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Torquoselectivity in Cyclobutenes Ring Openings and the Interatomic Interactions That Control Them Jose Enrique Barquera-Lozada J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b08771 • Publication Date (Web): 10 Oct 2016 Downloaded from http://pubs.acs.org on October 15, 2016

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The Journal of Physical Chemistry

Torquoselectivity in Cyclobutenes Ring Openings and the Interatomic Interactions That Control Them José Enrique Barquera-Lozada* Instituto de Química, Universidad Nacional Autónoma de México, Circuito exterior, Ciudad Universitaria, Coyoacán, México, D.F., México 04510

Abstract Torquoselectivity has explained diasteromeric preferences of a number electrocyclic ring openings. The quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D) and the interacting quantum atoms (IQA) energy partition method are used to evaluate qualitatively and quantitatively the atomic interactions behind the torquoselectivity of a series of 3-substituted cyclobutenes. ELI-D topology and IQA's energies show that the interaction between the distal terminus carbon atom of cyclobutene (C4) with the substituent at C3 (R5) in the transition state governs torquoselectivities. In case of 3-borylcyclobutene, this interaction is so strong that a protocovalent bond is actually formed between B5 and C4. The evaluation of the inter-atomic energies allowed us to identify an additional interaction that contribute to a minor extent to the stabilization of the TS. Despite the fact that C4,R5 interaction is the main cause of the torquoselectivity, a bonding path (BP) between these two atoms was not observed. However, the lack of a BP between C4 and R5 does not mean that the topology of the electron density was not affected by the interaction of these two atoms. Surprisingly, we found a strong correlation between the density at the bond critical point (BCP) and the BP shape of C3-C4 breaking bond with the observed activation energies and torquoselectivities.

Introduction According to Woodward and Hoffmann rules, there are two allowed conrotatory mechanisms for a 4n electrons electrocyclic reaction and two disrotatory for a 4n + 2 electrons electrocyclic reaction. Before 1984, it was thought that steric effects were responsible for the observed preference for one of the two

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possible stereoisomers produced by these reactions. That same year a set of experiments questioned the steric effect explanation for the diasteromeric preferences in 3,4-disubstituted cyclobutenes ring openings.1 Soon after, Houk et al. explained the diasteromeric preference by means of molecular orbital (MO) theory and it became clear that the observed preference was due to electronic effects.2 Houk and coworkers named this type of stereoselectivity, torquoselectivity. Torquoselectivity is the energetic difference between the transition state (TS) in which a terminal substituent in an electrocyclic ring opening rotates inward and the TS in which this substituent rotates outward. This selectivity was explained based on the energies of the HOMO and LUMO of the TS of cyclobutene electrocyclic ring opening.2,3 The HOMO is a breaking σ-bond orbital, therefore, the TS is a good electron donor, while the LUMO is the C3-C4 σ*-antibond orbital, then, the TS is also a good electron acceptor. In an inward rotation, a substituent in the position 3 or 4 with a filled π-orbital overlaps with the also filled breaking σ-bond orbital (Scheme 1). This four electron interaction raises the energy of this particular TS. On the other hand, in an outward rotation there is little overlap between the substituent π-orbital and the C3-C4 σ-bond orbital. If the substituent has an energy low lying empty π-orbital, the inward rotation would be favored, as the 2-electron interaction between the σ-bond orbital and the empty π-orbital stabilize the inward TS. Since there is little overlap between the C3-C4 σ-bond and a substituent π-orbital in an outward rotation, the outward TS is not stabilized by this interaction. The torquoselectivity concept was later extended for systems with larger rings (1,3cyclohexadienes, cyclopentyl cation)4–9 or systems with substituents without π-orbitals.10–13 An interesting case are silyl substituted cyclobutenes. It has been found experimentally that the silyl group promote a preference for the inward rotation product, in contrast, a methyl group produces an outward product. Several explanations were given for this effect, but the most convincing one is the one given by Murakami and Houk.10,11 According to them, the stabilization of the inward TS comes from the interaction between the substituent Si-R σ*-antibond orbital with the C3-C4 σ-bond orbital of the cycle. This interaction is stronger in silyl substituted cyclobutenes than in methyl substituted ones, as the LUMO for the silyl (Si-R σ*) is lower in energy than the methyl (C-R σ*). These are just a few examples, where the concept of torquoselectivity was used to explain the observed reactivity. Torquoselectivity is one the concepts born from computational chemistry that had proved it usefulness in many experimental chemistry studies.3,14–22


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Scheme 1. Even though MO theory has successfully explained the observed torquoselectivity trends, a quantitative evaluation of the energies of the most important inter-atomic interactions that stabilize inward and outward TSs has not yet been possible. One the most successful theories that had been largely used for studying the chemical bonding is the quantum theory of atoms in molecules (QTAIM).23–32 QTAIM uses the electron density to study well defined localized parts of a system, instead of dealing with the whole molecule. The electron density can be obtained from ab initio calculations and directly from X-ray diffraction experiments. Moreover, QTAIM allows classifying interactions within a molecule with the molecular graph (set of bond-paths (BP) and its critical points (CP) that define its molecular structure). As mentioned, QTAIM has helped in the understanding of several reactions, among them are the pericyclic reactions.33–37 For example, Calvo-Losada et al. found that the patterns in the topology of the laplacian of the electron density (∇2ρ(r)) can be used to distinguish between pericyclic and pseudopericyclic [4 + 2] cycloadditions.36 Rode et al. used the ellipticity at the bond critical points to distinguish pericyclic and pseudopericyclic [2 + 2] cycloadditions of cumulenes.33 Another scalar function that has been used to study the chemical bond, with a lot of success, is electron localization function (ELF).38–41 This scalar field is closely related to the electron localizability indicator(ELI-D) but the later does not use a free electron gas as an arbitrary reference.42–45 Using Thom's catastrophe theory, ELF function has also been used to study reaction paths of several types of reactions.46–48 One of those reactions is the cyclobutene ring opening mechanism.49–51 In these studies, Andrés and Morales-Bayuelo had found that the reaction mechanism for the cyclobutene ring opening is a pseudo radical electronic reorganization and not a pericyclic reorganization. Unlike electron density, both, ELF and ELI-D, include information of electron pairing, by means of the inclusion of pair density integrals. The electron pairing is a fundamental idea in the Lewis concept of bond. Following this line of thoughts, Blanco and coworkers developed the 3 ACS Paragon Plus Environment


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interacting quantum atoms (IQA) energy partition method.52 Using the atomic basins derived from the electron density, this method allows to calculate the atomic energies, even if the virial theorem is not fulfilled, such as a system that is not in a stationary state. Furthermore, it allows the partition of the atomic energy in intra and inter atomic terms. The inter-atomic term is the sum of the IQA's interaction energies between a specific atom and all the remaining atoms in the molecule. The capability of IQA partition scheme to define atomic energies and interaction atomic energies has been widely used in the description of several chemical bond scenarios.53–58 In this contribution, with the aid of QTAIM, ELI-D topology and IQA energies, we quantify the energy of the atomic interactions that are mainly responsible for the observed torquoselectivity trends and the effect that such interactions have over the electron density distribution.

Computational methodology All the structures were geometry optimized without any constrain with the M06-2x/6311+G(2d,p) method.59 M06-2x functional has proved to be a good choice for the calculation of activation energies.60 A frequency calculation was performed for all TSs and ground states to check that only one or no frequencies were imaginary, respectively. Intrinsic reaction coordinates (IRC) was calculated for TSs, in order to get the reaction path of the analyzed ring openings. All these calculations were done with Gaussian 09 sofware.61 The wave functions extracted from the Gaussian 09 calculations were used to perform a topological analysis of ρ(r), ∇2ρ(r) and ELI-D fields. The ρ(r) and

∇2ρ(r) topology was obtained with Aimall62 and Dgrid63 software. Both softwares give essentially the same results. ELI-D topology and maps were obtained with Dgrid software. The molecular graphs showed in this contribution were plotted with Aimall. The contour maps of ∇2ρ(r) and ELI-D were plotted with Paraview software. The IQA's calculations were done with Aimall. Since DFT methods do not provide a well defined second order density matrix, the inter-atomic VxAB term cannot be unambiguous defined. In Aimall for the M06-2x method, the VxAB term is just approximately calculated. However, in this contribution we analyze relative trends. The main objective of this work is to understand the torquoselectivity of a series of 3-substituted-cyclobutene ring openings. The correlation between the torquoselectivities calculated from the sum of the IQA atomic energies with the same torquoselectivities but calculated from ab initio energies is almost perfect (R2 = 0.99). Then, the observed trends are fully recovered and the conclusion reached from IQA energies are valid.


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Results and Discussion The activation energies for a series of electrocyclic ring openings of 3-substituted cyclobutenes were calculated at M06-2x/6-311+G(2d,p) level (Table 1). In general, the energetic barriers are significantly lower than the ones previously obtained with HF/small-basis set and are higher than the ones calculated with the B3LYP functional.4,10,64 It is well known that almost always, M06-2x functional gives higher barriers than B3LYP functional.59,60 Despite these differences, the energetic trends are very similar.

Table 1. Activation energies and activation free energies of the inward and outward electrocyclic ring openings of 3-subtituted cyclobutenes calculated at M06-2x/6-311+G(2d,p) level. The corresponding torquoselectivity values (∆∆E‡ = ∆E‡,inTS – ∆E‡,outTS and ∆∆G‡ = ∆G‡,inTS – ∆G‡,outTS) are also shown. All the energies are in kcal/mol. ∆E‡,inTS ∆E‡,outTS BH2 SiF3 SiF2H SiFH2 SiH3 COOH2+ CHO COOH CO2CFH2 CF2H CF3 CH3 NH2 Cl

13.28 31.14 29.67 30.16 33.76 21.97 28.91 34.58 37.04 37.46 37.60 40.26 41.00 40.80 47.03

∆∆E‡ ∆G‡,inTS ∆G‡,outTS

31.99 -18.71 36.96 -5.82 37.61 -7.94 36.58 -6.42 36.36 -2.60 27.27 -5.30 34.15 -5.24 33.76 0.82 31.39 5.65 35.90 1.56 39.07 -1.48 39.12 1.14 34.84 6.16 24.34 16.46 32.74 14.29

13.40 30.44 29.02 29.46 32.74 20.55 28.20 33.70 35.72 36.15 36.30 38.82 39.54 39.03 45.20

∆∆G‡

30.42 -17.02 35.33 -4.90 35.85 -6.84 34.83 -5.37 34.50 -1.76 25.72 -5.17 32.66 -4.45 32.14 1.56 29.98 5.74 33.71 2.44 36.72 -0.42 36.35 2.46 32.42 7.11 22.80 16.23 31.09 14.11

Molecular graphs of inward and outward TSs. Analysis of the electron density (ρ(r)) topology and other related fields for a series of TSs of 3-substituted cyclobutene ring openings shows clear topological differences between TSs that are substituted with electron acceptor groups (e.g., BH2) and TSs that are substituted with an electron donor (e.g., Cl). Figure 1 shows the molecular graphs of the inward and outward ring opening TSs of the BH2 (strong electron acceptor) and Cl (strong electron donor) 3-substituted cyclobutenes. In all the analyzed TSs, there is an interaction path between C3 and 5 ACS Paragon Plus Environment


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C4. Moreover, ρ(r) at its bond critical point (BCP) is very small in comparison with any other C-C bond in the cyclobutene, what is indicative that the C3-C4 bond is almost broken in the TS or is already broken, as previous ELF studies of cyclobutene ring opening had suggested.49,51 Specifically, for the inward TS (inTS) of the 3-borylcyclobutene, the ρ(r) at the BCP significantly decreases. The relative density at the C3-C4 BCP ( ∆ρ(r)‡,inTS = ρ(r)inTS - ρ(r)cycloMin) is -0.918 e/Å3. Besides the low density at C3-C4 BCP, it is very clear from the molecular graph that the C3-C4 interaction path is strongly bended towards the C3-B5 bond, indeed the angle between the BPs, B5~C3~C4, is 4.8° while the geometrical angle between the C3-C4 and C3-B5 bonds, B5-C3-C4, is 58.0° (it is also possible to define a geometrical angle between the BCP at the C3-C4 BP, C3, and the BCP at C3-B5 BP, B5•C3•C4 is 36.9°). This indicates that the C3-C4 breaking bond electron density is in part shifting toward the C3-B5 bond.

Figure 1. Molecular graphs (molecular structures) BH2-inTS, b) BH2-outTS, c) Cl-inTS and d) CloutTS. The small yellow points are the BCP. The numbers close to the BCP are the relative densities ( ∆ρ(r)‡,in = ρ(r)inTS - ρ(r)cycloMin, e Å-3 ) at the BCPs. e) Plot of the difference between the R5~C3~C4 BP angle with the geometrical angle R5•C3•C4 angle (defined as the angle between the C3-C4 BCP, C3, and C3-B5 BCP) versus the activation energies of the series of inTS.


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On the other side of the series is the Cl (strong electron donor) substituted cyclobutene. In this case, the inTS has a ∆ρ(r)‡,inTS at the C3-C4 BCP of -1.117 e/Å3, what could indicate that C3-C4 bond weakens more than in the BH2 case. This is in agreement with the activation energy of its inTS. Although the direction of the C3-C4 BP bending is not very clear at first glance, when we compare Cl5~C3~C4 angle (104.9°) with Cl5-C3-C4 angle (95.2°) or with Cl5•C3•C4 angle (94.4°), it becomes clear that the BP is bending to the opposite direction in comparison to borylcyclobutene. The C3-C4 BP is bending away from the C3-R5 bond in case of chlorocyclobutene . This shows that there is no electron density shifting from the C3-C4 breaking bond toward the C3-Cl5 bond. Table 2 shows ∆ρ(r)‡ at the C3-C4 BCP and the difference between the BPs angles R5~C3~C4 with the geometrical angles R5-C3-C4 (∆θ = R5~C3~C4° - R5-C3-C4°) and R5•C3•C4 (∆φ = R5•C3•C4° - R5-C3-C4°) for the whole series of substituted cyclobutenes. In case of inTS, ∆ρ(r)‡ at the C3-C4 BCP presents a strong correlation with the activation energies (R2 = 0.91). The ∆ρ(r)‡ is higher for most stable inTSs, that are cyclobutenes substituted with strong electron acceptors. The angles differences, ∆θ or ∆φ, also show a strong correlation with the relative energies of the inTSs (figure 1e, 0.84 and 0.88, respectively). Good electron attractors bend the C3-C4 BP toward the C3-R5 bond, while good electron donors bend it away from the C3-R5 bond. On the other hand, for the outward TSs (outTS), there is no correlation between ∆E‡ and the ∆ρ(r)‡ at the C3-C4 BCP (0.08) or between ∆E‡ and ∆θ (0.04) or ∆φ (0.07). Therefore, the stabilization of outTSs is not related with C3-C4 breaking bond. The only strong correlation that we found in case of outTSs is the one between ∆E‡ and ∆ρ(r)‡ at the C3-R5 BCP (0.88). Then, the main stabilization channel in case of outTS seems to be the interaction of C3 with R5. With more evidences at hand, later in this paper, we are going to discuss it in more detail. Table 2. Relative density ( ∆ρ(r)‡,inTS = ρ(r)inTS - ρ(r)cycloMin, e Å-3 ) at the C3-C4 BCP, difference between the BPs angles R5~C3~C4 with the geometrical angle R5-C3-C4 (∆θ = R5~C3~C4° - R5-C3C4°) and difference between the BPs angles R5~C3~C4 with the geometrical angle R5•C3•C4, defined as the angle between the C3-C4 BCP, C3, and C3-B5 BCP (∆φ = R5•C3•C4° - R5-C3-C4°). ∆ρ(r)‡,inTS ∆ρ(r)‡,outTS ∆θinTS ∆φinTS ∆θoutTS ∆φoutTS BH2 SiF3 SiF2H SiFH2 SiH3 COOH2+ CHO

-0.918 -1.001 -1.001 -1.005 -1.026 -0.920 -1.033

-1.067 -1.000 -1.006 -1.000 -1.014 -0.913 -1.022

-58.0 -9.1 -11.5 -11.1 -5.8 -14.4 -4.4

-36.9 -5.0 -7.3 -7.0 -2.7 -9.3 -1.7

8.8 4.1 5.0 5.6 5.7 -2.2 1.2

8.4 4.1 5.3 5.6 5.6 -2.0 1.8



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COOH CO2CFH2 CF2H CF3 CH3 NH2 Cl

-1.040 -1.087 -1.064 -1.070 -1.079 -1.075 -1.083 -1.117

-1.017 -1.068 -1.052 -1.059 -1.058 -1.052 -1.020 -1.082

2.1 1.8 3.2 2.7 3.6 6.4 7.5 9.7

4.5 3.1 4.7 4.4 5.9 7.3 9.3 10.6

0.2 5.8 0.4 -0.4 -1.8 2.9 -2.5 -7.3

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0.8 6.1 1.5 0.3 -0.9 3.5 0.0 -6.2

IQA's inter-atomic energies of the most important interactions. The analysis of the delocalization indices (DI) and the IQA's energies shows that the C4---R5 interaction is the main responsible factor for the direction of the bending of the C3-C4 BP in inTSs and for the magnitude of ∆ρ(r)‡ at the C3-C4 BCP. The relative delocalization indices ( ∆DI‡ = DITS - DIMin ) for the most relevant interactions are shown in Table 3. As expected, C4---R5 DIs are larger for the inTS than for its corresponding substituted cyclobutene (positive ∆DI‡) in all cases, except for the C4---Cl5 interaction. The more energetic an inTS, the less ∆DI‡, what suggests that the electron delocalization between C4 and R5 plays a main role in the inTS stabilization. For the 3-clorocyclobutene inTS(Cl-inTS), the delocalization between C4 and Cl5 diminish in the inTS. This behavior shows that in Cl-inTS the C4--Cl5 interaction is not stabilizing the inTS. On the contrary, for outTSs, electronic delocalization between C4---R5 is smaller than in its corresponding cyclobutene (negative ∆DI‡) and there is no trend between the relative energy of the outTS and the ∆DI‡. Therefore, the C4---R5 interaction seems not be decisive for the stabilization of the outTS. Table 3. IQA interaction relative energies (∆IE‡= IETS – IEMin) and relative delocalization indices (∆DI‡= DITS – DIMin) of relevant interactions and its corresponding inward - outward differences (∆∆IE‡, ∆∆DI‡). All energies in kcal/mol C4-R5 C4-R5

BH2 SiF3 SiF2H SiFH2 SiH3 COOH2+ CHO COOH CO2CFH2 CF2H CF3

∆IE‡,inTS

∆IE‡,outTS

-43.1 -27.1 -27.5 -26.5 -20.4 -13.5 -9.4 -11.1 -7.5 -4.4 -7.6 -10.2

-3.3 -11.7 -10.4 -9.7 -10.6 -0.7 -2.5 -5.4 -8.1 -0.9 -3.1 -6.4

C3-R5 C4-R5

∆∆IE‡

-39.9 -15.4 -17.1 -16.8 -9.8 -12.7 -6.9 -5.7 0.5 -3.5 -4.5 -3.8

C3-R5

∆IE‡,inTS

∆IE‡,outTS

-133.2 -13.0 -7.6 -6.4 -9.5 -11.4 -9.1 -9.9 -8.6 -3.5 -6.2 -8.3

-157.9 -10.8 -11.5 -11.6 -11.1 -11.7 -6.8 -6.9 -7.5 -4.2 -4.8 -6.5

C3-C4 C3-R5

∆∆IE‡

24.7 -2.2 3.9 5.1 1.6 0.3 -2.3 -3.0 -1.1 0.7 -1.3 -1.8


C3-C4

∆IE‡,inTS

∆IE‡,outTS

56.4 56.9 56.7 56.8 56.4 50.6 52.0 52.0 53.2 51.8 52.2 52.7

56.2 55.2 54.9 54.7 55.2 46.2 49.7 49.2 51.2 50.5 50.1 50.2

C3-C4

∆∆IE‡

0.1 1.6 1.8 2.1 1.2 4.4 2.3 2.7 2.1 1.3 2.1 2.4

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CH3 NH2 Cl

BH2 SiF3 SiF2H SiFH2 SiH3 COOH2+ CHO COOH CO2CFH2 CF2H CF3 CH3 NH2 Cl

-0.7 7.3 5.5

1.4 8.1 8.5

C4-R5

C4-R5

∆DI‡,inTS

∆DI‡,outTS

0.061 0.013 0.021 0.024 0.012 0.097 0.058 0.030 0.015 0.017 0.014 0.002 0.003 0.030 -0.110

-0.128 -0.007 -0.009 -0.011 -0.010 -0.015 -0.021 -0.016 -0.010 -0.027 -0.024 -0.019 -0.024 0.013 -0.147

-2.1 -0.7 -3.0

C4-R5

-0.9 -17.2 61.6

-2.6 -43.1 60.3

C3-R5

C3-R5

∆∆DI‡

∆DI‡,inTS

∆DI‡,outTS

0.189 0.020 0.030 0.035 0.022 0.112 0.079 0.046 0.024 0.044 0.037 0.021 0.027 0.017 0.037

-1.214 -0.010 -0.011 -0.014 -0.015 0.183 0.067 0.058 -0.014 0.024 0.023 0.019 0.019 0.105 -0.744

-1.195 0.006 0.011 0.012 0.011 0.160 0.072 0.051 0.039 0.038 0.024 0.016 0.041 0.085 -0.728

1.7 25.8 1.4

52.1 49.3 52.1

50.3 45.0 50.2

C3-C4

C3-C4

∆∆DI‡

∆DI‡,inTS

∆DI‡,outTS

-0.019 -0.016 -0.021 -0.026 -0.026 0.023 -0.005 0.007 -0.054 -0.014 0.000 0.003 -0.022 0.020 -0.016

-0.386 -0.400 -0.403 -0.406 -0.413 -0.469 -0.444 -0.441 -0.443 -0.427 -0.435 -0.441 -0.426 -0.443 -0.432

-0.416 -0.412 -0.412 -0.415 -0.415 -0.403 -0.404 -0.399 -0.413 -0.408 -0.397 -0.400 -0.403 -0.406 -0.415

C3-R5

1.8 4.3 1.9

C3-C4

∆∆DI‡

0.030 0.012 0.008 0.009 0.002 -0.066 -0.039 -0.042 -0.030 -0.019 -0.037 -0.041 -0.023 -0.037 -0.017

In order to have a better insight of the strength of the more important stabilizing or destabilizing interactions in the TS of the cyclobutene ring opening, we perform an IQA analysis. First, we analyze the relative IQA atomic energies ( ∆AE‡= AETS – AEMin) for all atoms. In case of inTSs, there was no significant correlation between the atomic energies and the activation energies but for the R5 atom (R2 = 0.83, table 4). This means that R5 atom is the principal channel for the stabilization of the inTSs. As mentioned IQA partition energy scheme allows the separation of the energy in intra and inter atomic contributions. The inter atomic contribution is the interaction energies between all atom pairs. Hence, it is possible to obtain the interaction energy of an atom pair, even if there is not a BP between them. We found no correlation between IQA C3-C4 interaction relative energy ( C3-C4 ∆IE‡= C3-C4IETS – C3-C4IEMin) or ∆DI‡ with the activation energies of the inTSs. At first, this was surprising, because we found a strong correlation between the densities at the C3-C4 BCP with the activation energies of inTSs. This means that the observed trend for ∆ρ(r)‡ at the C3-C4 BCP should not be directly caused by the C3-C4 interaction but by other interactions. The R5 atomic energies were the ones correlated with the inTSs activation energies, so one possible interaction for the stabilization of inTSs could be C4---R5 interaction. Indeed, the IQA C4---R5 interaction relative energy (

C4-R5

∆IE‡) correlates significantly

with ∆ρ(r)‡ at the C3-C4 BCP (R2 = 0.89, figure 2, we remove the protonated cyclobutene-3-carboxylic 9 ACS Paragon Plus Environment


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acid from the series due to the fact that this inTS has a second important stabilization mechanism, as we are going to describe later) and with the shape of the C3-C4 BP (∆φ, R2 = 0.81). The trend for C4-R5 ∆IE‡ is clear: the more energetic the interaction C4---R5, the lower the barrier for the inward ring opening. This is consistent with the results of Houk and coworkers. They showed, using MO analysis, that the interaction between the C3-C4 breaking σ-orbital (HOMO) with a low lying empty or high lying filled R5 orbital, which points toward the breaking orbital, is responsible for the stabilization or destabilization of the inTS.2,3,10,64,65 The IQA's interaction energies allows us to realize that in case of BH2-inTS, the inTS is remarkably stabilized by the C4---B5 interaction. According to these energies, this specific interaction is 43.1 kcal/mol stronger in the 3-borylcyclobutene inTS than in its ground state. On the contrary, for the TSs of 3-aminocyclobutene and for the 3-chlorocyclobutene, the C4---N5 and C4---Cl5 interactions do not stabilize the inTS, they destabilize the inTS by 7.3 and 5.5 kcal/mol, respectively. When the substituent is a strong electron donor, the C4---R5 interaction destabilizes the inTS but when the substituent is an electron acceptor, the interaction stabilizes the inTS. For the outward ring openings, as in the case of ∆DI‡, there is no correlation between C4-R5∆IE‡ and the barrier height, what confirms that the C4---R5 interaction does not determine the stability of outTSs. The difference between IQA C4---R5 interaction energy of inTS and the one of outTS (C4-R5∆∆IE‡ = R5

∆IE‡,inTS -

C4-R5

C4-

∆IE‡,outTS) shows that C4---R5 interaction defines the observed torquoselectivity. This

means that the main cause of the observed diasteromeric preference (cis or trans) in substituted cyclobutene ring openings is the strength (positive or negative) of the C4---R5 interaction in the inTSs. Table 4. Relative atomic energies (∆AE‡= AETS – AEMin) and relative charges ( ∆q‡= qTS – qMin) of R5 atom. All energies in kcal/mol ∆AE‡,inTS ∆AE‡,outTS BH2 SiF3 SiF2H SiFH2 SiH3 COOH2+ CHO COOH CO2CFH2 CF2H CF3 CH3 NH2

-31.43 -5.35 -6.40 -5.47 0.18 -33.88 -3.82 -2.83 2.49 1.40 0.33 0.64 4.74 -1.63

-0.11 1.37 2.22 2.46 2.47 -25.42 -4.30 -2.62 2.63 -2.63 -0.97 0.58 -4.10 -16.65

∆q‡,inTS

∆q‡,outTS

-0.09 0.01 0.01 0.01 0.03 -0.15 0.00 0.00 0.03 0.01 0.00 0.01 0.03 0.00

0.00 0.00 0.00 0.00 0.00 -0.10 -0.03 -0.02 0.00 -0.01 -0.01 -0.01 -0.02 -0.11


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Cl


11.83

2.59

0.05

0.04

Figure 2. Plot of C3-C4 ∆ρ(r)‡ versus C4-R5 ∆IE‡ of inward TSs.

Topological analysis of ∇2ρ(r) and ELI-D maps of C4---R5 interaction. The analysis of the laplacian of the electron density and ELI-D maps clearly shows the cause of the strength of the C4---R5 interaction. The strength of this interaction is directly related with the deepness of the charge depletion or the low electron localizability zone at the vicinity of R5 atom in the ∇2ρ(r) or ELI-D field, respectively. This depletion or low localizability region is pointing toward a charge concentration at the vicinity of C4 or a non-bonding, monosynaptic basin, V(C4), respectively (Figure 3). In general, all the inTSs present a very similar ∇2ρ(r) topology, although BH2-inTS has some remarkable differences. In the C3,C4,R5 plane, all inTS have a charge concentration region, at the vicinity of C4, that is more or less pointing toward a charge depleted zone at the vicinity of C5 (Figure 3a shows CH3-inTS case). After performing a search of the CPs of ∇2ρ(r) field around each atom, we found that the charge concentration region close C4, in the C3,C4,R5 plane, is actually close to a (3,-1) CP (saddle point, SP), which is slightly out of the C3,C4,R5 plane and out of the cyclobutene ring. The charge depletion region close to R5, in the C3,C4,R5 plane, is close to a (3,+1)CP (charge depletion, CD), which is also slightly out of the C3,C4,R5 plane and also out of the cyclobutene ring. For BH2-inTS, the picture is a little different, the charge concentration of C4 in the C3,C4,R5 plane is very close to an actual (3,-3)CP (charge concentration, CC), instead of a (3,-1)CP. This CC points toward a SP and this SP toward another CC that is close to a catastrophe scenario according to Thom's catastrophe theory. In general, a



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covalent bond has a similar sequence of CP (CC, SP, CC), see for comparison the C-Cl bond in figure 3c. The topology of the C4--B5 interaction is similar to the one described by Llusar and others as a protocovalent bond.65,66 Moreover, only for 3-borylcyclobutene, the IRC shows the formation of a BP between C4 and R5 after overcoming the TS (see SI). The C4-B5 BP is been formed from a conflict catastrophe of the C3-C4 BP. Consequently, for this particularly case, there is a protocovalent interaction between C4 and B5, what explains the high interaction energy between these two atoms. On the other side, Cl-inTS, like most of the inTS, has a (3,-1)CP close C4 that points toward a (3,+1) CP close Cl5. The comparison between figure 3a and 3c shows that in case of Cl-inTS the (3,+1) CP is less deep than for CH3-inTS. This suggests that the interaction of the depleted region close R5 with the concentrated region close C4 seems to be the responsible factor of the C4---R5 interaction.

Figure 3.∇2ρ(r) contour maps of a) CH3-inTS, b) BH2-inTS and c) Cl-inTS and ELI-D contour maps of d) CH3-inTS, e) BH2-inTS and f) Cl-inTS in the C3,C4,R5 plane. Yellow filled circles, filled tringles, empty tringles and empty circles are (3,-3), (3,-1), (3+1), (3,+3) CPs, respectively. All the CPs are slightly above the C3,C4, R5 plane and are projected on the plane. In ∇2ρ(r) contour maps: Negative (solid) and positive (dashed) contour lines are drawn from ±0.1 to ±1000.000 e Å-5 (log scale, 15 steps). Color code: ≥ 5.0 e Å-5 (dark blue), 0.0 e Å-5 (white) and ≤ -5.0 e Å-5 (dark red). White background numbers ∇2ρ(r) values at the CP. Lines pointing a contour line indicate its ∇2ρ(r) values. In ELI-D maps: Localization contour lines are drawn at 0.60, 0.64, 0.68 (dashed lines), 1.15, 1.22 and 1.35 (solid lines). Color code: ≤ 0.6 (dark blue), 0.95 (white) and ≥ 1.3 (dark red). ELI-D values (normal) at relevant CPs and electronic population in V(C4) basin (italic) are also showed.


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In some systems, the analysis of ∇2ρ(r) field was very difficult because of the lack of a sharp structure in the valence region. One pathological case was SiXnHm-inTS systems, there is hardly any valence structure around Si (see SI). Either ELI-D or ELF scalar fields had shown topological similarities with ∇2ρ(r) that had been elegantly explained by Kohout and colleagues.67 Both scalar fields had a practical advantage over ∇2ρ(r), they recover a sharper picture of the valence region. Contrary to ∇2ρ(r), ELI-D or ELF (which is an approximation to ELI-D) recover the shell structure up to Xe with the correct electron population in each shell.68,69 ELI-D recover the shell structure even in momentum space.70 We used ELI-D field to study our series of compounds. All the inTSs have essentially the same ELI-D topology, a (3, -3) CP (maximum or attractor) close C4 pointing toward R5 (see for example CH3-inTS in figure 3d). The corresponding basin for this attractor is a low populated basin (V(C4)). This monosynaptic basin is created after the C3-C4 bond breaking, as J. Andrés et al. and A. Morales-Bayuelo had described for the ELF topology.49,51 At the R5 vicinity, there is a region with low electron localizability that points more or less toward V(C4) basin. In this region, in most of the cases, there are two CPs, a (3, +3) CP (minimum or repellor) and a (3, +1) CP. The (3, +1) CP is the one in the outer shell of R5. As in the case of ∇2ρ(r) scalar field, all these CPs are not in the C3,C4,R5 plane, they are out of the cyclobutene ring. In case of the inTS with the best electron attractor substituent, BH2-inTS, there is no (3, +1) CP, there is only a very deep minimum in the vicinity of B5 that is pointing directly toward V(C4) basin. In this special case, the V(C4) is highly populated, 0.81e. In almost all remaining systems the population of the V(C4), it is around 0.2e. In accordance with

∇2ρ(r), such a highly populated V(C4) suggests that there is a protocovalent bond between C4 and B5 in the case of BH2-inTS. This strong interaction between C4 and B5 is the reason of the stabilization of BH2-inTS. Contrary, Cl-inTS has a very shallow region of low electron localizability in the vicinity of Cl5, almost nonexistent. Only a (3, +1) CP at Cl5 is pointing to V(C4) basin (figure 3f) and the region close to (3, +1) CP is not low in electron localizability. Therefore, the reason of the destabilization of C4---Cl5 interaction in the inTS is the interaction of the localized electrons in V(C4) basin with the localized electrons around the Cl. These results suggest that in order to favor the C4---R5 interaction, it is necessary that there is a high electron localization domain at C4 that points toward a very low electron localization domain at R5. The previous analysis is also useful to understand why the C4---Si5HnFm interaction is stronger than the C4---C5HnFm interaction. From figure 4a and figure 3d, it is evident that the low localizability region at Si5 in SiH3-inTS is much deeper than the low localizability region at C5 in CH3-inTS, what 13 ACS Paragon Plus Environment


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shows the better ability of Si to rearrange its electrons around itself to enhance an interaction. It is also clear that the V(C4) do not significantly change from SiH3-inTS to CH3-inTS. Then, the main reason for the higher interaction energy between C4---Si5 in SiH3-inTS than for C4---C5 in CH3-inTS is the very deep electron localizability domain around Si5, as opposed to the far less deep electron localizability domain around C5. The electrons localized in V(C4) basin interacts more favorably with really deep low localizability at Si5. These results agree with the molecular orbital explanation for the lower activation energy of the SiH3-inTS in comparison to the activation energy of CH3-inTS. From MO point of view, the Si5-H σ* orbital is of lower energy than the C5-H σ* orbital, what allows, in case of SiH3-inTS, a better interaction of the breaking C3-C4 σ orbital with Si5-H σ* orbital.10 In order to show that the deepness of the low electron localization domain at R5 correlates strongly with the strength of the C4---R5 interaction, we analyze the series of inTS substituted with SiH3, SiH2F, SiHF2 and SiF3. Houk and coworkers show that, for the SiH3 substituent, the exchange of one H by a F reduce the energy of Si5-H σ* orbital, what enhances the C4---Si5 interaction. This lowers the activation energy of the inTS.10 The IQA interaction energies and DI (table 3) show that the substitution of one H by a F increases the ∆IE‡,inTS and ∆DI‡,inTS between C4 and Si5, which match the Houk's picture. Actually, there is a good correlation (R2 = 0.89) between the activation energy of the progressively fluorinated inTS and the IQAs C4---Si5 interaction energy (figure 5). The ELI-D maps of SiH3, SiH2F, SiHF2 and SiF3 -inTSs show that the size of the low localizability region at Si, pointing to V(C4), increase with the progressive fluorination of SH3 substituent (figure 4). Indeed, the value of ELI-D at the (3, +1)CP decreases progressively with the fluorination, indicating a lower localizability in the region. This progressively lowering of the electron localization at Si allows better interaction of electrons in V(C4) basin (formed after the breaking of the C3-C4 bond) within this region. However, the progressive fluorination also generates that the (3, +1) CP is progressively farther from the vector defined by C4 and Si5 (figure 4). The angle between the C4, Si5 and (3, +1) CP is significantly larger for SiHF2 and SiF3 (31.9° and 35.5°, respectively) than for SiH3 and SiH2F (25.6° and 26.5°, respectively). A larger angle means that the interaction between the low electron localizability zone with the electrons located in V(C4) basin is less effective. In part, this explains, why the IQA C4---Si5 interaction energy does not keep significantly growing, when going from the monofluorinated to the difluorinated or to the trifluorinated inTS. The fluorination of the CH3 substituent has a similar effect in the topology of ELI-D (see SI). From these observations, we can say with more certainty that the main factor that controls C4---R5 interaction energy, which in turn, controls the relative stability of inTSs, is 14 ACS Paragon Plus Environment

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the deepness of the low localizability region at R5 that points toward the V(C4).

Figure 4. ELI-D contour maps of a) SiH3-inTS, b) SiH2F-inTS, c) SiHF2-inTS and d)SiF3 in the C3,C4,Si5 plane. Yellow filled circles, filled tringles, empty tringles and empty circles are (3,-3), (3,-1), (3+1), (3,+3) CPs, respectively. All the CPs are slightly above the C3,C4, Si5 plane and are projected on the plane. Localization contour lines are drawn at 0.60, 0.64, 0.68 (dashed lines), 0.96, 1.15, 1.22 and 1.35 (solid lines). Color code: ≤ 0.6 (dark blue), 0.95 (white) and ≥ 1.3 (dark red). ELI-D values (normal) at relevant CPs and electronic population in V(C4) basin (italic) are also showed.

Figure 5. Plot of C4---R5 relative interaction energy ( C4-R5∆IE‡ = C4-R5IEinTS – C4-R5IEMin) versus the activation energies of inTSs



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Auxiliary stabilizing interactions. There are other possible mechanisms for the stabilization of the cyclobutene ring opening TSs, apart from the interaction of the localized electrons (pseudo-lone pair) at C4, formed after the breaking of the C3-C4 bond, with a zone of low electron localizability at R5 (figure 6a). A second mechanism consists in the delocalization of the electron density of the breaking C3-C4 bond, close to C3 (V(C3) in ELI-D maps), into the substituent (figure 6b). This mechanism can be enhanced, if the substituent has π orbitals that are able to delocalize the electrons of the breaking C3-C4 bond. For this purpose, the more planar the C4- C3H3-R5Z5 segment, the more stabilization can be given via hyperconjugation. This mechanism can afford a significant amount of stabilization energy, as the C3-R5 ∆IE‡ values suggest (table 3). This mechanism also seems to be the cause for the high correlation (R2 = 0.88) between ρ(r) at the C3-R5 BCP and the ∆E‡ of the outTSs. However, in the majority of cases, this second mechanism is not determinant or plays a secondary role for the observed torquoselectivity (∆∆E‡). The reason is that this mechanism occurs to a similar extent, either in the inward TSs or in the outward TSs, contrary to C4---R5 interaction that is significantly stronger in inward TSs. Nevertheless, we spot two cases where the last statement is not true. Borylcyclobutene and aminocyclobutene have a positive and very high ∆∆IE‡ (24.7 and 25.8 kcal/mol, respectively), what means that the C3-R5 interaction strongly favors the outTS over the inTS. This is reflected in the geometry of the TSs. In both, aminocyclobutene and borylcyclobutene, the substituent adopt a more planar conformation in the outTS than in the inTS. The C3,H5,H5,B5 dihedral angle in outTS of borycyclobutene is 1° while in the inTS is 11°. Something similar happens for the aminocyclobutene, the C3,H5,H5,N5 dihedral angle in outTS is 24° while in the inTS increase to 34°. Houk and coworkers have explained the stabilization of the NH2-outTS from the MO point of view. They have stated that the lone pair of the of N5 line up with the σ* orbital of the breaking C3-C4 bond.10,64 The ELI-D analysis shows that in NH2-outTS the electrons localized in the V(C3) basin and the N5 lone pair basin (V(N5)) move toward the C3-N5 bonding region. Indeed, the electronic population in the ELI-D C3-N5 bonding basin (V(C3,N5)) is higher in the outTS (2.10 e, see Figure S7) than in the inTS (1.86 e). In addition, the population in the V(C3) is lower for outTS (0.22 e) than for inTS (0.32 e) and the population in V(N5) is also lower for outTS (1.67 e) than for inTS (1.96 e). This transfer of electrons to V(C3,N5) basin propitiates a stronger interaction between C3 and N5, which is responsible of the significant stabilization of the aminocyclobutene outTS. In case of the borylcyclobutene, the outTS is energetically favored over the inTS by C3-B5 bond but this is not 16 ACS Paragon Plus Environment

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enough to overrule the stabilization gained by the inTS with the C4---B5 interaction.

Figure 6. Illustrations of the two main mechanism for the stabilization of the TS of an electrocyclic ring opening of a 3-substituted cyclobutene. a) Interaction of the localized electrons at the V(C4) with a low localizability region at R5 (substituent). b) Transfer of the electrons of the C3-C4 breaking bond (V(C3)) toward the C3-R5 bonding basin (V(C3,R5). Below: ELI-D isosurfaces representing both scenarios.

COH, COOH, COO- and COOH2+ substituents also have π orbitals where the electrons in V(C3) can be delocalized. However, for all these cases the C3-C5 interaction energy only slightly favors the inTS. Even for the protonated cyclobutene-3-carboxylic acid, C3-C5 interaction marginally favors the outTS (table 3). Therefore, the delocalization of V(C3) electron over the substituent π orbitals do not play an important role for the discrimination between the outward and the inward TSs. The discrimination between outward and inward TSs for these systems should be governed by the C4---C5 interaction. Nevertheless, protonated cyclobutene-3-carboxylic acid was very puzzling. In previous works has been stated that the low lying π*COO acceptor orbital is the responsible factor of the considerably low energy of COOH2+-inTS.71 In principle, the π*COO acceptor orbital at C5 could strongly interact with the C3-C4 breaking σ orbital. We were expecting that the C4---C5 interaction energy would be significantly larger than in other similar cases but as can be seen from table 3 this is not the case. The C4---C5 interaction energy in COOH2+-inTS is very similar to COOH-inTS, which 17 ACS Paragon Plus Environment


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have a much larger activation energy. Table 4 shows the relative IQA atomic energies ( ∆AE‡= AETS – AEMin) for R5 atom. There are four cases that stand out, B5 at the BH2-inTS, N5 at the NH2-outTS and C5 at COOH2+-inTS and at COOH2+-outTS. This means that in case of protonated cyclobutene-3carboxylic acid, C5 is strongly stabilized in both TSs but the stabilization is better in the inTS. IQA theory let us separate the intra and inter atomic contribution from the atomic energy. Therefore, it is possible to know, if an atom is being stabilized via an interaction or by itself. In case of COOH2+-inTS, the C5 intra atomic contribution to the relative IQA atomic energy is -77.20 kcal/mol and the inter atomic contribution is 43.32 kcal/mol, which means that the intra contribution controls the stabilization of C5. In the outTS, the picture is similar, the intra contribution is -52.83 kcal/mol and the inter contribution is 27.40 kcal/mol. It is clear that in the TS of the protonated cyclobutene-3-carboxylic acid, C5 is being stabilized by an intra mechanism. One possible intra mechanism for the stabilization of the TSs is the reduction of the positive charge at C5. Only the four cases in which R5 is strongly stabilized have a significant reduction of the charge at R5. COOH2+-inTS and COOH2+-outTS reduce their charge in reference to the protonated cyclobutene-3-carboxylic acid ground state by 0.15e and 0.10e, respectively. The fact that C5 in COOH2+-inTS reduces its charge more than in COOH2+-outTS coincide with a larger stabilization of C5 in COOH2+-inTS than in COOH2+-outTS. From the ELI-D topology, we were able to calculate the charge inside V(C4) basin that is being formed directly after the breaking of the C3-C4 bond. As mentioned, for the vast majority of analyzed systems, the population of V(C4) was around 0.2e but for COOH2+-inTS the population is just 0.08e. Then, due to the closeness of C5 to V(C4) basin in the inward TS, C5 is able to take charge from this basin and stabilizes its positive charge. Consequently, the ability to reduce the charge at C5 is one important mechanism for the stabilization of the inward and outward TSs of the protonated cyclobutene-3-carboxylic acid. However, this mechanism is more enhanced in the inward TS than in the outward TS due to the closeness of C4 and C5 atoms, what correlates with the preference for the inward over outward TS.

Conclusions The topological analysis of scalar fields that depends on the density and on the pair density has proved its usefulness for understanding of energetic trends in a series of conrotatory ring openings. QTAIM theory, ELI-D field and IQA energy partition method have been successfully used to explain the observed activation energy trends in a series of 3-substituted-cyclobutenes ring openings. There are


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two possible ways for a 3-substituted-cyclobutene ring opening: an inward or an outward rotation of the substituent. We found two interactions that are the main reason for the stabilization of the TS for the ring openings. One is the interaction of the proximal terminus carbon (C3) with the substituent (R5). In this interaction, the electrons of the breaking C3-C4 bond move toward the C3-R5 bond, what increases the double bond character of C3-R5. This is reflected in the electronic depopulation of the ELI-D V(C3) basin and the population of the V(C3-R5) basin. In general, this mechanism, while important for the stabilization of the TSs, does not play a significant role in the torquoselectivity. Both, inward TS or outward TS, are stabilized to the same degree by this mechanism. However, there are exceptions, in case of the 3-amino-cyclobutene, this mechanism significantly favors the outward TS over the inward one and it is determinant in the observed rotational preference. The other source of stabilization of the TSs is the interaction of the distal terminus carbon (C4) with the substituent (R5). Contrary to the C3-R5 interaction, C4---R5 interaction is only important for the inward TS stabilization, what makes this interaction the main responsible factor for the observed rotational preferences (inward or outward) in the studied 3-substituted-cyclobutenes. The strength of the interaction mainly depends on the deepness of the low electron localizability region at R5 that is pointing to electrons localized at ELI-D V(C4) basin, formed after the breaking of the C3-C4 bond. The substituents that have this low localizability region are the ones with empty π orbitals, like BH2, or the ones that are able to polarize its charge, like SiH3. In case of the positive charge COOH2+-cyclobutene, the rotation preference also comes from the interplay of V(C4) with R5 but with a different mechanism. In addition to the C4---R5 interaction, QTAIM and ELI-D maps reveal that the electrons from the breaking C3-C4 move into the positive charged C5. The electronic population in the V(C4) basin significantly decreases while the C5 positive charge decreases. The decrease of the C5 positive charge internally stabilizes this atom and the whole TS. It is peculiar that the atomic interaction mainly responsible (C4---R5) for the observed torquoselectivity does not have a BP between these two atoms. This interaction is so strong in case of 3-boryl cyclobutene TS that the topology of ∇2ρ(r) and ELI-D indicate the formation of a protocovalent bond. However, it is remarkable that the shape and ρ(r) at the BCP of C3-C4 is not just affected for the interaction between these atoms but also for the interaction between C4---R5. The influence of the C4---R5 interaction is so important that both, C3-C4 BP shape and ρ(r) at its CP, correlate strongly with the IQA C4---R5 interaction energy and not with the IQA interaction energies of C3-C4. Therefore, in case of inward TS, the C4---R5 interaction is the main responsible factor of the 19 ACS Paragon Plus Environment


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C3-C4 BP density and shape. Our findings show that a bond path between a given pair of atoms not only reflects the features of the interaction of these atoms, but also reflects the characteristics of contiguous interactions. In summary, besides the alternative explanation that QTAIM, ELI-D and IQA's offer to torquoselectivity, we also were able to quantify energetically to which extent the main stabilizing interatomic interaction (C4-R5) is stronger than other secondary stabilization interactions. Moreover, we were able to spot interesting aspects of the electronic nature of the C4---R5 interaction that were not evident in previous MO analysis, such as the protocovalent interaction in 3-boryl cyclobutene or the charge reduction at C5 in COOH2+-cyclobutene. We expect that this study will be used as a reference point for future analyses of inter-atomic interactions and the electron density of other pericyclic reactions.

Supporting Information

∇2ρ(r) contour maps and ELI-D maps for the compounds, IRC of Boryl and chlro cyclobutene, xyz coordinates of all investigated molecules. This material is available free of charge via the Internet at http://pubs.acs.org.

Corresponding Author * Email: [email protected] Phone: +5255 5622 4770 Ext. 46610

Acknowledgements The author wants to thank DGTIC-UNAM for the computer time (project: SC16-1-IR-60) and DGAPA-UNAM (project: IA201316) for the financial support. The author thanks Gladys E. Cortés, María M. Aguilar, José D. Vázquez and María C. Martínez for computer support. The author also thanks Raffaela Menzinger for the English proof-reading of the manuscript.

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Torquoselectivity in Cyclobutenes Ring Openings and the Interatomic Interactions that Control Them


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