Orbiting transition state

Recent mechanistic discussions of unimolecular decompositions of organic ions have invoked ion—molecule complexes as reaction intermediates [102, 105, 361, 634]. The complexes are proposed to be bound by long-range ion—dipole forces and to be sufficiently long-lived to allow hydrogen rearrangements to occur. The question of lifetime aside, there is more than a close similarity between the proposed ion—dipole intermediate and the assumed loose or orbiting transition state of phase space theory. 

FIGURE 17. Potential energy diagram for the C4H6 system. Tight and orbiting transition states are indicated by and O , respectively. Reproduced from Reference 84 by permission of the American... 

What this clearly shows is that the angular momentum barrier is much greater for the H loss than for the CH3 loss channel. This could be a result of a centrifugal barrier with an orbiting transition state, as suggested by Meisels et al. (1979), or it could be due to a vibrator transition states in which the H loss channel proceeds via a tighter transition state (Booze et al., 1993 Bowers et al., 1983). 

PHASE SPACE THEORY AND ORBITING TRANSITION STATE PHASE SPACE THEORY... 

Orbiting Transition State Phase Space Theory... 

Chesnavich and Bowers (1977a,b 1979) modified the phase space theory model by assuming (a) an orbiting transition state located at the centrifugal barrier, and (b) that orbital rotational energy at this transition state is converted into relative translational energy of the products. The Hamiltonian used for this orbiting transition state/phase... 

Here the temperature is that of the transition state, while in the previous chapter the temperature referred to the products. In the case of a dissociation with no barrier and an orbiting transition state, these temperatures should be nearly the same. Because of dynamical constraints imposed by the centrifugal barrier, Eq. (10.60) is not general. In fact, Klots has shown that E) 2k T. However, for reactions with loose transition states which lose polarizable neutral monomers (i.e., not H atoms) the lower (two-dimensional) limit will be nearly correct. 

Figure 11. Kinetic energy release distribution for metastable loss of CH4 from nascent Co(C3Hg)+ collision complexes. The "unrestricted" phase space theory curve assumes the entrance channel contains only an orbiting transition state, the exit channel has only an orbiting transition state (no reverse activation barrier), and there are no intermediate tight transition states that affect the dynamics. The "restricted" phase space theory calculation includes a tight transition state for insertion into a C-H bond located 0.08 eV below the asymptotic energy of the reactants.

Figure 12. Schematic potential energy surface for the reaction Co + C3H8 Co(C2H4)+ + CH4. The dashed portion schematically shows the effect of angular momentum on the initial orbiting transition state and the tight C-H insertion transition state. A collision in which the system passes over the centrifugal barrier may not result in reaction due to reflection at the second barrier.

The absence of the (R) alcohol product can be explained from the greater steric hindrance observed in transition states C and D, which would lead to the formation of the (R) product. Transition states C and D are again related to each other through attack of the aldehyde from the opposite apex of the p-orbital. Transition state C is related to A by attack at the opposite face of the prochiral carbonyl moiety (as B is to D). 

For the theoretician, clusters are also convenient model systems to evaluate the performance of dissociation rate theories. By comparing the results of numerically exact molecular dynamics (MD) trajectories to the predictions of rate theories, the various approximations inherent to these theories can be unambiguously tested and possibly improved upon. Previous authors have critically discussed how the Rice-Ramsperger-Kassel (RRK), ° Weisskopf, and Phase Space Theory of Light and Pechukas, Nikitin, Klots, Chesnavich and Bowers respectively compare for the thermal evaporation of atomic clusters. This work was subsequently extended by the present authors to rotating and molecular clusters. From these efforts it was concluded that phase space theory (PST), in its orbiting transition state version, was quantitatively able to describe statistical dissociation. This chapter is not devoted to a detailed presentation of phase space theory and the reader is encouraged to consult the cited work. 

Variations of the evaporation rate constant of the (H2O)50 cluster, as predicted by phase space theory (PST) in its orbiting transition state version, and values of the rate constant obtained from statistical molecular dynamics (MD) trajectories at high energies. The inset shows the decay of the number of clusters N(t) having resisted evaporation as a function of time, at three internal energies denoted next to the curves and in logarithmic scale. 

The orbiting transition state phase space theory (OTS/PST)... 

Phase space orbiting transition state theory works much better for the calculation of KERDs than for that of the rate constants, thereby demonstrating that the former are controlled by the long-range part of the potential whereas the latter are governed by its shorter range. In addition, Klots has introduced a set of effective temperatures to parametrize the observed distributions. The SACM has also demonstrated its usefulness in the case of weakly bonded species. 

Carbenes A Testing Ground for Electronic Structure Methods Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Mpller-Plesset Perturbation Theory Natural Orbitals Transition State Theory Unimolecu-lar Reaction Dynamics. 

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