Minimum-energy crossing points

Figure 10. Arrhenius plot of the thermal rate constants for the 2D model system. Circles-full quantum results. Thick solid (dashed) curve present nonadiabatic transition state theory by using the seam surface [the minimum energy crossing point (MECP)] approximation. Thin solid and dashed curves are the same as the thick ones except that the classical partition functions are used. Taken from Ref. [27].

A and A = 0.1 eV. The adiabatic ground potential energy surface is shown in Fig. 11. The present results (solid line) are in good agreement with the quantum mechanical ones (solid circles). The minimum energy crossing point (MECP) is conventionally used as the transition state and the transition probability is represented by the value at this point. This is called the MECP approximation and does not work well, as seen in Fig. 10. This means that the coordinate dependence of the nonadiabatic transmission probability on the seam surface is important and should be taken into account as is done explicitly in Eq. (18). 

Figure 24. Electron-transfer rate versus electronic coupling strength. The temperature is T = 500 K. Solid line with circle-present results from Eq. (126) with the transition probability averaged over the seam surface. Solid line with square-present results with the transition probability taken at the minimum energy crossing point (MECP). Dashed line-Bixon-Jortner theory Ref. [109]. Dotted line-Marcus s high temperature theory. Taken from Ref. [28].

SCHEME 10.15 Qualitative examples for reactions taking place with different spin states involved. Dashed curves indicate reaction paths with higher spin state. Black dots indicate minimum energy crossing points (MECPs). 

The minimum energy crossing point on Ai and Bi surfaces of the phenyl cation (9 X=H) was located by Harvey et al. This point with C2V symmetry lies only 0.12 kcal/mol (CCSD[T]) above the triplet state minimum. At this point, spin-orbit coupling, evaluated at the CASSCF(6,7) level by using a one-electron operator with effective nuclear charges. 

Proposed mechanistic pathway for bis(imidazolium) formation (MECP = minimum energy crossing point).-... 

J. C. Green, J. N. Harvey, R. Poll. Theoretical investigation of the spin crossover transition states of the addition of methane to a series of Group 6 metallocenes using minimum energy crossing points. /. Chem. Soc., Dalton Trans., (2002) 1861-1866. 

The termination of the polymerization reaction by BHE to the chromium center and subsequent dissociation of the resulting olefin is found to require about 25 kcal mol and to be thermodynamically much less feasible than the alternative termination process by BHT to a monomer. The latter process involves spin change two minimum-energy crossing points (MECPs) and further transition states and intermediates have been identified [39]. The termination reaction may also be controlled by the use of polymerization additives [40]. 

Application of the UMP2 and G3 methods has revealed the complex mechanisms for reaction of O3 with 1-butene (CH3CH2CH=CH2), for both adiabatic and non-adiabatic reaction channels, and shown that the minimum energy crossing points play a key role. The site selectivity of the addition of O3 to either carbon atom of the double bond of 1-butene is unremarkable. The mechanisms of formation of butenols are also discussed and shown to occur not only by ketoenol tautomerization but also by a rearrangement and decomposition reaction involving the intermediate epoxide compound. ... 

The two surfaces that cross at the minimum energy crossing point must have a mechanism that couple the two. In the standard nonrelativistic electronic structure theory, there is no mechanism for interaction between the two... 

Singlet and Triplet States of Phenyl Cation. A Hybrid Approach for Locating Minimum Energy Crossing Points between Noninteracting Potential Energy Surfaces. 

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