Calculation of reactive cross sections and microcanonical rates from kinetic and thermochemical data

In general, kinetic rate data may be represented by van't Hoff's four-parameter equation. When this is true, the mathematical properties of the Laplace transform may be used to derive phenomenological equations that describe the energy-dependent reactive cross sections and microcanonical rates in terms of the same four parameters. Since the macroscopic rate data and microscopic expressions are related by the Laplace transform, these microscopic descriptions do not imply new information; they simply express the information contained in the rate data in another form. The Monte Carlo techniques used to determine confidence envelopes for the rate data may also be used to provide confidence envelopes or "bounds" for the energy-dependent properties. These microscopic expressions may be used to compare and contrast theoretical calculations or as a starting point in RRKM or master equation calculations. Both the forward and reverse H + O-2 <-> OH + O reactions and the associative reaction CH3 + CH3 --> C2H6 are used to illustrate the above ideas. In the first example, the cross section for the reverse reaction shows that it is not dominated by the dipole-quadrupole interaction. The cross section for the forward reaction is obtained by fitting rate data from 158 to 5300 K and peaks just above the threshold of 8354 K. In the second example, comparison to recent theoretical calculations highlights the importance of angular momentum and the centrifugal barrier.