The mechanism of a barrierless reaction: hidden transition state and hidden intermediates in the reaction of methylene with ethene

Hyun Joo, Elfi Kraka, Wolfgang Quapp, Dieter Cremer
2007 Molecular Physics  
The chelotropic addition reaction of singlet methylene to ethene yielding cyclopropane (reaction 1) was investigated with the help of the Unified Reaction Valley approach (URVA) using different levels of theory (B3LYP, MP2, MP4, CCSD(T), G3) and two basis sets (6-31G(d,p), 6-311++G(3df3pd)). At all levels of theory, reaction (1) proceeds without barrier and transition state (TS). Nevertheless, reaction (1) possesses a distinct mechanism comprising four different reaction phases: 1) a van der
more » ... es: 1) a van der Waals phase, in which the stereochemistry of the reaction is decided; 2) an electrophilic attack phase, in which charge is transferred from ethene to methylene to establish a weak bonding interaction between the reaction partners typical of those encountered in TSs of CC bond forming reactions; c) a nucleophilic attack phase, in which charge transfer between methylene and ethene is reverted and a trimethylene biradical structure is formed; d) a ring closure phase, in which the trimethylene structure closes to the three-membered ring. The URVA analysis identifies a hidden TS and two hidden intermediates at the transitions from one phase to the next. If methylene is replaced by difluorocarbene (reaction 2) or germylene (reaction 3), the 4-phase mechanism is retained, however the hidden TS and one of the hidden intermediates are converted into real TS and real intermediate thus establishing 2-step mechanisms with strongly different energy profiles along the reaction path. of the reaction path whereas small curvature enhancements are related to the preparation of the reaction complex for the chemical processes. [2,4-6] The height of the curvature peaks can be related to the strength of the bonds being broken/formed, which has an influence on the reaction barrier and the reaction energy. [1,2] Based on the sequence and the position of curvature peaks, a TS region, in which the chemical processes occur, can be distinguished from a) van der Waals regions in entrance and exit channel, in which the first interactions between the reactants forming the reaction complex develop (note that the term reaction complex does not imply the existence of a stable van der Waals complex [1,2]), and b) preparation regions, in which the reactants prepare for the actual chemical processes. [1, 2, [4] [5] [6] We note that a van der Waals region can be observed along the reaction path even if a van der Waals complex does not exist. The curvature of the reaction path is related to the curvature couplings, which result from a coupling between the vibrational modes orthogonal to the reaction path and the translational mode of the reaction 3 complex along the reaction path. The curvature couplings provide information how energy can be transferred from vibrational modes into the reaction path mode and vice versa, [12, 13] which can be used for mode selective rate enhancement. Similarly, analysis of coupling between vibrational modes along the reaction path leads to an understanding of energy dissipation during the reaction. URVA as any other related mechanistic analysis is based on the existence of a unique reaction path, which is defined by the IRC path being identical to the minimum energy path (MEP). Although just a minority of reacting molecules may follow exactly the MEP for a given temperature larger than zero, knowledge of the MEP is in so far essential as it is representative for all similar paths and therefore the mechanistic analysis has to be carried out just once. This changes in the case of barrierless reactions, which do no longer possess a TS. The MEP (IRC path) depends on the existence of a TS and accordingly a MEP can no longer be determined in the case of barrierless reactions. Accordingly, URVA can only be carried out provided a reasonable alternative to the MEP is found in the case of barrierless reactions so that it is still justified to perform the mechanistic analysis just once and to consider the results of this analysis to be representative for the reaction mechanism. The problem encountered for the mechanistic analysis of barrierless reactions has to be seen on the background of the fact that many chemical reactions proceed without an activation enthalpy although reliable quantum chemical methods suggest the existence of a small barrier and by this a TS. Such a TS can be used for the calculation of MEP and the mechanistic analysis despite lack of any chemical relevance of barrier and TS. The MEP obtained for these reactions are still representative for many other similar reaction paths followed by the reaction complex in a statistical manner. If a TS does not exist at all, it will be necessary to obtain an insight into some basic features of the PES concerning the barrierless reaction in question. It has to be clarified whether there is still a reaction valley that starts at the minimum of the reactants and terminates at an energy plateau as it is the case for many dissociation reactions. In recent work, [14] we have demonstrated that the PES can be systematically explored with the help of Newton trajectories (NTs; originally coined reduced gradient following curves). [15,16] NTs have the property of connecting the valley minimum with the energy plateau of a barrierless reaction where the NTs, despite of different starting directions, bundle in the exit channel of the valley before it merges into the energy plateau. [14] It has been shown that the bundling of NTs can be used to determine a starting point for a path downhill from the energy plateau to the minimum. The path follows the valley floor and by this provides a reasonable and representative reaction path, along which the mechanistic analysis can be performed. [14] There are however also situations where the reaction valley is no longer distinctive but opens to a broad bowl leading up to the energy plateau as found in the case of a cirque created by a mountain glacier. [14] Again, the basic features of such a cirque can be explored with the help of NTs and again it is possible to define a reasonable reaction path, along which a representative mechanistic analysis can be carried out. In previous work, we have discussed the computational implications of determining for a barrierless reactions a reasonable reaction path. In the current work, results of the previous study are utilized to answer the basic question whether analysis of the mechanism of a barrierless reaction can be of any general use. As a suitable barrierless reaction we investigate the chelotropic addition of singlet methylene, CH 2 ( 1 A 1 ), to ethene thus yielding cyclopropane (reaction 1, Scheme 1a). The chelotropic reactions between carbenes and alkenes have been investigated numerous times in the last 50 years [17-30] ever since Skell [17, 19] and later Doering [18] provided the first experimental evidence for a two-step mechanism of these reactions. In the first step (see Scheme 1c), the vacant pπ-orbital of the carbene interacts with the π-bond of the alkene in an electrophilic manner, which implies a non-linear approach of the carbene to the alkene. In the second step, the electrophilic attack is followed by a nucleophilic attack involving the occupied (sp 2hybridized) lone-pair orbital of singlet carbene after reorientation of the carbene in a more perpendicular manner relative to the double bond (Scheme 1c). Hence, the carbene-alkene reactions follow a non-least motion (non-linear) rather than a least motion (linear) path, which is in line with the theory of symmetryallowed and symmetry-forbidden chelotropic reactions. [31] Early theoretical support for this mechanism was provided by Hoffmann [21] who used semiempirical Extended Hückel calculations for an investigation of reaction (1). Experimental proof for the non-least motion path turned out to be more difficult, however Houk and co-workers [32] succeeded in providing such proof on the basis of kinetic isotope measurements and quantum chemical calculations in the case of the addition of CCl 2 to pent-1-ene. After sophisticated quantum chemical calculations of the ab initio or density functional (DFT) type became generally available, reactions between ethene and CH 2 ( 1 A 1 ) [23] [24] [25] 30] or other carbenes CX 2 (X = H) [26-30] were investigated and described in more detail. These investigations focused exclusively on the energetics of the carbene addition reactions, their stereochemistry, and the description of the stationary points along the reaction path. So far, a complete mechanistic analysis as it can be obtained by utilizing URVA or similar methods based on the RPH is not available. In the case of reaction (1), a two-step mechanism is not possible because of the missing barrier. Nevertheless, one assumes (without actual proof) a similar reaction mechanism as for other carbene addition reactions. Apart from this, it is a general tendency among chemists to consider barrierless reactions as less interesting. We will show in this work that a barrierless reaction such as (1) can possess a complicated reaction mechanism, which provides detailed information about other chelotropic addition reactions of the same type. Furthermore, we will demonstrate that a TS encountered for other carbene-alkene addition reactions becomes already obvious from the analysis of the barrierless reaction (1). We will develop in this connection the concept of a "hidden TS" that properly complements the concept of "hidden intermediates" previously established in connection with the mechanistic analysis of symmetry-forbidden reactions. [4] For the purpose
doi:10.1080/00268970701620677 fatcat:ssvhint3cfdinmqwzct5pqyj6u