CONTROL OF CHEMICAL-REACTIVITY BY QUANTIZED TRANSITION-STATES

We review the basic principles of quantized transition state control of microcanonical ensemble rate constants and state-selected rate constants. Selected examples are presented for the H + H-2 and O + H-2 reactions. The following aspects are emphasized: (i) We can calculate accurate quantal microcanonical rate constants up to high energies. (ii) These rate constants show resolvable structure which may be attributed to quantized transition states. (iii) The energy dependence of the microcanonical rate constants can be explained quantitatively using a transition state plus tunneling model based on these quantized transition states. (iv) Fitting the model of quantized transition states plus tunneling to the accurate quantum dynamics yields energies, transmission coefficients, and effective barrier widths for individual energy levels of the transition state. (v) The energy level spectrum can be assigned using the conventional model for a complex with a missing degree of freedom. The spectrum is in good agreement with that predicted by the adiabatic theory of reactions or variational transition state theory. The deviations may provide a quantitative test of approximations typically involved in such calculations, e.g., neglect of anharmonic mode couplings. (vi) The individual transmission coefficients show that the quantitative errors in transition state theory (about 10% at the highest energy considered) result from large breakdowns for a few bend-excited levels rather than from small (say 10%) breakdowns for all transition state levels. (vii) The transition state effective barrier widths can be understood both in terms of the barrier widths of vibrationally adiabatic potential curves and in terms of resonance theory. (vii) Transition state resonance theory also allows predictions of transition state lifetimes on the basis of fits to the energy derivative of the microcanonical rate constant. (ix) We can calculate half-collision transition probabilities for specific reactant states to proceed to particular states of the activated complex and for particular states of the activated complex to proceed to specific states of the products; this allows for a very detailed picture of how state-to-state reactions occur. (x) The analysis of state-selected reactivity in terms of passage through particular transition states explains trends in the dependence of rate constants on initial vibrational and rotational quantum numbers.