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1.  Introduction
– Statistical
2006 Reaction Dynamics & Kinetics - Section 1

Section 1: Introduction – Statistical Mechanics

  In the canonical ensemble, molecules exchange energy mutually, but the total energy of the ensemble is preserved. The energy distribution in the canonical ensemble is the "Boltzmann distribution". It is the ensemble that we usually observe, e.g., the air in a room. The equilibrium thermodynamic property of the ensemble, such as enthalpy or entropy, can be defined as a function of temperature.
  On the other hand, in the microcanonical ensemble, energy is exchanged among vibrational motions and/or internal rotational motions, but the total energy of a molecule is kept constant. Usually, such an ensemble is expected in a fast phenomenon. For example, imagine molecules excited by a laser light. Upon excitation, all the molecules are expected to have same energy, and dissociate within very short time, in the orders of ps (= 10−12 s). The excited molecule does not have time to exchange energy with other molecules, but the energy may be distributed in the various modes of vibration.
  The microcanonical statistics is also applied to the unimolecular decomposition reactions in the fall-off region, where the energy required for decompostion is provided by the collisions with other molecules, but, because of the fast dissociation of excited molecules, the internal energy distribution significantly deviates from the Boltzmann distribution, especially at high energy. Theoretical details for the unimolecular reactions will be discussed in the section 6.


Microcanonical ensemble, Degeneracy, Density of states, Canonical ensemble, Boltzmann distribution, Partition function, Chemical equilibrium

Lecture note

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