A Bonding Evolution Analysis for the Thermal Claisen Rearrangement. An Experimental and Theoretical Exercise for Testing the Electron Density Flow

A comprehensive theoretical investigation of the thermal Claisen rearrangement of allyl vinyl ether (AVE) to allylacetaldehyde has been carried out. We present the use of the electron localization function (ELF) to monitor the bonding evolution aspects in the course of this thermal rearrangement and the results are compared with a photo-impulsive process where instantaneous vibration frequencies are monitored [I. Iwakura, Phys. Chem. Chem. Phys., 2011, 12, 5546-5555]. Our results reveal an asynchronous electron density rearrangement inasmuch that the breaking of the C3-O bond and the formation of C1-C5 do not take place simultaneously. We also demonstrate how the bonding evolution brings about the natural appearance of the curly arrows representing the electronic flow in molecular rearrangements. This holds the key to gaining an unprecedented insight into the mapping of the electron density flow while the bonds change throughout the reaction progress.


Introduction
During the progress of a given chemical reaction, molecular structural changes from reactants to products take place via transition structures and/or possible intermediates. The results of fundamental research studies -both theoretical and experimental-have allowed the localization and determination of those stationary points on potential energy surfaces (PESs) to fully clarify the mechanism behind chemical reactions. Nevertheless, a further step 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), in contrast to the electronic wave-function, is a physical observable and therefore represents a well-defined property for analysis. ρ(r) is an experimentally accessible scalar field and a local function defined within the exact manybody theory. A deeper analysis in chemical reactivity can thus be achieved in order to identify the electron density flow as a function of reaction progress, while chemical events such as breaking/forming bonds and/or rearrangements of pairs of electrons are monitored. In this sense, previous theoretical studies have been reported and a connection between electron density ρ(r) distribution and chemical reactivity is found. 1-13 In addition, developments in ultrafast electron and X-ray diffraction have led to experiments where molecular dynamics can be followed on the time scale of a chemical reaction. [14][15][16] Examples include the seminal works of Zewail on femtosecond dynamics 17 or those based on X-ray diffraction, 18,19 electron diffraction, 20 or laser-induced recollision. [21][22][23][24] In particular, an ultrafast spectroscopy system with a visible ultrashort-pulse laser developed by Kobayashi et al. [25][26][27] makes it possible to obtain time-dependent frequency shifts of relevant molecular vibrational modes throughout the reaction. 28,29 This development is considered an innovative window to analyze the reaction mechanism of complex chemical rearrangements and also allows for a clear visualization of ultrafast structural changes in molecules during bond breaking/forming chemical events. Similarly, the remarkable properties of modern ultrashort X-ray and electron pulses seem to offer a very feasible alternative in the domain of ultrafast electronic processes of molecular systems. In particular, the degenerated Cope rearrangement of semibullvalene has been used as an example to illustrate the X-ray imaging of chemically active valence electrons during a pericyclic reaction. 30 This approach allows the extraction of the changes in ρ(r) throughout the reaction progress, which are directly related to bondmaking and bond-breaking processes, namely, the chemical valence electron density from the overall X-ray scattering pattern -which itself is dominated by the core electrons. This The motivation behind this study essentially arises from the works concerning the photo-impulsive Claisen rearrangement of allyl vinyl ether (AVE) reported by Iwakura and co-workers. 31,32 The photo-impulsive reaction is induced with Raman processes, where only a fraction of the molecular vibration modes are excited to high-level vibrational excited states with a few-optical-cycle visible pulse, which ensures the reaction is triggered coherently.
Although the thermal reaction may not be completely ruled out, the photo-impulsive process in the ground state, which is neither a photo-nor a thermal-reaction, follows the same reaction pathway as that of the symmetry-allowed thermal rearrangement in the ground state. The frontier orbitals of the photo-impulsive reaction in the electronic ground state can therefore be thought to be same as those of the thermal reaction. 28 Taking this into account, we present an alternative representation of the reaction mechanism for the thermal Claisen rearrangement of AVE in its respective ground state within the framework of the bonding evolution theory (BET), 33 which combines the joint use of the electronic localization function (ELF) 34,35 and Thom's catastrophe theory (CT) 36 allowing direct comparison with photoimpulsive reaction systems.

Computational details
The optimization and characterization of all stationary points on the PES as well as the calculation of the intrinsic reaction coordinate (IRC) 37,38 pathway have been performed with Gaussian 09. 39 The B3LYP 40,41 electron density functionals, together with the 6-311+G(d,p) 42 basis set, have been used for all atoms; as in previous studies the use of this methodology has been successfully tested. 6,7,10,11 For each point obtained on the IRC pathway, the topological analysis of the ELF was performed using the TopMod package, 43 considering a cubical grid with a step-size smaller than 0.05 bohr. The topological partition of the ELF gradient field 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. 44  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, since hydrogen atoms have a valence shell; they are therefore called protonated disynaptic.
Additionally, the basin population obtained by integration of the electronic density defines the number of electrons shared in a bond or in lone pairs. Taking this into account, the electronic density flow can be evaluated, thus indicating the changes in structure of the system, that is, the connectivity among atoms along the reaction coordinate. It also serves as a basis for a better understanding of such processes by undertaking a meaningful assessment of the physical origins of potential energy barriers. Thus, the reaction is represented as a sequence of ELF topological domains called structural stability domains (SSDs). Accordingly, by using the molecular structure defined through the ELF topology, the reaction mechanism can be rationalized in terms of chemical events (i.e., bond forming or breaking processes, creation and annihilation of electron pairs) that are directly related to the corresponding SSD. For the sake of brevity, details concerning the theoretical aspects of the ELF, CT, and BET analyses as applied to single-step intermolecular processes are available elsewhere, 5 while its applicability to more complex processes including multi-step and/or intermolecular reactions has also been previously shown by us. 6,7,10,11

Results and discussions
The In addition, the ν s C=C of the vinyl and allyl groups appears at around 1650 cm -1 just after the photo-irradiation; nevertheless from 500 to 800 fs the ν s C=C splits into two red-and blue-  Table 1 and Figure 2

Conclusions
In summary, a complete bonding evolution analysis provides a significant guide with which to elucidate chemical reaction mechanisms. Thus, valuable information is obtained to applications. This analysis can be used for the study of different organic and inorganic chemical reactions, thus changing the way in which we think about reaction mechanisms.

Notes
The authors declare no competing financial interest

Acknowledgments
The authors are grateful to Generalitat Valenciana for PrometeoII/2014/022 and Scheme1 Figure 1. IRC reaction pathway with their corresponding structural stability domains (SSDs) for the thermal rearrangement of AVE to allylacetaldehyde. Bellow the graph, a schematic representation of the reaction mechanism for each SSD from the ELF analysis (full lines and ellipses represent disynaptic and monosynaptic basin, respectively. Dotted lines indicate a large basin population. For the sake of clarity, protonated disynaptic basins and monosynaptic V i=1,2 (O) basins are omitted.    SSD-I  SSD-II  SSD-III  SSD-IV  SSD-V  SSD-VI  SSD-VII  SSD-