MOLECULAR PARTITION FUNCTIONS Introduction

In the last chapter, we have been introduced to the three main ensembles used in statistical mechanics and some examples of calculations of partition functions were also given. In chemistry, we are concerned with a collection of molecules. If the molecules are reasonably far apart as in the case of a dilute gas, we can approximately treat the system as an ideal gas system and ignore the intermolecular forces. The present chapter deals with systems in which intermolecular interactions are ignored. The next chapters will include detailed consideration of intermolecular forces. In ensemble theory, we are concerned with the ensemble probability density, i.e., the fraction of members of the ensemble possessing certain characteristics such as a total energy E, volume V, number of particles N or a given chemical potential μ and so on. The molecular partition function enables us to calculate the probability of finding a collection of molecules with a given energy in a system. The equivalence of the ensemble approach and a molecular approach may be easily realized if we treat part of the molecular system to be in equilibrium with the rest of it and consider the probability distribution of molecules in this subsystem (which is actually quite large compared to systems containing a small number of molecules of the order of tens or hundreds). Since we are dealing with number of particles of the order of Avogadro number, the ensemble description and the molecular descriptions are equivalent. The energies of atoms and molecules are quantized. While atoms have only electronic energy levels, molecules have quantized energy levels arising from electronic, vibrational and rotational motion. A schematic energy level diagram is shown in Fig. 3.1.