Transition state theory validation limits

This equilibrium hypothesis is, however, not necessarily valid for rapid chemical reactions. This brings us to the second way in which solvents can influence reaction rates, namely through dynamic or frictional effects. For broad-barrier reactions in strongly dipolar, slowly relaxing solvents, non-equilibrium solvation of the activated complex can occur and the solvent reorientation may also influence the reaction rate. In the case of slow solvent relaxation, significant dynamic contributions to the experimentally determined activation parameters, which are completely absent in conventional transition-state theory, can exist. In the extreme case, solvent reorientation becomes rate-limiting and the transition-state theory breaks down. In this situation, rate con-... 

The plots in Fig. 2 suggest that the limits of validity of transition state theory may be fairly narrow or altogether nonexistent, contrary to the prediction made by Kramers. The nonequilibrium effects duly treated for extremely low friction may start being felt before the TST plateau is approached. This is more likely to occur for the lower barriers and larger ratios... 

Let us turn now to the corresponding inelastic cross-section. The matrix elements (/, M L + 2S J, M) vanish except for / —/ = 1. Hence, near the forward direction we observe only the dipole-allowed transitions, i.e., the /—> / 1 transitions out of the Hund s rule ground state. Beyond the limit of small K, higher-order transitions contribute to the cross-section, and these are the main subject of the subsequent theory valid for arbitrary values of k. The small-K result we present for inelastic events, / = / 1, is of limited practical value since the minimum value of c is usually quite large owing to the kinematic constraints on the scattering process. Even so, the result is a useful guide to the size of the cross-section, and a welcome check on a complete calculation. 

An interesting, but probably incorrect, application of the probabilistic master equation is the description of chemical kinetics in a dilute gas.5 Instead of using the classical deterministic theory, several investigators have introduced single time functions of the form P(n1,n2,t) where P(nu n2, t) is the probability that there are nl particles of type 1 and n2 particles of type 2 in the system at time t. They use the transition rate A(nt, n2 n2, n2, t) from the state with particles of type 1 and n2 particles of type 2 to the state with nt and n2 particles of types 1 and 2, respectively, at time t. The rates that are used are obtained by assuming that only uncorrelated binary collisions occur in the system. These rates, however, are only correct in the thermodynamic limit for a low density system. In this limit, the Boltzmann equation is valid from which the deterministic theory follows. Thus, there is no reason to attach any physical significance to the differences between the results of the stochastic theory and the deterministic theory.6... 

The tensors which enter theoretical expressions are transition tensors 7, for a transition between an initial state i and a final state /. The Placzek polarizability theory for vibrational Raman scattering [56], which we use here, is valid in the far from resonance limit, i and / are then vibrational states. If we assume that they differ for normal mode p, then the transition tensors can be written as... 

It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. 

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