Transition structure lifetime

The transition state concept, once understood in static terms only, as the saddle point separating reactants and products, may be fruitfully expanded to encompass the transition region, a landscape in several significant dimensions, one providing space for a family of trajectories and for a significant transition state lifetime. The line between a traditional transition structure and a reactive intermediate thus is blurred The latter has an experimentally definable lifetime comparable to or longer than some of its vibrational periods. 

If the reaction is considered on the molar scale, the activated complexes are the molecular species at the hypothetical free energy maximum which separates reactant and product molecules. The distinction between an activated complex (transition structure), which is a real molecular species, though of exceedingly short lifetime, and transition state, which is a hypothetical thermodynamic state on the molar scale, is important though frequently confused [7]. 

Importantly, motion along the reaction coordinate at the saddle point has no restoring force, so the transition structure has only 3 N — 7 real vibrations. Indeed, passage through the saddle corresponds to conversion of the vibration along the reaction coordinate into a translation, so that ksT = hv, where v is frequency of this hypothetical vibration. At 25°C, v = 6 x 1012 s 1 equivalently, the lifetime of a transition structure is 1.7 x 10-13 s and methods capable of observing labile species on this time scale ( transition state spectroscopy ) have been developed, permitting many of the assumptions about their behaviour to be tested directly [1],... 

The fact that we are now able to compute transition energies, lifetimes of excited states, etc... with an accuracy competitive with the uncertainty of the most precise experimental measurements is not only satisfying for the theoreticians ego but has also a very fundamental impact. For example, the last value for the fine structure constant recommended by the 2000 CODATA could not have been obtained without the measurement of the anomalous magnetic... 

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Finke has reported remarkable catalytic lifetimes for the polyoxoanion- and tetrabutylammonium-stabi-lized transition metal nanoclusters [288-292]. For example in the catalytic hydrogenation of cyclohexene, a common test for structure insensitive reactions, the lr(0) nanocluster [296] showed up to 18,000 total turnovers with turnover frequencies of 3200 h [293]. As many as 190,000 turnovers were reported in the case of the Rh(0) analogue reported recently. Obviously, the polyoxoanion component prevents the precious metal nanoparticles from aggregating so that the active metals exhibit a high surface area [297]. 

---