Equilibrium Properties of Nonspherical Molecules

The above descriptions of the equilibrium properties of matter were based on spherically symmetric intermolecular interactions. These descriptions work well for nonpolar, compact molecules as described in Chap. 1. Equilibrium properties for molecular systems described by nonspherical, asymmetric intermolecular interactions are considerably more difficult to treat algebraically due to the additional degrees of freedom. Nonetheless, we can follow the same procedures as in Secs. 4.1 and 4.2 to write the equilibrium density function as 

Problem 4.11 involves the determination of U and S for a system of dipoles (dilute polar gas). The Further Reading section at the end of this chapter can be consulted for further treatments and examples. 

This completes our description of the thermodynamic basis functions in terms of the configurational and momenta density functions obtained directly from the equilibrium solution to the Liouville equation. As will be shown in the next chapter, the nonequilibrium counterparts (local in space and time) of the thermodynamic basis functions can also be obtained directly from the Liouville equation, thus, providing a unified molecular view of equilibrium thermodynamics and chemical transport phenomena. Before moving on, however, we conclude this chapter by noting some important aspects of the equilibrium solution to the Liouville equation. 

Some of the more intriguing problems in equilibrium statistical mechanics involve multicomponent and multiphase systems. For single phase, multicomponent systems we can readily extend the methodologies given here. For example, if Na represents the number of molecules of component a, then 

If we again assume pairwise additivity, we can contract Eq. (4.36) over any two molecules, where one molecule is with component a a e 1, L) 

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