Variational transition state

It may be iisefiil to mention here one currently widely applied approximation for barrierless reactions, which is now frequently called microcanonical and canonical variational transition state theory (equivalent to the minimum density of states and maximum free energy transition state theory in figure A3,4,7. This type of theory can be understood by considering the partition fiinctions Q r ) as fiinctions of r similar to equation (A3,4.108) but with F (r ) instead of V Obviously 2(r J > Q so that the best possible choice for a... 

Poliak E 1993 Variational transition state theory for dissipative systems Acf/Vafed Barrier Crossinged G Fleming and P Hanggi (New Jersey World Scientific) p 5... 

Gershinsky G and Poliak E 1995 Variational transition state theory application to a symmetric exchange in water J. Chem. Phys. 103 8501... 

Poliak E, Tucker S C and Berne B J 1990 Variational transition state theory for reaction rates in dissipative systems Phys. Rev. Lett. 65 1399... 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

Variational RRKM calculations, as described above, show that a imimolecular dissociation reaction may have two variational transition states [32, 31, 34, 31 and 36], i.e. one that is a tight vibrator type and another that is a loose rotator type. Wliether a particular reaction has both of these variational transition states, at a particular energy, depends on the properties of the reaction s potential energy surface [33, 34 and 31]- For many dissociation reactions there is only one variational transition state, which smoothly changes from a loose rotator type to a tight vibrator type as the energy is increased [26],... 

Figure A3.12.9. Comparison of the unimolecular dissociation rates for HO2—>H+02 as obtained from the quantum mechanical resonances open circles) and from variational transition state RRKM step...

Truhlar D G and Garrett B C 1980 Variational transition-state theory Acc. Chem. Res. 13 440-8... 

Hu X and Hase W L 1989 Properties of canonical variational transition state theory for association reactions without potential energy barriers J. Rhys. Chem. 93 6029-38... 

Song K and Chesnavich W J 1989 Multiple transition states in chemical reactions variational transition state theory studies of the HO2 and HeH2 systems J. Chem. Rhys. 91 4664-78... 

Variational transition state theory (VTST) is formulated around a variational theorem, which allows the optimization of a hypersurface (points on the potential energy surface) that is the elfective point of no return for reactions. This hypersurface is not necessarily through the saddle point. Assuming that molecules react without a reverse reaction once they have passed this surface... 

For the accurate, a priori calculation of reaction rates, variational transition state calculations are now the method of choice. These calculations are capable of giving the highest-accuracy results, but can be technically dilficult to perform... 

Reviews of transition state theory and variational transition state theory are... 

CVT (canonical variational theory) a variational transition state theory technique... 

UFF (universal force field) a molecular mechanics force field unrestricted (spin unrestricted) calculation in which particles of different spins are described by different spatial functions VTST (variational transition state theory) method for predicting rate constants... 

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Benzofuroxan 79 can be generated from 2-nitrophenyl azide 80 (Scheme 49). Neighboring-group assistance within the pyrolysis leads to a one-step mechanism with an activation barrier of 24.6 kcal/mol at the CCSD(T)/6-31 lG(2d,p) level [99JPC(A)9086]. This value closely resembles the experimental one of 25.5 kcal/mol. Based on the ab initio results for this reaction, rate constants were computed using variational transition state theory. 

D. G. Truhlar and B. C. Garrett, Variational transition state theory, Annu. Rev. Phys. Chem. 35, 159 (1984). 

S. C. Tucker, Variational transition state theory in condensed phases, vaNew Trends in Kramers Reaction Rate Theory, P. Hanggi and P. Talkner (eds.), Kluwer Academic, The Netherlands, 1995, pp. 5—4-6. 

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

Allison TC, Trahlar DG (1998) Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunnelling. In Thompson DL (ed) Modern Methods for Multidimensional Dynamics Computations in Chemistry. World Scientific, Singapore, p 618... 

Fernandez-Ramos A, Ellingson BA, Garrett BC, Trahlar DG (2007) Variational transition state theory with multidimensional tunneling. In Lipkowitz KB, Cundari TR, Boyd DB (eds) Reviews in Computational Chemistry, Vol 23. Wiley-VCH, New York, p 125... 

Calculations have identified three transition states (TS) for an SN2 reaction.4"6 Two are variational, one of which is located along the X + RY association reaction path, and the other along the XR + Y" association reaction path i.e. see Figure 1. Variational transition state theory (VTST) calculations show that the third TS is located at the central barrier.4... 

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,... 

Canonical variational transition state theory, with transitional modes treated as harmonic oscillators refs. S... 

S. C. Tucker, Variational transition state theory in condensed phases, in New Trends in... 

Three possibilities were considered to account for the curved Arrhenius plots and unusual KIEs (a) the 1,2-H shift might feature a variational transition state due to the low activation energy (4.9 kcal/mol60) and quite negative activation entropy (b) MeCCl could react by two or more competing pathways, each with a different activation energy (e.g., 1,2-H shift and azine formation by reaction with the diazirine precursor) (c) QMT could occur.60 The first possibility was discounted because calculations by Storer and Houk indicated that the 1,2-H shift was adequately described by conventional transition state theory.63 Option (b) was excluded because the Arrhenius curvature persisted after correction of the 1,2-H shift rate constants for the formation of minor side products (azine).60... 

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