MICROCANONICAL TRANSITION-STATE THEORY RATE COEFFICIENTS FROM THERMALRATE CONSTANTS VIA INVERSE LAPLACE TRANSFORMATION

On the basis of concepts from the mathematical theory of approximation of functions, we propose a method of deriving microcanonical transiti on state theory rate coefficients, both as a function of the total ene rgy and the total angular momentum, from thermal data, namely, the lim iting high-pressure rate coefficients. The method does not require the knowledge of the frequencies and degeneracies of the transition state and is general in that it allows for non-Arrhenius forms of thermal d ata, but it only applies to reactions possessing an intrinsic energy b arrier, It is shown that the derived microcanonical rate coefficient i s almost identical to the computed Rice-Ramsperger-Kassel-Marcus (RRKM ) microcanonical rate coefficient using explicit frequencies and degen eracies of the transition state, and furthermore, that the difference between the two is uniformly distributed over the entire range of tota l energy and the entire range of the total angular momentum. Compariso n of the microcanonical coefficients from the proposed method with tho se from a standard nonvariational RRKM calculation is presented for th e unimolecular decomposition of the ethyl radical and the unimolecular isomerization of methyl isocyanide. The agreement is shown to be exce llent. A theoretical analysis of the fine structure of the microcanoni cal rate coefficient near the threshold of the reaction is enunicated and the difficulty of extending the method to obtain variational micro canonical rate coefficients is described. We also, briefly, speculate on the possible merits of certain theoretical methods of analysis for coping with the representation of thermal data, whose argument is the temperature which is of semiinfinite range.