How a Quantum Chemical Topology Analysis Enables Prediction of

Letter pubs.acs.org/JPCL

How a Quantum Chemical Topology Analysis Enables Prediction of Electron Density Transfers in Chemical Reactions. The Degenerated Cope Rearrangement of Semibullvalene Patricio González-Navarrete,† Juan Andrés,*,† and Slawomir Berski‡ †

Departamento de Química Física y Analítica, Universitat Jaume I, 12071 Castelló de la Plana, Spain Faculty of Chemistry, University of Wroclaw, F. Joliot-Curie 14, 50-383 Wroclaw, Poland

‡

S Supporting Information *

ABSTRACT: Recent works on the reaction mechanism for the degenerated Cope rearrangement (DCR) of semibullvalene (SBV) in the ground state prompted us to investigate this complex rearrangement in order to assign experimentally observed contrast features in the simulated electron distribution. We present a joint use of the electron localization function (ELF) and Thom's catastrophe theory (CT) as a powerful tool to analyze the electron density transfers along the DCR. The progress of the reaction is monitored by the structural stability domains of the topology of ELF, while the change between them is controlled by turning points derived from CT. The ELF topological analysis shows that the DCR of SBV corresponds to asynchronous electron density rearrangement taking place in three consecutive stages. We show how the pictures anticipated by drawing Lewis structures of the rearrangement correlate with the experimental data and time-dependent quantum description of the process. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

T

allow a Lewis type of arrow representation in terms of electronic fluxes between neighboring bonds, revealing their asynchronous nature. The DCR of SBV corresponds to a complex and coupled forming and breaking of chemical bonds, and it has been widely studied in order to provide relevant insights into those properties that are related to pericyclic reactivity.10−14 As shown in Scheme 1, the net structural outcome is the breaking/

o a large extent, chemistry can be viewed as the art of making and breaking bonds, and understanding the basic science behind this has been one of the main challenges of theoretical and computational chemistry. A reaction mechanism represents a sequence of elementary steps by which overall chemical change occurs, describing in detail what takes place at each stage of a chemical transformation, that is, chemical bonds are breaking/forming processes, electron pair rearrangements, transformation of formally double to simple bonds or vice versa, and so forth. Measurements visualizing the progress of chemical reactions on their natural time scale can be considered the holy grail of chemical physics as it is now done for the resolution of molecular structure by using ultrafast electron diffraction1 or X-ray diffraction.2 Furthermore, recent advances in the emerging area of attosecond physics3 (providing realtime access to the motion of electrons on atomic and subatomic scales) and real-time vibrational spectroscopy4−6 by a few femtosecond pulse laser (enabling the observation of dynamic behavior of molecular vibrations during chemical reactions) have been recently achieved. The motivation of our investigation essentially arises from the results of three recent works concerning electronic mechanistic aspects of pericyclic reactions. Bredtmann, Manz, et al.,7,8 by means of selective laser pulses, monitored electronic fluxes that accompany the breaking and making of covalent bonds during the degenerated Cope rearrangement (DCR) of semibullvalene (SBV). In addition, these authors9 have carried out time-dependent quantum simulations in order to analyze the electronic fluxes as the reaction proceeds, and their results © XXXX American Chemical Society

Scheme 1

forming of the C2−C8/C4−C6 bonds and the transformations of formal single C2−C3 and C7−C8 bonds to double ones, while an opposite behavior takes place in C3−C4 and C6−C7 bonds. The delineation of factors that control the pair electron reorganization on this rearrangement is complicated. Although a large number of experimental and computational studies have mainly been focused on the energy barriers (with special attention in the transition states, TSs) and the rearrangement of Received: July 18, 2012 Accepted: August 20, 2012

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dx.doi.org/10.1021/jz300974v | J. Phys. Chem. Lett. 2012, 3, 2500−2505

The Journal of Physical Chemistry Letters

Letter

Figure 1. Energy profiles for the DCR of SBV calculated by means of the IRC method. Below the graph, a schematic representation of the reaction mechanism for each figure is depicted from the perspective of the ELF analysis (full lines and ellipses represent disynaptic and monosynaptic basins, respectively; dotted lines indicate a large basin population).

the geometrical parameters,12,15−21 the electronic mechanism concerning DCR of SBV is still not well understood.22 One step further is based on the idea that it is reasonable to think that an adequate representation of these chemical events should be given by a physical observable defined in coordinate space. The electron density, ρ(r), is the best choice because it is a local function defined within the exact many body theory, and it is also an experimentally accessible scalar field. Therefore, in the deeper study of chemical reactivity, we want to identify how electron density transfers occur as a function of reaction progress, which constitutes the motivation of the present work. In doing so, we can provide a connection between the ρ(r) distribution and the chemical reactivity. The importance of ρ(r), as a fundamental property of an electronic system containing all information of physical relevance, is highlighted by the Hohenberg−Kohn theorem.23 ρ(r) of a molecule contains information not only on the atomic structure and electronic properties but also on the nature of the chemical bonds that lead ultimately to chemical reactivity. Very recently, Stalke24 has provided an introduction to the basics of ρ(r) investigations from a theoretical point of view. Herein, we present an alternative representation of the electron density transfers during the DCR of SBV in the ground state in the domain of quantum chemical topology (QCT), a subarea of quantum mechanics,25 in which different methods based on the seminal work of Bader are included.26,27 In doing so, we show how the DCR of SBV can be analyzed. To this end, we have developed the joint use of an electronic localization function (ELF)28,29 and Thom's catastrophe theory (CT).30,31 In this framework, the mechanism of chemical reactions can be rationalized in terms of chemical events (bond-forming or -breaking processes, creation and annihilation of electron pairs) that drive the chemical rearrangement. This analysis allows us to understand the electronic structure and related properties of

the reactants as the reaction takes place, providing a nice guide to elucidate the mechanism of chemical reactions and further understanding of the chemical reactivity. This methodology proposed by Krokidis et al. is known as bonding evolution theory (BET)30 (more details concerning theoretical aspects of the Thom’s CT and BET are available in the Supporting Information). Thus, questions such as how could the electronic reorganization proceed along the reaction path, is the electronic density flowing synchronously, in which direction, and do the bond forming/breaking processes take place at the TS may be answered. This combined method that we use herein has been described in much detail previously32−41 In particular, in the present work, we want to assess the usefulness of this theoretical protocol by comparing with previous results obtained by means of selective laser pulses experiments and time-dependent quantum simulations.7−9 Complementarily, from the ELF topological and CT analysis, it is also possible to symbolize the electronic transfer in pericyclic reactions suggesting a graphical representation of curved arrows in Lewis structures as the reaction proceeds. It will also be a challenge to extend the present investigations to complex reactions of other systems. In order to analyze the electron density transfer, we have traced the intrinsic reaction coordinate (IRC)42,43 pathway from reactant to product. B3LYP/6-311+G(2d,p) calculations have been performed using the Gaussian 0944 code in order to localize the structures involved in the chemical rearrangement. For each point obtained on the IRC pathway, we have carried out the topological analysis of the ELF field by means of the TopMod package45 considering a cubical grid of step size smaller than 0.1 bohr.46 The ELF function is a convenient tool for the analysis of chemical bonding as it reveals regions in molecular space where the probability of finding an electron pair is high; thus, numerical values of the ELF are mapped on 2501



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the interval (0,1) facilitating its analysis. The topological partition of the ELF gradient field29 yields basins of attractors that can be thought of as corresponding to atomic cores, bonds, and lone pairs. In molecules, two types of basins are found, (i) core basins surrounding nuclei and labeled C(A) (where A is the atomic symbol of the element) and (ii) valence basins that are characterized by the number of core basins with which they share a boundary. This number is called the synaptic order.47 Thus, there are monosynaptic, disynaptic, trisynaptic basins, and so on. Monosynaptic basins, labeled V(A), correspond to the lone pairs of the Lewis model, and polysynaptic basins correspond to the shared pairs of the Lewis model. In particular, disynaptic basins, labeled V(A,X), correspond to two-center bonds, trisynaptic basins, labeled V(A,X,Y), to three-center bonds, and so on. The valence shell of a molecule is the union of its valence basins. As hydrogen nuclei are located within the valence shell, they are counted as a formal core in the synaptic order because hydrogen atoms have a valence shell. Therefore, they are called protonated disynaptic. In addition, the electronic population of the bonding basin, obtained by integration of the electronic density, defines the number of electrons shared in a bond. Accordingly, by using the molecular structure defined through the topology of ELF, the knowledge of the electronic density transfers is a valuable completion of the structural evolution, which describes the change in structure of a system, that is, the connectivity among atoms, along a chemical reaction, and serves as a basis for a better understanding of such process, as well as to undertake a meaningful assessment of the physical origins of potential energy barriers. According to the theory of dynamics systems, it can be considered structurally stable if a small perturbation is only possible for values of the control parameters in well-defined ranges, namely, structural stability domains (SSDs), where all of the critical points are hyperbolic and separated by catastrophic points at which at least one critical point is nonhyperbolic. Along the reaction pathway, the chemical system goes from a given SSD to another by means of bifurcation catastrophes occurring at the turning points (TPs). The bifurcation catastrophes occurring at these TPs are identified according to Thom’s classification.31 The energy profile along the reaction coordinate is reported in Figure 1 together with the SSDs representing the different ELF topologies along the reaction coordinate. The electronic rearrangement reveals five different SSDs, which can be viewed as a sequence of chemical events. The SSDs are separated by respective TPs derived from CT that are responsible for the topological changes of the system. For each point obtained on the IRC pathway, we have evaluated the basin populations of some specific attractors with the aim of following their respective evolutions in the different SSDs. Our calculations predict an energy barrier of 4.45 kcal/mol, in good agreement with previous studies carried out by Bader and co-workers48 at the B3PW91 level. The ELF topology of SBV presents eight core basins of carbon C(Ci=1,8) (blue button), which characterize the electron density of core regions (see Figure 2a) with basin populations of 2.09 e. In addition, the formal single C−C bonds of SBV are represented by only single disynaptic basins V(C,C) (green button) between the respective core carbon basins C(C). The V(C2,C3) and V(C7,C8) disynaptic basin populations were calculated to be to 2.14 e, slightly higher than that expected for formal single bonds. Conversely, the formal double C3C4

Figure 2. Snapshots of the ELF localization domains for (a) SBV, (b) turning point-I (TP-I), and (c) the TS. Color code: blue for core basins, red for monosynaptic basins, white for protonated disynaptic basins, and green for disynaptic basins.

and C6C7 bonds are not reflected by a pair of disynaptic basins Vi=1,2(C3,C4) and Vi=1,2(C6,C7), as sometimes observed,49 but only single V(C3,C4) and V(C6,C7) disynaptic basins were found. The V(C3,C4) and V(C6,C7) disynaptic basins integrate the electronic charge to 3.42 e. A quantitative analysis is further achieved by integrating the electron density over the volume of the basin yielding basin populations in order to understand how the electron density transfers are proceeding during the chemical rearrangement. Figure 3 shows the evolution of the basin population along the

Figure 3. Basin populations along the IRC path of the DCR. Basin population in electrons.

IRC pathway of the five SDDs, while the basin populations are summarized in Table1. The integration of the electronic charge over the ELF basins along SSD-I reveals the following (see Figure 3): (1) A pronounced decrease in the V(C2,C8) basin population is observed (0.29 e). (2) A very small increment of the V(C2,C3) basin population takes place (0.09 e) while the V(C3,C4) basin population decreases (0.05 e). (3) The V(C1,C5) basin population practically remains constant, indicating that electronic charge is not mainly transferred 2502



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Table 1. Integrated Electron Populations of the ELF Basins in Different Structural Stability Domains (SSDs) of the DCR of SBV Calculated for the Initial and Final Points of Each SSDa SDD

SSD-I

species

semibullvalene

Rx d(C2−C8) V(C1,C5) V(C1,C2) V(C2,C3) V(C3,C4) V(C2,C8) V(C4,C5) V(C2) V(C8) ΔE

reactive 1.610 1.90 1.83 2.14 3.42 1.61 1.97

SSD-I

SSD-II

SSD-III TS

−3.06b 1.614 1.90 1.83 2.15 3.42 1.59 1.97

−2.29c 1.735 1.90 1.89 2.24 3.37 1.32 1.98

1.64

−2.15b 1.759 1.89 1.91 2.26 3.35

−1.34c 1.902 1.88 2.00 2.47 3.24

−1.21b 1.926 1.89 2.01 2.83 3.22

0.00 2.120 1.89 2.06 3.02 2.93

1.99 0.63 0.63 2.13

2.00 0.38 0.38

2.01

2.06

0.68d

a Increments of energy within each SSD in kcal/mol (ΔE = ΔElast − ΔEinitial); the reaction coordinate (Rx) is in amu1/2 bohr, and the distances are in angstroms. bInitial point of the SSD. cLast point of the SSD. dCalculated energy between the first point of the SSD-III and the TS.

Figure 2c). While the change of the energy between the TP-II and TS is calculated to be 0.68 kcal/mol, the SDD-III is found to be the longest SDD along the chemical process. Subsequently, after reaching the TS, the basin population analysis of the SSD-IV and SSD-V can be interpreted as SSD-II and SDD-I, respectively. Using the notation previously defined by Berski et al.36 (see more details in Supporting Information), the sequence of TPs can be represented as 5-C†[F]2TS[F†]2C-0. According to the above findings, the reaction mechanism can be illustrated as it is depicted in Scheme 2, in which the curly arrows stand for

toward the C1−C5 region. Additionally, the V(C1,C2) basin population increases slightly (0.06 e) as a consequence of the internal electronic redistribution. Note that the SSD-I entails an energetic cost of 1.64 kcal/mol and eight points along the IRC pathway. The first turning point (TP-I) indicates a cusp (C†) type catastrophe (connecting SSD-I and SSD-II). It takes place at −2.15 amu1/2 bohr and d(C2,C8) = 1.759 Å. The valence disynaptic basin V(C2,C8) is transformed into two monosynaptic basins, V(C2) and V(C8) (see Figure 2b), which have been localized in the region of C2 and C8 carbon atoms, respectively. At the beginning of the SSD-II, both V(C2) and V(C8) monosynaptic basin populations are calculated to be 0.63 e and electron density is highly delocalized. From a strictly topological point of view, one may state that the C2−C8 bond has been broken. Along SSD-II, it is possible to observe a continuous increase of the V(C2,C3) basin population while V(C2) and V(C8) basins populations decrease progressively until their annihilation. This fact indicates that the electron density from V(C2,C8) basin and the respective V(C2) and V(C8) monosynaptic basins along SSD-I and SSD-II, respectively, may be transferred toward the C2−C3 region and its symmetric analogue (C7−C8 region). The gradual decrease of the V(C3,C4) basin population along both SSD-I and SSD-II is even more pronounced along SSD-III, pointing out that the electron density is principally transferred toward the C4 region (and its symmetric analogue the V(C7,C6) basin, toward the C6 region.). It is worth noting that SSD-II is the most energetic SDD that entails an energetic cost of 2.13 kcal/mol and seven points along the IRC pathway. Subsequently, the TP-II is found in the region between SSD-II and SSD-III at −1.21 amu1/2 bohr and d(C2−C8) = 1.926 Å. Two simultaneous fold ([F]2) catastrophes are identified in the region of C2 and C8 atoms. Both the V(C2) and V(C8) attractors are annihilated. The nonbonding V(C2) and V(C8) monosynaptic basins are not observed, and from a chemical point of view, there are no signs of the former C2−C8. The electron density is distributed on the ring formed by the cyclic carbon skeleton C1−C2−C3−C4−C5-C6−C7−C8. Note that the V(C1,C5) basin population does not undergo significant changes even at the TS, while the V(C1,C2) basin population reaches its maximum value at this point; see Table 1 and Figure 3. Interestingly, the breaking/forming processes of C2−C8 and C4−C6 bonds are not taking place at the TS structure (see

Scheme 2

electron density transfers accompanying the breaking of chemical bonds and the forming of new chemical bonds or the rearrangements of electron pairs, together with associated transitions from single to double bonds or vice versa. From this type of analysis, we can conclude that this reaction can be dissected in three consecutive stages; the first stage yields to the C2−C8 bond-breaking process with no significant electronic rearrangement. The second part of the reaction path can be viewed as a reorganization of the valence molecular shells with concomitant reorganization of C3−C4 and C6−C7 bonds, from double to single, while an opposite behavior appears in the C2−C3 and C7−C8 bonds. In the third stage, the C4−C8 bond-forming process takes place. This result shows that the reaction DCR of SBV corresponds to asynchronous electron density rearrangement. Although most current research is focused on the accurate prediction of energy barriers and reaction energies of chemical reactions, an understanding of their origin based on the electron density is desirable. This approximation can adequately describe the thermal DCR of SBV, showing the order, direction, and asynchronicity of the electron flux to be in 2503



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(3) Krausz, F.; Ivanov, M. Attosecond Physics. Rev. Mod. Rev. 2009, 81, 163−234. (4) Iwakura, I.; Yabushita, A.; Kobayashi, T. Direct Observation of the Molecular Structural Changes during the Claisen Rearrangement Including the Transition State. Chem. Lett. 2010, 39, 374−375. (5) Iwakura, I. The experimental Visualisation of Molecular Structural Changes during both Photochemical and Thermal Reactions by Real-Time Vibrational Spectroscopy. Phys. Chem. Chem. Phys. 2011, 13, 5546−5555. (6) Abe, M.; Iwakura, I.; Yabushita, A.; Yagi, S.; Liu, J.; Okamura, K.; Kobayashi, T. Direct Observation of Denitrogenation Process of 2,3Diazabicyclo 2.2.1 Hept-2-ene (DBH) Derivatives, Using a Visible 5-fs Pulse Laser. Chem. Phys. Lett. 2012, 527, 79−83. (7) Bredtmann, T.; Manz, J. Electronic Bond-to-Bond Fluxes in Pericyclic Reactions: Synchronous or Asynchronous? Angew. Chem., Int. Ed. 2011, 50, 12652−12654. (8) Bredtmann, T.; Manz, J. Optimal Control of the Initiation of a Pericyclic Reaction in the Electronic Ground state. J. Chem. Sci. 2012, 124, 121−129. (9) Andrae, D.; Barth, I.; Bredtmann, T.; Hege, H.-C.; Manz, J.; Marquardt, F.; Paulus, B. Electronic Quantum Fluxes during Pericyclic Reactions Exemplified for the Cope Rearrangement of Semibullvalene. J. Phys. Chem. B 2011, 115, 5476−5483. (10) Zimmerman, H. E.; Grunewald, G. L. The Chemistry of Barrelene. III. A Unique Photoisomerization to Semibullvalene. J. Am. Chem. Soc. 1966, 88, 183−184. (11) Quast, H.; Herkert, T.; Witzel, A.; Peters, E.-M.; Peters, K.; von Schnering, H. G. 2,6-Dicyano-1,5-dimethyl-4,8-diphenylsemibullvalene. Synthesis, Structure and the Reactions with Triplet Oxygen. Chem. Ber. 1994, 127, 921−932. (12) Williams, R. V. Homoaromaticity. Chem. Rev. 2001, 101, 1185− 1204. (13) Cheng, A. K.; Anet, F. A. L.; Mioduski, J.; Meinwald, J. Determination of the Fluxional Barrier in Semibullvalene by Proton and Carbon-13 Nuclear Magnetic Resonance Spectroscopy. J. Am. Chem. Soc. 1974, 96, 2887−2891. (14) Martin, H. D.; Urbanek, T.; Walsh, R. Thermal Behavior of C8H8 Hydrocarbons. 2. Semibullvalene: Kinetic and Thermodynamic Stability. J. Am. Chem. Soc. 1985, 107, 5532−5534. (15) Hoffmann, R.; Stohrer, W. D. Cope Rearrangement Revisited. J. Am. Chem. Soc. 1971, 93, 6941−6948. (16) Dewar, M. J. S.; Lo, D. H. Ground States of Sigma-Bonded Molecules. XIV. Application of Energy Partitioning to the MINDO [Modified Intermediate Neglect of Differential Overlap] /2 Method and a Study of the Cope Rearrangement. J. Am. Chem. Soc. 1971, 93, 7201−7207. (17) Jackman, L. M.; Fernandes, E.; Heubes, M.; Quast, H. The Effects of Substituents on the Degenerate Cope Rearrangement of Semibullvalenes and Barbaralanes. Eur. J. Org. Chem. 1998, 1998, 2209−2227. (18) Williams, R. V. Semibullvalenes and Related Molecules: Ever Closer Approaches to Neutral Homoaromaticity. Eur. J. Org. Chem. 2001, 2001, 227−235. (19) Hrovat, D. A.; Williams, R. V.; Goren, A. C.; Borden, W. T. B3LYP Calculations on Bishomoaromaticity in Substituted Semibullvalenes. J. Comput. Chem. 2001, 22, 1565−1573. (20) Brown, E. C.; Henze, D. K.; Borden, W. T. Are 1,5Disubstituted Semibullvalenes That Have C2v Equilibrium Geometries Necessarily Bishomoaromatic? J. Am. Chem. Soc. 2002, 124, 14977− 14982. (21) Hrovat, D. A.; Brown, E. C.; Williams, R. V.; Quast, H.; Borden, W. T. How Important is Bishomoaromatic Stabilization in Determining the Relative Barrier Heights for the Degenerate Cope Rearrangements of Semibullvalene, Barbaralane, Bullvalene, and Dihydrobullvalene? J. Org. Chem. 2005, 70, 2627−2632. (22) Ichikawa, Y.; Sakai, S. Theoretical Study on the Cope Rearrangement Mechanisms and the Homoaromaticity of Semibullvalene, Barbaralane, and 1,5-Methanosemibullvalene. J. Phys. Org. Chem. 2012, 25, 409−419.

good agreement with those of the previous works developed by Bredtmann, Manz, et al.7−9 It is important to remark that our study is based on the Born−Oppenheimer approximation, which implies that the electron density rearranges following the motion of the nuclei. However, a clear line of improvement must be properly taken into consideration for nonadiabatic effects; in this context, many excellent review articles on the theory of nonadiabatic transitions have been published.50 In particular, Prezdo and coworkers have discussed the importance of time domain DFT simulation, including nuclear motions, on electron density transfer to investigate how the electron−phonon plays a key role in the electron-transfer process51,52 In summary, our work provides very rich information to facilitate visualization and conceptualization of chemical reactions, and we are capable of probing chemical events such as the breaking/forming of chemical bonds, transformation of formally double to simple bonds, and so forth, allowing a Lewis type representation of curly arrows associated to electron density transfers. The present methodology is based on physical laws and quantum theoretical insights, and it can be considered as an appropriate tool to tackle chemical reactivity with a wide range of possible applications and the universal behavior that it predicts. It is our hope that it will be used for the study of different organic and inorganic chemical reactions and, overall, that they help to change the way in which we think about reaction mechanisms.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information concerning complete refs 2 and 44, computational details, electron localization function, Thom’s catastrophe theory, bonding evolution theory, minimumenergies structure of SBV and the TS in Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +34 964728083. Fax: +34 964728066. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by Generalitat Valenciana for Prometeo/2009/053 project, Spanish Ministry Ministerio de Economiá y Competitividad for Project CTQ2009-14541-C02, as well as to Fundación Bancaixa-Universitat Jaume I (UJI) for financial support during S.B.'s research stay at UJI. P.G.-N. gratefully acknowledges the Postdoctoral grant provided by UJI. Finally, the authors are also grateful to the Servei d’Informatica, Universitat Jaume I, and the Wroclaw Centre for Networking and Supercomputing for generous allocation of computer time.

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REFERENCES

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