Microcanonical variational transition-state

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

The SN2 identity exchange reaction of chloride with chloroacetonitrile (equation 23) was studied in an FT-ICR spectrometer and also theoretically by means of statistical theories (RRKM with the microcanonical variational transition state) and high-level ab initio calculations238. 

Cf. R. A. Marcus, J. Chem. Phys. 45,2630 (1966). This paper contains this criterion (p. 2635), but mistakenly ascribes it to Bunker, who actually uses, instead, a minimized density of states criterion [D. L. Bunker and M. Pattengill, J. Chem. Phys. 48, 772 (1968)]. This minimum number of states criterion has been used by various authors, for example, W. L. Hase, J. Chem. Phys. 57, 730 (1972) 64, 2442 (1976) M. Quack and J. Troe (Ref. 21) B. C. Garrett and D. G. Truhlar, J. Chem. Phys. 70, 1593 (1979). The transition state theory utilizing it is now frequently termed microcanonical variational transition state theory (/iVTST). A recent review of /tVTST and of canonical VTST is given in D. G. Truhlar and B. C. Garrett, Ann. Rev. Phys. Chem. 35,159 (1984). 

Calculations on electrophilic additions to acetylene were reported for a number of hydrocarbon cations, including CH" [129], C3H3" [130, 131], and phenylvinylium ion [132]. It was predicted that the cyclopropenylium cation, the most stable form of C3H, forms an ion-molecule complex with acetylene but does not undergo further addition [131]. The linear propargyl cation, however, reacts with acetylene without an apparent barrier, to form many different C5H5 isomers [130,131]. Wang et al. computed the AMI potential energy surfaces and carried out RRKM and microcanonical variational transition-state analysis for the rate of reaction of phenylvinylium ion with acetylene [132]. 

The transition state is taken to be the (3V - 7)-dimensional plane orthogonal to the reaction path at that value of s which minimizes the TST rate. For reactions at given energy [microcanonical variational transition-state theory (/uVT)], the bimolecular rate constant is given by [125]... 

S. C. Tucker and E. Poliak, J. Stat. Phys., 66, 975 (1992). Microcanonical Variational Transition State Theory for Reaction Rates in Dissipative Systems. 

Microcanonical variational transition state theory (VTST)... 

W (E, J) has an obvious interpretation as the number of open channels at the location q of the transition state. As one varies the position q of the transition state one finds the optimum choice at the position of a minimum value, W(E.J.q) . Therefore, such approximations are also called microcanonical variational transition state theory. Sometimes the variational procedure has been used with the minimum density of states criterion in equation (117) ... 

CVT = canonical variational transition state theory /xVT = microcanonical variational transition state theory TST=transition state theory VTST = variational TST. 

Classical Methods in Microcanonical Variational Transition State Theory... 

The location of the dividing surface that minimizes Eq. [22] is defined as which specifies the microcanonical variational transition state thus,... 

Fig. 2. Cumulative reaction probability for collinear H + H2 H2+H and collinear D 4- H2 DH + H as a function of energy above the barrier (E-V ). For each reaction the results obtained by conventional transition state theory and microcanonical variational transition state theory are both shown.

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