Chapter 2 - The Statistical Mechanical Foundation

Abstract

A summary of the most important definitions and relationships needed to apply either classical mechanics (CM) or quantum mechanics (QM) to the statistical analysis of molecular fluids is provided. The concept of a state is defined in terms of a phase space point in CM while it becomes a wavefunction, and preferably an energy eigenfunction, in the case of QM. The great difference between the formalism and the nature of the numerical challenge met in using CM or QM to do statistical mechanics is discussed. In CM the states are easy to define and use but they form a continuum and must be quantized in accord with the correspondence principle in order to yield partition functions and thermodynamic properties. In QM the energy eigenstates must be obtained by challenging mathematical or numerical methods but, when found, the statistical and thermodynamic properties are more readily calculated. Quantum effects are normally dominant for electrons, very important for vibrations, significant for rotations at low temperatures but unimportant for translations – unless we deal with very light molecules at very low temperatures.