**Lecture 1 -- Introduction**

Statistical Mechanics is one of the fundamental branches of theoretical science. It concerns itself primarily with the prediction of the behavior of large numbers of atoms and molecules from the basic laws describing the interactions of small numbers of atoms or molecules. Within the broader field of theoretical chemistry, statistical mechanics occupies a central place between thermodynamics, which treats the behavior of bulk matter without reference to the possible validity of the atomic hypothesis, and quantum mechanics, which treats the electronic structure of single molecules but does not readily treat systems containing substantial numbers of unbonded atoms.

Statistical mechanics requires a description of the motions of individual
atoms and molecules. Such motions may be treated either with classical or
quantum mechanics. In some cases (e.g., internal molecular motions or
translational motions of light atoms (He, Ne) at low *T*), the use of quantum
mechanics is mandatory. However, modern chemistry and modern statistical
mechanics largely treat systems in which the quantum nature of matter is not
readily apparent, quantum theory only being invoked to generate a list of the
allowed energies of the system. To calculate the shapes of molecules, the
forces between them, or the stages of a chemical reaction, quantum mechanics
is needed. To treat translation and rotation (but not internal vibration) of
molecules in liquids, classical mechanics is almost always good enough. (It
is a substantial surprise to some to learn that HCl, when dissolved in liquid
Argon, still has recognizable, discrete rotational energy levels.) The bulk
of modern research in statistical mechanics has been based on classical
statistics. While quantum topics appear below, we will primarily discuss
classical statistical mechanics.

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