Finding the Transition State of Quasi-Barrierless Reactions by a Growing String Method for Newton Trajectories:  Application to the Dissociation of Methylenecyclopropene and Cyclopropane

Abstract

A method for finding a transition state (TS) between a reactant minimum and a quasi-flat, high dissociation plateau on the potential energy surface is described. The method is based on the search of a growing string (GS) along reaction pathways defined by different Newton trajectories (NT). Searches with the GS-NT method always make it possible to identify the TS region because monotonically increasing NTs cross at the TS or, if not monotonically increasing, possess turning points that are located in the TS region.The GS-NT method is applied to quasi-barrierless and truly barrierless chemical reactions. Examples are the dissociation of methylenecyclopropene to acetylene and vinylidene, for which a small barrier far out in the exit channel is found, and the cycloaddition of singlet methylene and ethene, which is barrierless for a broad reaction channel with C s -symmetry reminding of a mountain cirque formed by a glacier.

A stunning example for a spontaneous reaction with a complex mechanism: the vinylidene–acetylene cycloaddition reaction

“…The mechanistic pattern based on van der Waals, preparation, and TS regions is also found for reactions without a TS as described for the methylene-ethene addition reaction [12,13]. The latter proceeds without a barrier in one strongly exothermic step although four different reaction phases can be distinguished: (1) a van der Waals phase; (2) an electrophilic attack phase 2668 E. Kraka et al…”

“…However, URVA provides still useful qualitative results in this situation [14,15]. The theoretical basis of URVA has been described previously [12][13][14][15][16][17][18][19][20][21][22] and therefore just some essential quantities of the URVA analysis are summarized here. We use the IRC path as RP [48], which is the steepest descent path expressed in mass-weighted coordinates and following the valley floor line.…”

“…For the purpose of clarifying these questions, we have investigated the chelotropic addition of carbene to multiple bonds [12,13], which is normally described by an orbital symmetry principle [6]. A C 2v -symmetrical linear approach of a carbene head-on to the midpoint of a CC multiple bond is symmetryforbidden or, as can also be said on the basis of PMO theory, leads to destabilizing exchange repulsion between the reaction partners.…”

“…A C 2v -symmetrical linear approach of a carbene head-on to the midpoint of a CC multiple bond is symmetryforbidden or, as can also be said on the basis of PMO theory, leads to destabilizing exchange repulsion between the reaction partners. Therefore, the methylene-ethene addition follows a C s -symmetrical nonlinear path, which is clearly a non-least motion path [12,13]. In this work, we will investigate the chelotropic addition of singlet vinylidene (V) to acetylene (A) leading to methylenecyclopropene (MCP, reaction 1),…”

“…The RP is curved in those regions where major geometric and electronic changes of the RC take place. In previous work, we found that bond breaking and bond forming processes are indicated by a strong curving of the RP [12][13][14][15][16][17][18][19][20][21][22]. Smaller curvature enhancements often indicate a preparation of the RC for the actual chemical processes.…”