reaction.Coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 reduces the activation energy by only 0.7 kcalÁmol À1 , and slightly decreases the endo stereoselectivity; the P-DA reaction being anti facial stereoselective.While Ch 7 shows a lower reactivity than Cp 4 despite the slightly higher nucleophilicity of the former, ChOMe 8 presents the highest reactivity of this series of cyclic dienes in agreement with the experimental outcomes and its supernucleophilic character.
The activation Gibbs free energy of the P-DA reaction of NQ:Cr(CO) 3 complex 6 with Cp 4 in benzene, via TS-I-Cr-na, is 22.2 kcalÁmol À1 , the reaction being exergonic by À10.5 kcalÁmol À1 .Consequently, the experimental cycloadduct CA-I-Cr-na is obtained by kinetic control.Considering the activation Gibbs free energies, this P-DA reaction is completely endo and anti stereoselective, yielding a single cycloadduct.
Analysis of the geometrical parameters at the TSs involved in these P-DA reactions indicates that formation of the corresponding NQ:Cr(CO) 3 complex 6 does not cause any remarkable change in the TSs geometries.The P-DA reactions of the NQ:Cr(CO) 3 complex 6 with Cp 4 and Ch 7 take place through a one-step mechanism via slightly asynchronous endo TS.The presence of the -OCH 3 ER group in ChOMe 8 breaks the symmetry of Ch 7, the P-DA reaction taking place through a highly asynchronous TS-III-Cr-na.
Analysis of the GEDT at the TSs accounts for the polar character of these DA reactions of FEDF.Coordination of the Cr(CO) 3 complex to NQ 5 only increases slightly the GEDT at the most favorable TS-I-Cr-na by 0.02 e, in agreement with the poor acceleration found in these P-DA reactions.Interestingly, a high GEDT is observed in the P-DA reaction of NQ:Cr(CO) 3 complex 6 with ChOMe 8, 0.38 e (TS-III-Cr-na), as a consequence of the superelectrophilic character of the NQ:Cr(CO) 3 complex 6 and the supernucleophilic character of ChOMe 8.
An ELF topological analysis of the electron density of the endo TSs associated with the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Cp 4 indicates that coordination of the Cr(CO) 3 complex to the aromatic ring of NQ 5 does not produce any appreciable change in their electronic structure.ELF indicates that at the more favorable TS-I-Cr-na, no C À C single bond formation has started yet at this TS, in agreement with the distances between the two pairs of interacting carbons, ca.2.2 Å. 6 A comparative analysis of the decrease of the activation Gibbs free energies in the P-DA reactions of NQ:Cr(CO) 3 complex 6 and NQ:BF 3 19 with Cp 4 shows that the Cr(CO) 3 complex has no effective catalytic activity in these P-DA reactions, but only permits the reaction to take place experimentally with a total endo stereo and anti facial selectivity, yielding a single cycloadduct.

Supporting information summary
Table with the xB97X-D/6-311G(d,p) total electronic energies, in gas phase and in benzene, of the stationary points involved in the P-DA reaction of NQ 5 with Cp 4, in the absence and the in presence of the Cr(CO) 3 complex.Table with the xB97X-D/6-311G(d,p) enthalpies, entropies, and Gibbs free energies of the stationary points involved in the P-DA reaction of the NQ:Cr(CO) 3 complex 6 with Cp 4. Table with the xB97X-D/6-311G(d,p) gas phase total electronic energies of the stationary points involved in the P-DA reaction of NQ 5 with Ch 7 and ChOMe 8, in the absence and the in presence of the Cr(CO) 3 complex.Tables with the xB97X-D/6-311G(d,p) enthalpies, entropies, and Gibbs free energies of the stationary points involved in the P-DA reaction of the NQ 5 and NQ:BF 3 19 with Cp 4. Cartesian coordinates of the stationary points involved P-DA reactions of NQ 5 with Cp 4 in the absence and in the presence of the Cr(CO) 3 complex.Cartesian coordinates of the stationary points involved P-DA reactions of NQ 5 with Ch 7 and ChOMe 8, in the absence and in the presence of the Cr(CO) 3 complex.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Scheme 4 .
Scheme 4. Competitive reactions paths associated with the P-DA reactions of NQ 5 with Cp 4 in the absence and in the presence of the Cr(CO) 3 complex.

Figure 2 .
Figure 2. xB97X-D/6-311G(d,p) geometries of the TSs involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Cp 4. Distances are given in angstroms, Å. Distances in benzene are given in parentheses.

3. 4 .
Study of the P-DA reactions of NQ 5 with Ch 7 and ChOMe 8, in the absence and in the presence of the Cr(CO)3 complexIn order to understand the role of the electronic structure of the diene ring in these P-DA reactions, the DA reactions of NQ 5 with Ch 7 and ChOMe 8, in the absence and in the presence of

3. 5 .
Does the formation of the NQ:Cr(CO) 3 complex 6 have a catalytic effect?In 2009, Soto-Delgado studied the influence of LAs in the regioselectivity of P-DA reactions of 2methoxy-5-methyl-1,4-benzoquinone 15.42 Coordination of the BF 3 LA catalyst to one of

Figure 4 .
Figure 4. xB97X-D/6-311G(d,p) gas phase geometries of the TSs involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Ch 7 and ChOMe 8. Distances are given in angstroms, Å.

Table 6 .
GEDT values, in average number of electrons, e, at the TSs involved in the P-DA reactions of NQ 5 and the NQ:Cr(CO) 3 complex 6 with Ch 7 and ChOMe 8. TS-III-x 0.33 TS-III-Cr-xa 0.36

Table 2 .
xB97X-D/6-311G(d,p) relative electronic energies, in kcalÁmol À1 , of the stationary points involved in the P-DA reaction of NQ 5 with Cp 4, in the absence and the in presence of the Cr(CO) 3 complex.