Transition state theory and gas isotopic fractionation

Petroleum and natural gas generation processes can be approximated as carbon-carbon bond breakage of complex kerogen and hydrocarbon compounds. It is generally believed that a bond is easier to break than a bond (Schoell 1983, 1988  

In the previous section, the kinetics and mechanisms of hydrocarbon thermal cracking were examined using ab initio quantum mechanical calculations. In this section we will review how transition state theory (TST) can be applied to calculate the carbon isotopic fractionation associated with natural gas generation. 

Once the information about the reactants, transition states, and products are obtained, various models of transition state theory (TST) can be applied to calculate the rate of the reaction. At the level of the harmonic approximation, the TST formulae can be written as  

Where k is the rate constant, k is the transmission coefficient from the collision theory, Piunn is the tunneling correction, and the Qs are the standard partition functions (see Felipe et al. in this volume). By substituting appropriate carbon atoms with different isotopes on the molecule, one can calculate the ratio of the rate constants (kinetics isotopic effect). 

Ab initio methods provide the information needed in Equations (25) and (26) to calculate the rate constants and kinetic isotope effect of gas phase reaction as well as surface reactions. For example. Table 6 shows calculated activation energies and frequency factors for some elementary reactions involving atoms and radicals. The theoretical and experimental results agree with each very well. For detailed discussions on the relevant 

---