DFT Conformational Studies of Chiral Bis-Binaphthyl Porphyrins and

Article pubs.acs.org/Organometallics

DFT Conformational Studies of Chiral Bis-Binaphthyl Porphyrins and Their Metal Complexes Employed as Cyclopropanation Catalysts Emma Gallo,† Eric Rose,‡ Bernard Boitrel,§ Laura Legnani,∥ and Lucio Toma*,∥ †

Dipartimento di Chimica, Università di Milano, Via Golgi 19, 20133 Milano, Italy IPCM, UMR CNRS 7201, Université P. et M. Curie, UPMC Paris 06, Bâtiment F, 4 Place Jussieu, 75252 Paris Cedex 05, France § Institut des Sciences Chimiques de Rennes, UMR CNRS 6226, Université de Rennes 1, 263 avenue du Général Leclerc, CS 74205, 35042 Rennes Cedex, France ∥ Dipartimento di Chimica, Università di Pavia, Via Taramelli 12, 27100 Pavia, Italy ‡

S Supporting Information *

ABSTRACT: Three C2-symmetrical chiral porphyrins, derived from α,α,β,β-tetrakis(2-aminophenyl)porphyrin and holding two binaphthyl handles through dimethylene, methylene, or direct connections between the binaphthyl moieties and the amidophenyl pickets, have been submitted to a theoretical study to investigate their conformational properties. The porphyrin with no methylene spacer was shown to be a very rigid molecule, whereas its higher homologues showed a certain degree of conformational freedom resulting in two molecular arrangements that give significant contributions to the equilibrium population of each compound. The effect of complexation with zinc(II) was studied through the modeling of the corresponding complexes as well as the role of two N-methylimidazoles (NMI) coordinating the apical positions of zinc in these complexes. The computational data showed that only one of the two molecular architectures accessible for the free ligands can easily accommodate NMI, indicating that the presence of an additional group on the apical coordination positions selects the geometry most suitable to host this group. Finally, the supposed intermediate radical active species in the cyclopropanation catalyzed by a cobalt(II) porphyrin complex, in which the central metal ion coordinates one NMI and the CHCOOEt carbene, were modeled together with the transition states leading to them. It was shown that the cavity originated by the binaphthyl moiety surmounting the porphyrin is not large enough to host the carbene ethyl group, suggesting the opportunity to increase the size of the cavity in order to confer it hosting capability toward the alkyl group. With the ethyl group outside the cavity, the relatively high mobility of CHCOOEt allows it to assume conformations exposing both the carbene Re and Si faces to the approaching alkene, thus leading to a poorly selective process.

■

INTRODUCTION

confirmation of the experimental data or prediction of the conformational preferences. The three binaphthyl-handled porphyrins 1−3 (Chart 1) were reported by some of us some years ago;5a their cobalt complexes were used in the asymmetric cyclopropanation of olefins performed employing 0.5% of catalytic loads. Cyclopropanation occurred with good enantioselectivity but with modest diastereoselectivity. The best result was observed in the cyclopropanation of α-methylstyrene catalyzed by the cobalt derivative of porphyrin 2; the cis and trans diastereoisomers were obtained with enantiomeric excesses of 90 and 71%, respectively, with a turnover number (TON) of 200. Even though N-methylimidazole was added as a catalytic promoter, the reaction diastereoselectivity remained modest (cis/trans 34/ 66).

Porphyrin ligands coordinating a suitable metal ion are largely employed as homogeneous catalysts to promote many organic transformations, such as cyclopropanation of alkenes.1 The reactions become stereo- and regioselective when the porphyrin ligands contain chiral units.2 Among them, binaphthyl porphyrins have proven to be interesting chiral porphyrins since the pioneering work of Groves et al.3 on asymmetric epoxidations with chiral iron porphyrins. Successively, a number of other chiral binaphthyl porphyrins have been prepared and used, after metalation with FeCl2 or CoCl2, as catalysts for epoxidation4 or cyclopropanation reactions.5 In several cases, reactions showed interesting diastereo- and/ or enantioselectivity that can be rationalized if the 3D structure of compounds is known or can be hypothesized. The geometrical features of the systems can be determined through experimental techniques such as X-ray crystallographic or NMR studies and/or through theoretical calculations that allow © 2014 American Chemical Society

Received: July 21, 2014 Published: October 3, 2014 6081

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Chart 1. Structure of the Bis-Binaphthyl Porphyrins 1 (n = 0), 2 (n = 1), and 3 (n = 2)

Figure 1. Three-dimensional plot of the global minimum conformer 1A of the binaphthyl-handled porphyrin 1 (front and side views). The CH hydrogen atoms are omitted for clarity.

Table 1. Distances (Å) of the Proximal and Distal MeO Carbon Atoms from the Centroid of the Porphyrin in the Conformers of Compounds 1−3 and in Their Zinc and Cobalt Complexes free ligand

We decided to undertake a theoretical study on these binaphthyl porphyrins to shed light from a new point of view on the reactions that their metal complexes catalyze. In fact, a complete knowledge of the geometrical features of porphyrins 1−3 and their metal complexes could allow us to achieve a better comprehension of these systems with the consequent suggestion of possible structural modifications to improve their performance. Here this computational investigation is reported and discussed in comparison with known experimental data.

prox

dist

prox

dist

1A 2AA 2BB 2AB

4.19 3.57 6.63 3.73 6.68 5.99 7.81 6.07 7.91

7.15 7.79 6.39 7.83 6.41 8.94 8.05 8.98 7.86

4.41 3.92 6.58 4.00 6.61 5.96 7.74 6.04 7.85

7.17 7.88 6.32 7.94 6.32 8.90 8.05 8.94 7.83

3AA 3BB 3AB

■

RESULTS AND DISCUSSION All of the theoretical calculations were performed within the DFT approach at the B3LYP level6 with the 6-31G(d) basis set using the Gaussian09 package.7 The large molecular size did not allow the use of larger basis sets that would give rise to unreasonably longer computational time. Each starting geometry was optimized until the standard Gaussian09 convergence criteria on maximum and rms force and maximum and rms displacement were met. Among the three compounds under investigation, ααββC1 porphyrin 1 presents the shortest binaphthyl handle; consequently, its conformational mobility is very limited. Actually, when the structure was manually built and optimized, only one minimum energy conformer could be located (1A). The porphyrin is almost planar and presents a very slightly distorted ruffled type plane; it is characterized by an averaged deviation of the meso carbon atoms with respect to the porphyrin mean plane (dmeso) of 0.10 Å and a dihedral angle between each couple of opposite pyrrole planes (τpy) of about 6°. The structure has a C2 symmetry (Figure 1), the axis passing through two opposite pyrrole nitrogen atoms. This makes equivalent the “upper” and the “lower” sides of the molecule. The distance between the proximal methoxy groups (pointing toward the tetrapyrrolic core) from the centroid of the porphyrin ring is very short, whereas the corresponding distance for the distal methoxy groups (pointing outward from the tetrapyrrolic core) is much longer (Table 1). In addition to 1A, its isomer derived from the NH tautomerism of

zinc complex

conf

cobalt complex prox

dist

3.68 6.61 3.89 6.58

7.75 6.30 7.87 6.35

the porphyrin ring was located. It is almost as stable as 1A (Erel = 0.24 kcal/mol), and its geometry is quite superimposable. A greater conformational mobility was expected for ααββC2 porphyrin 2. Therefore, in a stepwise approach to the complete analysis of its conformational properties, the simplified structure 4, devoid of one handle (Chart 2), was first modeled through the optimization of all the predictable molecular geometries. Chart 2. Structure of the Model Single-Handled Binaphthyl Porphyrins 4 (n = 1) and 5 (n = 2)

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(3.65 vs. 7.80 Å), whereas in 4B they are both at a long distance from the centroid (6.68 and 6.36 Å). Then, the second handle was added to the simplified structures 4A,B, thus preparing two starting geometries, 2AA and 2BB, the former having both handles with the same arrangement as in 4A and the latter as in 4B. A third starting geometry, 2AB, was prepared with one handle arranged as in 4A and the other one as in 4B. The three geometries were fully optimized and the energies minimized. Conformer 2AA was found to be the global minimum, and 2BB was less stable by 0.94 kcal/mol (Table 2); the mixed handle topology conformer 2AB was slightly more stable than 2BB (0.81 kcal/mol). For each of these three conformers, an isomer derived from the NH tautomerism of the porphyrin ring was located. In 2AA the porphyrin presents a ruffled type plane characterized by dmeso = 0.28 Å and τpy = 16°. The dihedral angles between the two naphthyl planes (τnaphth) are both −78°. The C2 axis makes each structural element of the upper side of the molecule equivalent with the corresponding element of the lower side. Each of them closely resembled that found in 4A. For example, the two equivalent proximal MeOs are confirmed to be very close to the centroid of the porphyrin ring and the distal MeOs very far (Table 1). Conformer 2BB shows an almost planar porphyrin ring (dmeso = 0.10 Å and τpy = 6°) and maintains the geometrical features of the handles found for 4B. In the mixed conformer 2AB the two handle topologies of 4A,B are present (Table 1). On the basis of the relative energies, the percentage populations at 298 K of the three conformers of 2 were calculated through the Boltzmann equation, doubling the weight of 2AB for statistical reasons (Table 2). Compound 5 was modeled, and a number of different conformers were located. Table 3 shows that two of them, 5A,B, are significantly more stable than the others so that they account for more than 95% of the overall population. They are characterized by extended arms supporting the binaphthyl moiety, as can be seen from the values of the torsional angles τ1/τ1′ (N−CO−CH2−CH2), τ2/τ2′ (CO−CH2−CH2−C3′), and τ3/τ3′ (CH2−CH2−C3′−C2′), reported in Table 3, and from Figure 3. Also in this case the second handle was added to the simplified structures 5A,B, thus giving 3AA,BB,AB, which were fully optimized. Rather unexpectedly, the 3BB conformer is the global minimum and 3AB,AA are less stable by about 1 kcal/mol, the greater stability of 3BB being probably due to a better compatibility of the handle topology with the porphyrin puckering. For each of these three conformers, an almost isoenergetic isomer, derived from the NH tautomerism of the porphyrin ring, was located. In 3BB the porphyrin presents a ruffled type distorted plane characterized by dmeso = 0.16 Å and τpy = 9°. The dihedral angles between the two naphthyl planes (τnaphth) are both −75°. The two equivalent proximal MeOs are very distant from the centroid of the porphyrin ring as well as the distal MeOs (Table 1). Conformer 3AA shows a less distorted porphyrin ring (dmeso = 0.11 Å and τpy = 6°) and the MeOs at long distances from the centroid. In the mixed conformer 3AB the two handle topologies of 5A,B are present with features almost superimposable with those found in the single-handled compounds and in the corresponding homogeneous double-handled compounds. Data described above for compounds 1−3 can be compared with their experimental 1H NMR data.5a In particular, the chemical shift of the MeOs are diagnostic of their position with respect to the porphyrin system. For the proximal MeOs of 1 negative values of chemical shifts have been reported (δH

As expected, different molecular arrangements were located (Figure 2): 4A,B, which are almost isoenergetic conformers,

Figure 2. Three-dimensional plots of the minimum energy conformers of the model single binaphthyl-handled porphyrin 4. The CH hydrogen atoms are omitted for clarity.

and 4C, which is largely less stable than the other two. On the basis of the relative energy, the percentage populations at 298 K of the three conformers of 4 were calculated through the Boltzmann equation (Table 2), showing that conformer 4C Table 2. Relative Energies (Erel, kcal/mol), Population Percentages at 298 K (%),a and Selected Torsional Angles (deg)b of the Located Conformers of Compounds 4 and 2 conf

Erel

pop. %

τ1

τ2

τ1′

τ2′

τnaphth

4A 4B 4C 2AA 2BB 2AB

0.00 0.23 12.54 0.00 0.94 0.81

59.6 40.4 0.0 58.3 12.0 29.7

−52 126 34 −50 127 −52 125

148 −64 82 147 −63 148 −63

−78 −97 72 −79 −97 −77 −97

83 134 −117 83 133 83 134

−76 −68 −58 −78 −68 −77 −68

a

The weight of 2AB was doubled for statistical reasons. bDefinitions: τ1/τ1′, N−CO−CH2−C3′; τ2/τ2′, CO−CH2−C3′−C2′; τnaphth, C2′− C1′−C1″−C2″ (Chart 2).

does not give any contribution to the overall population. The main difference in the geometry of the conformers is in the orientation around the two C−C bonds of the two methylenes, described by the torsional angles τ1/τ1′ (N−CO−CH2−C3′) and τ2/τ2′ (CO−CH2−C3′−C2′) (Table 2 and Chart 2). This makes 4B the most “open” structure and 4C the most “closed” one; in the latter case a severe steric contact of one of the naphthalenes with the opposite meso phenyls causes a great destabilization of the structure that makes it an unpopulated conformer. The two nonequivalent methoxy groups show variable distances from the centroid of the porphyrin. In 4A the proximal MeO is at a shorter distance than the distal group 6083

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Table 3. Relative Energies (Erel, kcal/mol), Population Percentages at 298 K (%),a and Selected Torsional Angles (deg)b of the Located Conformers of Compounds 5 and 3 conf

Erel

pop. %

τ1

τ2

τ3

τ1′

τ2′

τ3′

τnaphth

5A 5B 5C 5D 5E 5F 5G 5H 5I 3AA 3BB 3AB

0.00 0.02 2.16 2.16 2.33 2.53 2.98 3.21 3.93 1.11 0.00 0.99

48.3 46.9 1.3 1.3 0.9 0.7 0.3 0.2 0.1 12.6 66.8 20.6

180 148 −175 −57 84 148 155 62 133 178 143 176 142

−172 179 −172 −176 −165 −174 −108 73 −48 −173 176 −173 177

70 75 70 −75 159 70 62 −130 −58 70 74 70 75

125 −160 −104 −146 91 −61 −91 −150 −122 127 −158 130 −155

166 69 −174 67 −177 −64 −170 75 70 166 69 164 68

66 68 −77 70 72 171 −75 77 101 66 68 66 69

−69 −75 −63 −73 −66 −69 −71 −67 −69 −69 −75 −70 −74

a The weight of 3AB was doubled for statistical reasons. bDefinitions: τ1/τ1′, N−CO−CH2−CH2; τ2/τ2′, CO−CH2−CH2−C3′; τ2/τ2′, CH2−CH2− C3′−C2′; τnaphth, C2′−C1′−C1″−C2″.

conformer 2BB becomes closer to that of 2AA, thus lowering the contribution of the latter conformer to the overall population and increasing that of the conformer that shows the proximal methoxy groups away from the porphyrin. In the ligand 3, no conformer with the proximal MeOs close to porphyrin was found, in agreement with the NMR data that show these groups resonating at 1.63−1.81 ppm.5a Considering that these porphyrins were employed as chiral ligands for the synthesis of cyclopropanation catalysts, the theoretical investigation of their metal derivatives was undertaken. First, a conformational analysis of zinc(II) complexes was performed to correlate this study to their already reported NMR data.5a Then, catalytically active cobalt(II) complexes were studied to rationalize previous catalytic results and suggest suitable ligand modifications able to improve the catalytic performance. In the zinc complexes of 1−3 reported by some of us,5a the influence of the central metal on the conformation of the porphyrin ligands was determined by comparing the chemical shifts of the proximal MeOs in the free ligands and in the complexes. It was observed that the insertion of the zinc atom in 1 and 3 produces small variations in the 1H NMR signals of these groups (in benzene, Δδ = 0.56 and −0.18 ppm, respectively). Conversely, a huge effect toward lower frequencies was observed in 2 (Δδ = 2.23 ppm). Thus, the zinc complexes 1-Zn−3-Zn were built by removal of the two porphyrin NH hydrogen atoms and insertion of the metal at the centroid of the tetrapyrrole system; then, these structures were fully optimized as reported above for the free ligands, using the 6-31G(d) basis set for all atoms except the effective core potential LanL2DZ basis set used for the metal ion, thus allowing us to determine the effects of the central zinc on the geometry and the energy of the various conformers. As far as complex 1-Zn is concerned, the presence of the central metal causes small changes in the geometry. The only conformer located, 1A-Zn, shows the proximal MeO methyl groups slightly farther from the centroid than in the free ligand (4.41 vs 4.19 Å, Table 1); moreover, the corresponding oxygen atoms at 4.70 Å do not coordinate zinc. The effect of zinc is much more pronounced in 2, as the energy ranking of the two conformers 2AA and 2BB is reverted. Actually, after optimization of the complexes, 2BB-Zn becomes the global minimum, more stable than 2AA-Zn by

Figure 3. Three-dimensional plots of the minimum energy conformers of the model single binaphthyl-handled porphyrin 5. The CH hydrogen atoms are omitted for clarity.

−0.65, −0.42, and −0.53 ppm, in chloroform, pyridine, and benzene, respectively). These values are in agreement with the very short distance from the centroid of the porphyrin systems reported above (4.19 Å, Table 1). Also for the proximal MeOs of 2, negative values of chemical shifts have been reported. However, in this case the value is much more solvent sensitive. In fact, whereas values of δH −0.51 and −0.42 were found in chloroform and benzene, the signal is deshielded to a value of 0.47 ppm in pyridine. This might depend on the influence of the solvent on the relative stability of the three populated conformers of 2. Thus, the energy of these conformers was recalculated using a polarizable continuum model (PCM)8 and the resulting data are summarized in Table 4. It can be seen that in pyridine, the most polar solvent, the energy of Table 4. Relative Energy Recalculated Using a Continuum Solvent Model (Erel, kcal/mol) and Population Percentages at 298 K (%)a of the Conformers of Compound 2 chloroform

a

pyridine

benzene

conf

Erel

pop. %

Erel

pop. %

Erel

pop. %

2AA 2BB 2AB

0.00 0.39 0.52

42.7 21.9 35.4

0.00 0.24 0.45

38.5 25.6 35.9

0.00 0.65 0.65

49.9 16.8 33.3

The weight of 2AB was doubled for statistical reasons. 6084

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2.63 kcal/mol, whereas 2AB-Zn shows an intermediate value of energy (1.39 kcal/mol). In 2AA-Zn the binaphthyl handles are bent toward the porphyrin systems so that the proximal MeOs, too close to zinc, destabilize the structure even if the methyl groups are pushed away to 3.92 Å from zinc in comparison to a distance from the centroid of 3.57 Å in the free ligand. Instead, in 2BB-Zn the presence of zinc does not affect the stability of the system and the metal is hosted without any perturbation (see the MeOs distances in Table 1). The great change in the energy ranking of the conformations determined by the metal on 2, and the consequent change in the population distribution, explains the large effect of zinc on the chemical shift of the proximal MeOs of 2. Conversely, in 3 the handles are far enough from the porphyrin to not be disturbed by the presence of zinc (Table 1) and the energy differences among the conformers 3AA-Zn, 3BB-Zn, and 3AB-Zn (0.97, 0.00, and 1.04 kcal/mol, respectively) remain almost unchanged with respect to the free ligand. In none of the located conformers of the three zinc complexes were the methoxy oxygen atoms found to be able to coordinate the central metal ion, always leaving unoccupied the apical positions in the coordination sphere of zinc. These positions can host ligands such as N-methylimidazole (NMI), often used as a catalytic promoter, and reactive species such as carbenes in the course of the catalytic cycle mediated by Co, Fe, or other transition-metal complexes. The additional ligands can in principle modify the geometry of the preexisting bisbinaphthyl porphyrin metal complex, with an induced fit mechanism, or can select among the accessible conformers of the metal complex the most suitable geometry. An examination of the three Zn complexes coordinated with two NMI molecules can shed light on the suitability of the metal porphyrin complexes to host additional ligands and the mechanism underlying the hosting process. The zinc complexes described in the literature5a were prepared and analyzed as mimics of the corresponding cobalt complexes. In fact, even if zinc(II) porphyrins usually display pentacoordination, the formation of octahedral complexes is also possible.9 Thus, the modeling of the zinc atom coordinated to two NMI molecules allows a better comparison of these results with those achieved by replacing the zinc(II) with a cobalt(II) atom in the tetrapyrrolic core. In this last case an octahedral cobalt active intermediate will be modeled (see below). The 1-Zn-NMI2 system was first modeled through insertion of NMI into the only populated conformer 1A-Zn. NMI was inserted into the porphyrin complexes with the unsubstituted nitrogen atom pointing toward the metal ion and its plane almost perpendicular to the porphyrin system; several starting geometries were prepared to take into account its various possible orientations (the methyl group pointing away from the binaphthyl and pointing toward it, the imidazole plane eclipsing the N1/N3 or N2/N4 porphyrin nitrogen atoms and eclipsing two opposite meso carbon atoms, etc.). There is not enough room between the handle and porphyrin to accommodate NMI without significant contacts. Thus, after the optimizations, only two minimum energy conformers were located, 1A1-Zn-NMI2 (Figure 4) and 1A2-Zn-NMI2. In both cases, the handles are forced away to minimize the steric repulsion between the proximal MeOs and NMI with lengthened proximal (4.87 Å) and distal (7.50 Å) MeOs distances from zinc; moreover, the imidazole plane, aligned along the direction of two opposite meso carbon atoms, is inclined with respect to the porphyrin

Figure 4. Three-dimensional plots of the most populated minimum energy conformers of the zinc complexes of 1−3 with Nmethylimidazole. The CH hydrogen atoms of the ligand and of NMI are omitted for clarity.

plane with an angle of 77 and 67° for 1A1-Zn-NMI2 and 1A2Zn-NMI2, respectively. The former conformer is preferred by 0.61 kcal/mol, the latter being destabilized by the unfavorable orientation of the imidazole methyl group toward one naphthalene of the binaphthyl system. When NMI was hosted by 2-Zn, building and optimizing the complexes with a procedure similar to that described above for 1A-Zn, a definite preference for the ligand geometry of conformer 2BB-Zn was found. The two conformers presenting this geometry were preferred by about 13 kcal/mol over those with the ligand in the 2AA-Zn geometry. The global minimum, 2BB1-Zn-NMI2 (Figure 4), presents the imidazole plane eclipsing the N2 and N4 porphyrin nitrogen atoms and disposed almost perpendicular to the mean porphyrin plane. The other populated geometry, 2BB2-Zn-NMI2, is less stable by 1.59 kcal/mol and differs only in the orientation of the imidazole methyl group pointing toward the binaphthyl handle. The orientations of imidazole with its plane eclipsing the N1 and N3 porphyrin nitrogen atoms are less stable by 6−7 kcal/ mol. 6085

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binaphthyl. Actually, when such structures were optimized and their energy minimized (Figure 5), a substantial difference in

Also in the case of 3-Zn a definite preference for a ligand geometry was found, with 3BB-Zn capable of better hosting. The most stable geometry of the 3AA-Zn type is 4 kcal/mol less stable than the global minimum conformer 3BB1-ZnNMI2 (Figure 4). The presence of NMI does not disturb the architecture of the ligand that can easily accommodate NMI. In this preferred geometry the imidazole plane eclipses the N2 and N4 porphyrin nitrogen atoms and is disposed almost perpendicular to the mean porphyrin plane. The other orientation of N-methylimidazole with the methyl group pointing toward the binaphthyl handle is less stable by 3.17 kcal/mol, whereas that with NMI eclipsing N1 and N3 is less stable by 2.96 kcal/mol. Attention was then focused on the cobalt complexes, which are not directly investigable by spectroscopic methods such as NMR, due to the paramagnetic character of cobalt. Conversely, the computational approach does not suffer from this limitation, so that the cobalt and cobalt/NMI complexes of ligand 2, which showed the best catalytic properties in the asymmetric cyclopropanation of alkenes,5a were submitted, with the same approach described for the zinc complexes, to the theoretical investigation with the obvious difference that an unrestricted functional was used with a doublet spin system (S = 1/2), known to be the lowest spin state in such cobalt complexes.10 Actually, after optimization of all the starting geometries obtained by replacement of zinc(II) with cobalt(II) in the zinc derivatives reported above, a strict geometrical correspondence between the cobalt and zinc complexes was found. In fact, the global minimum was found to be 2BB-Co, favored over 2AA-Co and 2AB-Co by 0.47 and 1.34 kcal/mol, respectively. In addition, the geometrical features were very similar (see the MeOs distances from the central metal in Table 1), and the Co−N distances were slightly shorter than those in the corresponding zinc complexes. The spin density was almost exclusively located on the cobalt atom. The agreement of the zinc and cobalt complexes was also observed when NMI was hosted in 2-Co. The same definite preference for the ligand geometry of conformer 2BB was maintained. The two preferred conformers 2BB1-Co-NMI2 and 2BB2-Co-NMI2 are almost superimposable with those found for the NMI zinc complexes. Moreover, it has been suggested5a that, in the reaction of cyclopropanation of α-methylstyrene with ethyl diazoacetate (EDA) catalyzed by 2-Co in the presence of NMI, the biscoordinated complex of 2-Co loses one NMI ligand and the subsequent reaction with EDA yields the active species in which the central metal coordinates the remaining NMI and the CHCOOEt carbene moiety (see Scheme S1 in the Supporting Information for the reaction mechanism). Experimental and theoretical studies, performed by de Bruin and Zhang,11 indicated the formation of a cobalt(III) carbene radical species generated by a metallo-radical activation of the diazo compound. In order to investigate how the carbene moiety can be hosted by the porphyrin ligand 2, the 2-Co-NMI-carbene complex was built by replacing one NMI with carbene in the optimized 2BB1-Co-NMI2 structure. The carbene was positioned by taking into account the geometry of the complex of cobalt porphyrin with CHCOOEt reported by Belof et al.10 Two substantially different orientations of the carbene moiety were envisaged, one with the ethyl group pointing inside the cavity originated by the binaphyl system surmounting the porphyrin and the other with the ethyl group pointing away from

Figure 5. Three-dimensional plots of the “outside” and “inside” complexes of 2-Co hosting one NMI and the CHCOOEt carbene. The CH hydrogen atoms of the ligand and of NMI are omitted for clarity. The carbon skeleton of CHCOOEt is shown in violet.

their relative stabilities was found with a neat preference (about 18 kcal/mol) for the outside orientation, indicating that there is not sufficient room in the cavity for an easy hosting of the ethyl group. Moreover, in the outside orientation the carbene moiety can assume a number of different arrangements, that reported in Figure 5 being representative of them. In both the inside and outside orientations the excess spin density is almost entirely located on the carbene carbon, with smaller densities on the carbonyl oxygen and on the metal (respectively, 0.89, 0.19, and 0.05 in the “outside” complex), in agreement with previous calculations on the much simpler system consisting of a cobalt porphyrin linking the CHCOOEt carbene.10 As reported in the Introduction, when the carbene complex reacted with α-methylstyrene to give the diastereoisomeric cis and trans cyclopropane adducts, a modest diastereoselectivity and a good enantioselectivity were observed.5a This means that all four possible approaches of the alkene to the carbene have a non-negligible probability to occur. The four intermediate radical species, derived from the attack of α-methylstyrene to the “outside” cobalt complex, were built by choosing the “parallel” arrangement of the approaching CC alkene bond with respect to the carbene carbon−cobalt bond.11c After their full optimization, similar values of relative energy were found (Table 5). In agreement with the experimentally observed preferred formation of the 1S enantiomer for both the cis and trans diastereoisomers of the cyclopropane adduct, the two intermediates derived from the attack to the Si face of the carbene was more stable by 1−2 kcal/mol than those derived from the attack to the Re face. In Figure 6 the two preferred radical species are reported, showing a very good complementarity of the ligand and the reactants hosted in its “active site”. In fact, the complex is stabilized by a hydrogen bond between the carbonyl group of the CHCOOEt carbene and an amide NH of the ligand and by a series of hydrophobic interactions, such as that between the terminal methyl group of CHCOOEt and two adjacent meso-phenyl groups. Conversely, a relatively external position is occupied by α-methylstyrene, therefore justifying the poor diastereoselectivity. The geometrical features 6086

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transition states leading to A−D were determined and the corresponding data are reported in Table 5. These data show a very good prediction of diastereoselectivity if the electronic energy is considered with a further improvement by addition of ZPE correction. The enantioselectivity is underestimated; nevertheless, the four transition states present an order of stability coherent with the experimental selectivity data.

Table 5. Relative Energies (Erel, kcal/mol) and Population Percentages at 298 K (%)b of the Intermediates Int-A−Int-D and the Transition States TS-A−Ts-D Leading to Them, Together with the Corresponding Predicted Selectivitiesa Int-A cis-(1S,2R) Int-B trans-(1S,2S) Int-C cis-(1R,2S) Int-D trans-(1R,2R) cis/trans eecis eetrans TS-A cis-(1S,2R) TS-B trans-(1S,2S) TS-C cis-(1R,2S) TS-D trans-(1R,2R) cis/transb eecisb eetransb

Erel

pop. %

(E + ZPE)rel

pop. %

0.00 0.91 1.73 1.98

76.6 16.6 4.1 2.7 80.7/19.3 89.8 71.7 38.5 30.8 4.7 26.0 43.2/56.8 78.3 8.4

0.00 0.89 1.58 1.83

74.8 16.6 5.2 3.4 80.0/20.0 87.1 66.0 32.0 40.5 3.0 24.5 35.0/65.0 83.1 24.6

0.00 0.13 1.25 0.23

0.14 0.00 1.55 0.30

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CONCLUSIONS The tree chiral porphyrins 1−3, derived from the atropoisomer α,α,β,β-tetrakis(2-aminophenyl)porphyrin and holding two binaphthyl handles on the two opposite faces through spacers of variable length, have been submitted to a theoretical study to investigate their conformational properties. The porphyrin 1 was shown to be a very rigid molecule, whereas its homologues 2 and 3 showed a certain degree of conformational freedom. This mobility derives from different orientations around the single bonds at the −CH2− and −CH2CH2− connections between the binaphthyl moieties and the amidophenyl pickets. Actually, both in 2 and 3 only two arrangements were shown to give significant contributions to the equilibrium population; their geometry was in agreement with 1H NMR data previously reported for these compounds.5a The effect of complexation with zinc(II) was studied through the modeling of the corresponding complexes as well as the role of two N-methylimidazoles coordinating the apical positions of zinc in these complexes. The computational data showed that in the case of 2 and 3 only one of the two molecular architectures accessible for the free ligand can easily accommodate NMI, indicating that the presence of an additional group on the apical coordination positions limits the conformational freedom of the ligand by selecting the geometry most suitable to host this group. Finally, the analogous complexes of porphyrin 2 with cobalt(II) were modeled together with the corresponding complex in which the central metal ion coordinates one NMI and the CHCOOEt carbene. It was shown that the cavity originated by the binaphthyl moiety is not large enough to host the ethoxycarbonyl group of the carbene, which prefers the outside orientation with a relatively high conformational mobility. Thus, it can expose, in the cyclopropanation reaction, both the Re and Si faces of its carbene carbon atom to the alkene. Moreover, the alkene approaches the carbene from a direction not affected by steric constraints, thus allowing it to assume both orientations leading to the cis and trans adducts. These results suggest the opportunity to increase the size of the cavity of the ligand to confer it hosting capability toward the ethyl group of the CHCOOEt carbene. With the ethyl in the cavity the mobility of the carbene is locked and this might result in a higher selectivity in the cyclopropanation reaction. The results described in the present paper demonstrate the usefulness of computational approaches in deepening the comprehension of porphyrin-based systems that may be of help in the design of new, better-performing catalysts. Some of us have recently reported5b the synthesis of a new chiral porphyrin where the methylene group of the porphyrin 2 chiral handle (Chart 1) was replaced by a benzylic unit, in order to strengthen the porphyrin conformation and enlarge the active space. The corresponding iron(III) complex promoted the cyclopropanation of alkenes with very high enantio- and diastereoselectivity.5b A theoretical investigation of this iron(III) porphyrin complex is currently in progress, and the results will be published in due course.

a

Experimental values: cis/trans 34/66; eecis 90%; eetrans 71%. bThe enantioselectivity prediction worsens if the entropic contribution is considered (eecis = 72.3%, eetrans = −17.3%), while the diastereoselectivity prediction is unaffected (cis/trans 35.1/64.9).

Figure 6. Three-dimensional plots of the intermediate radical species derived from the attack of α-methylstyrene to the Si face of the “outside” cobalt complex of 2-Co, hosting one NMI and the CHCOOEt carbene: (A) intermediate leading to the cis (1S,2R)cyclopropane adduct; (B) intermediate leading to the trans (1S,2S)cyclopropane adduct. The CH hydrogen atoms of the ligand and of NMI are omitted for clarity. The carbon skeletons of CHCOOEt and α-methylstyrene are shown in violet and green, respectively.

and the spin density distributions of these intermediates are in good agreement with those reported by de Bruin et al.11c for the reaction of cobalt porphyrin with methyl diazoacetate and methyl acrylate or styrene. In this reaction, the step leading to intermediates A−D is the rate-determining step11c and, on kinetic grounds, it should determine the observed selectivity. However, as can be seen in Table 5, whereas the enantioselectivity is very well rationalized from the relative energy values of the four intermediates, the diastereoselectivity is not, even if the ZPE correction is considered. Thus, the energies and the geometries of the four 6087

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Article

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ASSOCIATED CONTENT

S Supporting Information *

A text xyz file of all computed molecule Cartesian coordinates in a format for convenient visualization, computational details, and the suggested mechanism for the cyclopropanation reaction. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Italian Ministry of University and Research (PRIN 201011 grant, prot. 2010JMAZML, Italian network for the development of multivalent nanosystems) is gratefully acknowledged for financial support. CINECA is also acknowledged for the allocation of computer time.

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