The Mechanism of a Barrierless Reaction:
Hidden Transition State and Hidden Intermediates in the Reaction of
Methylene with Ethene

Hyun Joo,a Elfi Kraka,a Wolfgang Quapp,b and Dieter Cremer c

a Department of Chemistry, The University of the Pacific, Stockton, CA
95366, USA
ekraka.at.pacific.edu

b Mathematical Institute, University of Leipzig, Augustus-Platz, D-04109
Leipzig, Germany
quapp.at.rz.uni-leipzig.de

c Department of Chemistry and Department of Physics,
The University of the Pacific, Stockton, CA 95366, USA
dcremer.at.pacific.edu

Abstract: 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 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; 
3) a nucleophilic attack phase, in which charge transfer between 
   methylene and ethene is reverted and a trimethylene biradical 
   structure is formed;
4) 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.

Key words: reaction valley approach, barrierless reactions, 
methylene-ethene system, hidden transition state, hidden intermediates, 
difluoromethylene-ethene system, germylene-ethene system