Applications and Extensions of Statistical Theories

The RRKM rate constant as given by equation (6.73) in the previous chapter is expressed as a ratio of the sum of states in the transition state and the density of states in the reactant molecule. An accurate calculation of this rate constant requires that all vibrational anharmonicity and vibrational/rotational coupling be included in calculating the sum and density. The vibrational energy levels in units of wavenumbers can be represented by a power series  

A convenient way to represent the RRKM rate constant with anharmonicity is as a product  

Anharmonic corrections have also been determined for unimolecular rate constants using classical mechanics. In a classical trajectory (Bunker, 1962, 1964) or a classical Monte Carlo simulation (Nyman et al., 1990 Schranz et al., 1991) of the unimolecular decomposition of a microcanonical ensemble of states for an energized molecule, the initial decomposition rate constant is that of RRKM theory, regardless of the molecule s intramolecular dynamics (Bunker, 1962 Bunker, 1964). This is because a 

Molecule E (kcal) D,(kcal) Panh(E)/Ph( ) Method Reference 

Often the amount of information concerning a molecule or ion is insufficient to justify the inclusion of anharmonic terms, or even rotational effects. The RRKM equation can nevertheless be successfully employed, and it can yield relatively accurate rate constants. We begin this section with the simplest use of the RRKM equation, in which we assume harmonic frequencies and assume that 7 = 0. 

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