## Liquid-State Physical Chemistry: Fundamentals, Modeling, and Applications (2013)

### 7. Modeling the Structure of Liquids: The Integral Equation Approach

### 7.5. Molecular Fluids*

From the above sections it will be clear that an extension of this approach to molecular fluids is complex. At least the position coordinate set must be enlarged with angular coordinates that represent the orientation of a molecule is space. Two approaches are possible for this. The first approach employs the methods as discussed before, but with much stronger intramolecular interactions as compared to the intermolecular interactions. This enlarges the problem but without introducing new concepts. Of course, the reliability depends heavily on the balance between intra- and intermolecular interactions.

The second approach recognizes upfront that intramolecular interactions are much stronger, and takes the limit to rigid molecules. The rationale for this is that the structure of sufficiently rigid molecules in the condensed phase is hardly different from that in the gas phase__ ^{4)}__. This approach requires extra conjugated variables, thereby introducing some additional complexity.

Apart from the difference in methods there are some further considerations to make for molecular fluids. Spectroscopy teaches us that the time for one rotation of a molecule, say N_{2} at 1 bar and 25°C, is ∼ 3 × 10^{−11} s, much shorter than the typical time between the collision of molecules, of ∼ 2 × 10^{−10} s. In liquids, however, the molecules are much closer together and, assuming that during each vibration they actually touch, they can do so many times during one rotation because the typical vibration time of N_{2} is ∼1.4 × 10^{−14} s. In this case, the use of an uncoupled rotation partition function is less justified. Moreover, in a number of cases quantum corrections are required, in particular for the hydrogen atoms in the molecule. For example, in the case of H_{2}O, two internal vibrations have a wave number of about 3700 cm^{−1} which are so low that quantum corrections are required.