njit-etd2003-111 - New Jersey Institute of Technology

16
The classical RRK theory is based on the notion that the probability that a
molecule of s classical oscillators with total energy E has energy greater than E0 in one
chosen oscillator, which is the critical mode leading to reaction. The assumptions used to
derive the quantum RRK rate constant are similar to those for classical theory. In the
quantum theory it is assumed there are s identical oscillators in the molecule, all having
frequency v. The energized molecule has n quanta, so E = nhv. The critical oscillator
must have m quanta for dissociation occurrence, m = E0/hv.
The probability that one oscillator contains at least m quanta; probability (energy
> m quanta in chosen oscillator) is then equal t022 ' 23 :
Where A is a proportion constant.
The corresponding k1(E) of the Hinsheiwood expression is now derived. It refers
to energy transfer into a specific quantum state rather than into an energy range E to E +
dE, as
Both classical and quantum versions RRK theory were developed, and in the limit
of a large excitation energy E the two versions become identical.