Reaction Electronic Flux Perspective on the Mechanism of the

Article Cite This: J. Org. Chem. 2018, 83, 5969−5974

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Reaction Electronic Flux Perspective on the Mechanism of the Zimmerman Di-π-methane Rearrangement Ricardo A. Matute,*,†,‡,§ Patricia Pérez,∥ Eduardo Chamorro,∥ Nery Villegas-Escobar,† Diego Cortés-Arriagada,⊥ Barbara Herrera,† Soledad Gutiérrez-Oliva,† and Alejandro Toro-Labbé*,† †

Laboratorio de Química Teórica Computacional (QTC), Facultad de Química, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, 7820436, Santiago, Chile ‡ Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States § Centro Integrativo de Biología y Química Aplicada (CIBQA), Universidad Bernardo O Higgins, Santiago 8370854, Chile ∥ Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Universidad Andres Bello, Avenida República 275, 8370146 Santiago, Chile ⊥ Programa Institucional de Fomento a la Investigación, Desarrollo e Innovación, Universidad Tecnológica Metropolitana, Ignacio Valdivieso 2409, 8940577, San Joaquín, Santiago, Chile S Supporting Information *

ABSTRACT: The reaction electronic flux (REF) offers a powerful tool in the analysis of reaction mechanisms. Noteworthy, the relationship between aromaticity and REF can eventually reveal subtle electronic events associated with reactivity in aromatic systems. In this work, this relationship was studied for the triplet Zimmerman di-π-methane rearrangement. The aromaticity loss and gain taking place during the reaction is well acquainted by the REF, thus shedding light on the electronic nature of reactions involving dibenzobarrelenes.

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INTRODUCTION The di-π-methane (DPM), also called Zimmerman rearrangement,1 is a relevant photochemical reaction and formally a [π2 + σ2] rearrangement of 1,4-dienes. In bicyclic systems, it proceeds via triplet state upon sensitization, involving a complex two-step transformation. In the first step, formation of a σ-bond together with loss of ring aromaticity take place.2 The second step comprises the breaking of a σ-bond together with the recovery of ring aromaticity.2 Despite the extensive work on it, the nature of the electronic processes that drive the DPM rearrangement remain unclear. The most natural way to capture the electronic activity that explains the reaction mechanism is to track it along the intrinsic reaction coordinate (IRC=ξ) by means of the so-called reaction electronic flux (REF).3 The REF accounts for the electronic activity taking place during the reaction, negative REF values indicate that bond weakening/breaking processes drive the reaction mechanism, whereas positive REF values indicate that the reaction is led by bond strengthening/formation processes.3 Nonetheless, although direct interpretation of REF profiles can be challenging for reactions involving both loss and recovery of aromaticity, such analysis is likely necessary to understand the electronic nature of some sigmatropic rearrangements. In this work, a qualitative connection between REF and aromaticity for © 2018 American Chemical Society

a disrupted Mö bius system in the Zimmerman DPM rearrangement is established. The triplet sensitized rearrangement of dibenzobarrelene (DBB) (Scheme 1) is a well-known and representative aryl− aryl DPM reaction, which gives dibenzosemibullvalene (SBV) as product.2 The central barrelene in DBB confers the molecule the Möbius character since the out-of-phase overlap between perpendicular π-orbitals is in its nonplanar geometry (Scheme 1), and therefore its six π-electrons make barrelene an antiaromatic molecule because of the 4n + 2 rule for Möbius antiaromaticity. Indeed, barrelene is an antiaromatic Möbius system like cyclobutadiene is an antiaromatic Hückel system.4 Note that the benzo groups in DBB do not affect the Möbius character of barrelene.5 On the other hand, the reaction product (i.e, SBV) is a Hückel system (Scheme 1) since the extended delocalized π-system is disrupted in T1 upon sensibilization. In the lowest triplet state (T1), the triplet 1,2biradical (DBB*) rearranges first to a 1,4-biradical (BR-I) and then to a 1,3-biradical (BR-II) that decays through an intersystem crossing (ISC) channel to the ground-state product, SBV.2 The transition states in T1, TS-I and TS-II, Received: February 23, 2018 Published: February 27, 2018 5969

DOI: 10.1021/acs.joc.8b00499 J. Org. Chem. 2018, 83, 5969−5974

Article

The Journal of Organic Chemistry

Koopmans' theorem using the energies of frontier molecular orbitals HOMO and LUMO, εHOMO and εLUMO, respectively: μ ≈ −(I+A)/2 ≈ (εHOMO+εLUMO)/2.12

Scheme 1. Reaction Mechanism for the DPM Rearrangement of Dibenzobarrelenea

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RESULTS AND DISCUSSION The MEP and the reaction force profiles on T1 are shown in Figure 1a. The RFA of the MEP (see Figure 1a and Table 1)

a

Upon sensitization, competing one-step and two-step pathways take place on T1. The π-systems of DBB (Möbius reactant) and SBV (Hückel product) are shown below.

lead the corresponding transitions. The rate-determining step is governed by TS-I in T1. According to Matute and Houk,2 the triplet surface of the DPM rearrangement of DBB allows a shortcut on the potential energy surface (PES), bypassing the energetically shallow BR-I, thus leading to competing one-step and two-step mechanisms.

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COMPUTATIONAL METHODS

The electronic energies were calculated using unrestricted density functional theory (DFT) with the (U)M06-2X functional6 and 631G(d) basis set. The Nucleus Independent Chemical Shifts, NICS(0) and NICS(1)7, for each ring of DBB* (T1) and benzene (S0 and T1) were calculated at M06-2X/6-31G(d) level of theory. All quantum chemistry and NICS calculations were performed using Gaussian09 package.8 In addition, the topological analysis of the Electron Localization Function (ELF),15 was performed with the Topmod9 program. The Harmonic Oscillator Model of Aromaticity (HOMA) and the Ring Critical Points (RCPs) from Atoms-in-Molecules (AIM) Theory14 were computed using Multiwf n10. The Anisotropy Current Induced Density (ACID) was determined using the ACID software package.16 Aromaticity is related to changes in the electronic delocalization of the π-system along the reaction coordinate. It was assessed along the minimum energy path (MEP) of the T1 state connecting DBB*, BR-I, and BR-II. The MEP, defined by the reaction coordinate ξ in the PES, was explored by means of IRC calculations. The Gonzalez-Schlegel method11 for IRC was used as implemented in Gaussian09. The reaction force analysis (RFA) of the MEP was performed to obtain insights regarding the chemical driving force along the reaction coordinate. The formalism of RFA has its base on the differentiation of the energy with respect to the intrinsic reaction coordinate: F(ξ) = −(dE/dξ).12 It is a global property that helps to characterize the mechanism of any given chemical reaction.12 Partitioning of the energy according to the defined regions into W1 (reactant region), W2 (TS region, ξ < TS), W3 (TS region, ξ > TS), and W4 (product region) allows characterization of the chemical nature of the reaction and activation energies since in most cases both W1 and W4 typically account for a structural work whereas W2 and W3 mostly account for electronic effects.12 The reaction electronic flux (REF) is defined as J(ξ)=−(dμ/dξ), being μ the electronic chemical potential that accounts for the escaping tendency of electrons from an equilibrium distribution. Because of the discontinuity of the energy with respect to the number of electrons, μ has to be quantified using the finite difference approximation through the first ionization potential (I) and the electron affinity (A). Further approximation is done by means of the

Figure 1. Reaction plots on T1 for (a) MEP and reaction force, (b) REF, (c) HOMA and BO, and (d) electron density at the ring critical points (RCPs).

gives considerably higher values for W1 and W4 when compared to W2 and W3, respectively, for both TS-I and TS-II: the main Table 1. Energy (in kcal/mol) Contributions from the Reaction Force Analysis stagea

W1

W2

W3

W4

TS-I TS-II

7.25 1.75

3.50 1.04

−3.67 −5.52

−6.11 −11.33

TS-I: ΔE° = 0.97 and ΔE‡ = 10.75. TS-II: ΔE° = −14.06 and ΔE‡ = 2.79.

a

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Figure 2. Color-filled maps of the electron localization function (ELF), in two molecular planes of DBB* defined by the (a) C7−C5−C8a centers, (b) C2−C4−C9a centers, and (c) benzene (S0) at (U)M06-2X/6-31G(d) level. The maps use different colors to represent ELF value in different regions ranging from blue (no electron localization) to red (high electron localization). The topology of ELF in both six-membered rings of DBB* are equivalent, depicting the same delocalization topology pattern as revealed for benzene (S0).

electronic activity is needed to promote changes in these properties. Hence, the BO curves were contrasted in the same plot against the HOMA curves of both rings (Figure 1c). The HOMA for ring B is suffering first a sharp decline in TS-I that is then recovered in TS-II, thus indicating a loss followed by a recovery of the aromaticity in that ring; this electronic πdelocalization in ring B is effectively reflected on the REF profile in the T1 state. On the other hand, HOMA for ring A is steady along the TS-I region and just slightly decreases for TSII, reflecting the fact that the π-delocalization in ring A is slightly perturbed due to the formation of a benzyl radical at that step. Similar curves are obtained when the density at the RCP of ring A is computed (Figure 1d). In summary, the electronic activity detected by the REF is consistently confirmed with the HOMA, BO and RCP results. Note that since J(ξ) is a global property of the system it also accounts for low intensity induced electronic activity that emerges following the above described chemical changes. Further analysis by means of the calculation of the ELF for DBB* in two molecular planes (defined by the C7−C5−C8a and C2−C4−C9a centers) (Figure 2), along with the map of a benzene (S0) as reference of the most delocalized system was done. The ELF maps for both six-membered rings in DBB* are qualitatively similar to each other, revealing that both rings present the same delocalization topology pattern and high similitude to that shown by a ground-state benzene. Consistency of the results from HOMA, AIM, and ELF confirms the REF findings concerning the role of π-delocalized electrons on the reaction mechanism. This is the very first example in which the REF accounts mostly for π-reordering. An extension of the REF has been recently reported in which σ- and π-electronic activity can be tracked but restricted only for symmetric systems.18 Nonetheless, we need to be cautious with the assignment of aromaticity in T1 since a reversal of the aromaticity could be operating along the MEP. The reversal of aromaticity for systems in the lowest triplet state (T1) was predicted by N. C. Baird in 1972,19 hence known as Baird’s rule, although the term “Baird’s rule” seems to have been used for the first time by Fowler in 2008 (before any experimental support).20 Yet, Ottosson, Kilså, and co-workers in a combined experimental and computational study in 2007 explored the scope and limitations of Baird’s theory on triplet-state aromaticity,21 and earlier Wan and coworkers pioneered the experimental studies on the excited-state aromaticity concept (see e.g. ref 22), although Wan never cited Baird’s theory paper as he was unaware of its existence.

contribution in the activation energy is coming from structural and not from electronic changes. The REF profile that involves TS-I and TS-II is shown in Figure 1b, where it can be observed that most electronic activity takes place within and around the TS-I and TS-II regions. The TS-I is associated with a negative REF curve, which reveals a process of bond weakening (aromaticity loss) before the formation of the C12−C9a σ-bond that is exposed by a positive peak leaving the TS-I region. The bond order (BO) plot in Figure 1c confirms the formation of the C12−C9a σ-bond on the way from DBB* to the cyclopropane intermediate in BR-I. For the second step of the reaction, the REF plot shows a negative peak consistent with the C9−C9a σ-bond breaking followed by a positive peak assigned to the recovery of aromaticity. In summary, the REF profile reveals that the DPM rearrangement is driven by four main chemical events sequentially appearing along the reaction coordinate: aromaticity loss complemented with C12−C9a σ-bond formation in the first step, and C9−C9a σ-bond breaking ensuing with aromaticity recovery in the second step. The projection of the REF profile onto the energy profile allows quantification of the energy involved in the main chemical events; in the first step of the reaction, the aromaticity loss involves about 10 kcal/mol, and the ensuing formation of the C12−C9a σ-bond engages roughly 8 kcal/mol. In the second step of the reaction, the C9− C9a σ-bond breaking and aromaticity recovery involves approximately 3 and 6 kcal/mol, respectively. Five different methods were used to characterize the change in aromaticity along the reaction coordinate: HOMAs,13 RCPs,14 ELFs,15 NICS,7 and ACIDs.16 HOMA is defined as the normalized sum of squared deviations of bond lengths from an optimal value (i.e., a fully aromatic system); ELF is the measure of the likelihood of finding an electron with the same spin in the neighborhood space of a reference electron; AIM provides the analysis of the electron density in the RCPs; the NICS (specifically NICS(0)) calculates the absolute magnetic shielding at the center of a ring, although it can be calculated at certain distance above or below the center of the ring (e.g., 1 Å above the molecular plane for NICS(1)); and the ACID scalar field defines the density of delocalized electrons. In addition, bond order calculations using the Mayer scheme17 were performed to track bond formation and breaking from the cyclopropane intermediate, involving the C12−C9a and C9− C9a atoms, respectively. The slight shifting observed in the REF’s peaks with respect to the BOs and HOMAs descriptors indicates that previous 5971


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The Journal of Organic Chemistry Actually, there was experimental evidence on Baird aromaticity shortly after Colin Baird published his seminal theory paper19 because Saunders, Breslow, and collaborators discovered that the cyclopentadienyl cation is a ground-state triplet with D5h symmetry.23 Schleyer and co-workers later found it to be aromatic according to NICS and calculations of aromatic stabilization energies.24 Additional experimental studies on cyclopentadienyl cation has been reported by Wörner and Merkt.25 According to the Baird’s rule summarized above, in the case where reversal of aromaticity takes place, 4n π-electrons would lead aromaticity in detriment of 4n + 2. In this work, then the question that arises is if Baird’s rule19 is applicable to the Zimmerman DPM rearrangement of dibenzobarrelenes. In such a context, the REF, spin density distributions, NICS and ACID methodologies were used to characterize the delocalization (aromaticity) pattern in these systems and to elucidate either the aromatic or the antiaromatic nature of the six-membered rings in DBB*. The spin density distribution shown in Figure 3a confirms that the unpaired electrons in DBB* are localized at the

Figure 3. (a) Spin densities for DBB*, BR-I, and BR-II; (b) spin density distribution of structures with double-bond bridge (left) and saturated bridge (right) on T1PES.

Figure 4. Calculated NICS(0) and NICS(1) on both rings of DBB with saturated bridge (a), DBB* (b), and the intermediates BR-I (c) and BR-II (d).

bridging ethylene bond. In the 1,4-biradical intermediate, BR-I, one of the radical centers is delocalized in one of the rings; and the delocalization is switched to the other ring in the 1,3biradical intermediate, BR-II. It is quite remarkable, though, that the triplet excitation to DBB* is localized at the small ethylene moiety and not at the larger benzene rings. To obtain further insights on this, Figure 3b compares the spin density distribution of DBB* with the compound having a saturated bridge, whereas the Figure 4 compares both (together with the other T1 structures) in terms of NICS(0) and NICS(1). The high positive NICS values for the compound having a saturated bridge are indicative of its antiaromatic nature. Hence, it seems that the benzene rings of DBB* are able to completely avoid the unfavorable triplet excitation as the excitation instead localizes at the ethylene bridge, thus suggesting a T1 state antiaromaticity alleviation26,27 for the triplet excitation of dibenzobarrelenes. In addition, from Figure 4, the NICS(0) calculation for both rings of DBB* gives ∼−9 ppm, suggesting aromaticity, since ground-state benzenes show negative values (NICS(0) of −7.5 ppm in Figure 5) whereas antiaromaticity is associated with high positive values (NICS of +31.6 ppm in Figure 5). From the ACID calculations (Figure 5), the degree of electron delocalization can be roughly quantified by inspection

of critical isosurface values (CIVs) in which the topology of the ACID boundary surface becomes separated into independent enveloping surfaces. The first critical isosurface value, that is, for the two rings in DBB* (CIV = 0.076), is only slightly lower than the value obtained for benzene (CIV = 0.081). Moreover, the delocalization pattern in DBB* is analogous to the wellknown observed value for ground-state benzene, that is, portraying both strong diatropic (“aromatic”) and weak paratropic (“antiaromatic”) ring currents.16 In the case of triplet benzene, the ACID reveals only paratropic currents. Thus, in DBB* the two rings can be characterized as “aromatics” by contrasting against singlet and triplet benzene used as reference. In contrast, the paratropic currents of the triplet compound having a saturated bridge suggest antiaromaticity. These results are consistent with those found using the NICS methodology, thus indicating that the Baird’s rule is not applicable in this case due to the fact that the unpaired parallel spins do not coexist in the same ring in DBB*, BR-I, or BR-II (see NICS and ACID for BR-I and BR-II in the Supporting Information). Nevertheless, it is possible to argue that, at least in principle, the particular triplet state of DBB (which has the excitation localized in the benzene rings) could 5972



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Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.8b00499. ACID and ELF backgrounds and the corresponding discussions, optimized geometries, energies of all computed species, and additional computational details (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail (R.A.M.): [email protected]. *E-mail (A.T.-L.): [email protected]. ORCID

Ricardo A. Matute: 0000-0002-0644-3799 Eduardo Chamorro: 0000-0002-9200-9859 Nery Villegas-Escobar: 0000-0002-6370-617X Diego Cortés-Arriagada: 0000-0002-6709-1723 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the FONDECYT Grants No. 1140341, No. 1140343, and No. 1170837. N.V.-E. acknowledges the Ph.D. fellowship from CONICYT. We are indebted to Prof. Dr. Rainer Herges for kindly providing us a copy of the ACID software package.

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Figure 5. (U)M06-2X/6-31G(d) ACID isosurface (0.05 a.u.) of (a) benzene (S0) (left panel) and benzene (T1) (right panel) (b) DBB*and its saturated brigde analogue in (c). The magnetic field vector is parallel to the z-axis, pointing out of page (x−y plane), and the current density vectors plotted onto the ACID isosurface indicate the magnetically induced diatropic (clockwise) and paratropic (anticlockwise) flowing ring currents. The observed pattern in either direction will depend on the relative directions of the current flow and the applied magnetic field. Calculated NICS(0) values are given in units of ppm.

REFERENCES

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be destabilized because Baird’s rule, to such an extent that another triplet state, one with the excitation localized to the ethylene bridge instead, becomes the T1 state. If so, Baird’s rule on triplet-state (anti)aromaticity could still be operational, but in an indirect way.

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CONCLUSION Overall, our results show that the electronic flux along the intrinsic reaction coordinate in the triplet DPM rearrangement of DBB correctly accounts for the loss and recovery of aromaticity, thus leading to stepwise electronic events for both formation and breaking of sigma bonds. Hence, the nonstatistical dynamics nature2 of the Zimmerman DPM rearrangement and the recently reported carbon tunneling of this reaction28 should be envisioned together with our REF perspective to get complete understanding of its intricated mechanism. Moreover, the coupling between REF and aromaticity certainly paves the way toward a better understanding of the electronic nature in reactions involving aromatic molecules. 5973


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Reaction Electronic Flux Perspective on the Mechanism of the

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