In section 1, the concept of an ensemble (of molecules) in the statistical mechanics is shortly introduced. The following three sections (sections 2–4) serve as a summary of the energy levels in the molecules and the corresponding density of states and partition functions, which are components in statistical calculations. The last two sections summarize the framework of practical statistical calculations.
Section 1: «Introduction – Statistical Mechanics»
Two typical ensembles of molecules, canonical ensemble and microcanonical ensemble are introduced in this section, and their application to the rate theories will be discussed.
Section 2: «Electronic States of Atoms and Molecules»
Chemical reactions often involve the changes of electronic states, and thus, the degeneracy (or the statistical weight) changes from the reactants, via transition states (and/or the intermediates), to the products. A concise summary for proper counting of the degeneracy of elecronic states will be shown.
Section 3: «External Nuclear Motions»
In this section, external motions of nuclei in molecules, traslational motion and (external) rotation, are described and their quantum mechanical eigenstates, density of states, and partition function are formulated. Also, a brief summary is given for the rotational symmetry number and number of (optical) isomers.
Section 4: «Intramolecular Motions»
Vibrational motion and internal rotaion are described with their density of states and partition function. A concise summary of the treatment for free/hindered internal rotation is also given.
Section 5: «Canonical Statistics»
In this section, application of canonical statistics for thermodynamic functions and thermal rate theory are discribed.
Section 6: «Microcanonical Statistics»
Microcanonical variation of the rate theory, RRKM or microscopic rate constant, and its application to the unimolecular reactions will be discussed.
Suggestions for Further Reading
For basic subjects including thermodynamics, statistical thermodynamics, quantum mechanics of electronic states and nuclear motions, and etc.;
- P. Atkins and J. de Paula, Atkins' Physical Chemistry, 7th Ed., Oxford University Press (2002).
For trasitional statistical mechanics of gas-phase molecules;
- J. H. Knox, Molecular thermodynamics - An Introduction to Statistical Mechanics for Chemists, John Wiley & Sons (1971).
- D. A. McQuarrie, Statistical Mechanics, University Science Books (2000).