Transition state calculations

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... 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

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]. 

In order to gather more information about this problem, it was deemed worthwhile to follow the energetics of the alkylation reaction of water by methyl-, ethyl-, and fluo-roethyldiazonium ions. The main goal of these calculations was to establish whether transition-state calculations can provide information about hard versus soft electrophilic character of these species.12 Computations at Hartree-Fock and MP2 level were performed using the 6-31G basis set. It was found that both at the Hartree-Fock level and when correlation energy affects were included, the ethyl and fluoroethyl species do not show the presence of a transition state, while the methyl species show a small transition state. It was concluded that transition state computations cannot shed light on the characters of these species. 

Geometric Parameters of Transition State Calculated for Radical Abstraction Reactions sec-R02 + RH by Equations (6.11), (6.35)-(6.37) [35]... 

Diastereoisomeric transition states calculated for propene primary insertion in a model of the Ewen achiral metallocenes are shown in Figure 1.20. The two possible diastereomeric transition states correspond to si (Figure 1.20a) and re (Figure 1.20b) insertions of the monomer for the case of a si chain (i.e., a growing chain in which the last monomeric unit has been obtained by a cis addition of a -coordinated monomer molecule) and are suitable for like (isotactic) and unlike (syndiotactic) propagations, respectively.142,143... 

Compound 53 has an orifice just wide enough to allow the potential entry of small ions, atoms (He), or molecules (H2, D2, T2) inside its cavity as judged from high-level transition state calculations at the density functionally theory level (B3LYP/6-31G, Figure 19).1791 The low barrier of insertion for helium makes it a specially attractive target, but other spe-... 

Figure 4. Transition states calculated for the slippage of BPP34C10 over the model tetraarylmethane stoppers when R is equal to (a) Et and (b) /-Pr. (c) Superposition of both transition states.

Lifshitz, A. Tamburu, C. Suslensky, A. Dubnikova, F. Decomposition of Anthranil. Single Pulse Shock-Tube Experiments, Potential Energy Surfaces and Multiwell Transition-State Calculations. The Role of Intersystem Crossing. Phys. Chem. A 2006, no, 8248-8258. 

Bond Length Bond Angle Equilibrium Structure Transition State Calculated... 

Another series of closely related reactions for which transition-state calculations have greatly helped in providing an understanding of the observed trends is the addition to deuterium-substituted alkenes. Szwarc and co workers (Feld et al., 1962) have determined secondary deuterium isotope effects for methyl and trifluoromethyl radicals by comparing the rate of addition to a terminal alkene with the rate for the deuterium-substituted alkene (25). Isotope effects for cyclopropyl radical addition have been measured by Stefani and coworkers (1970). For these three radicals a small inverse isotope effect (kJkK)... 

Transition-state calculations for the deuterium isotope effects and for the A-factors for addition of methyl and trifluoromethyl radicals to fluoroethylenes all point to the same conclusion, namely, that there must be appreciable loss of double-bond character in the alkene carbon-carbon double bond on passage to the transition state. 

Figure 12. Molecular orbital diagram for an FegOjg cluster used to understand the orbitals involved in Fe Fe3 charge transfer. The absorption band observed near 13,000 cm 1 in the spectra of mixed-valence silicates is due to the transition from the Fe2 (t2g)- Fe3+(t2g) orbitals. A transition state calculation for that energy in the cluster presented here gives 10,570 cm"1 in fair agreement with experiment.

The application of isotope effects studies of reaction mechanism includes comparison of experimental values of isotope effects and predicted isotope effects computed for alternative reaction pathways. On the basis of such analysis some of the pathways may be excluded. Theoretical KIEs are calculated using the method of Bigeleisen and Mayer.1 55 KIEs are a function of transition state and substrate vibrational frequencies. Equilibrium isotope effects are calculated from substrate and product data. Different functionals and data sets are used in these calculations. Implementation of a one-dimensional tunnelling correction into conventional transition-state theory significantly improved the prediction of heavy-atom isotope effects.56 Uncertainty of predicted isotope effect can be assessed from the relationship between KIEs and the distances of formed or broken bonds in the transition states, calculated for different optimized structures.57 Calculations of isotope effects from sets of frequencies for optimized structures of reactants and transition states are facilitated by adequate software QUIVER58 and ISOEFF.59... 

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