We shall now generalize the results of the previous section to molecular
liquids . We view the liquid at first as being a mixture of
atomic liquids, containing as many components as there are atoms in the
molecule. Eq. (2.3) then simply generalizes to

(2.23) |

where is the density of -atoms at a distance

(2.24) |

the OZ equation becomes

(2.25) |

Dividing by and Fourier transforming we get in matrix notation

Here is the diagonal matrix with elements . The transition to -space is only for reason of simpler notation.

We of course know that the correlations between the atoms are partly due to
the fact that they form molecules. Therefore we write

where stems from the intramolecular correlations and from the intermolecular correlations .

In the ideal gas limit we may approximate

(2.28) |

which, when introduced into the OZ equation (2.26) yields

(2.29) |

We therefore write in general

where is called the intermolecular part of the direct correlation function matrix. Introducing Eqs. (2.27) and ( 2.30) into the OZ equation we get after some algebra

where we have used the fact that and commute. For pure molecular liquids this follows from the fact that is equal to the molecular density times the unit matrix. A proof for molecular mixtures is a little bit more involved. Once we know the intramolecular correlation we may calculate the intermolecular correlation from Eq. ( 2.31) by using one of the closure relations

= | (2.32) | ||

= | (2.33) |

which we simply try in analogy with similar calculations on simple liquids. Of course this may turn out to be a very crude approximation. Experience so far shows that it works well as long as one is interested in describing the local structure in the liquid. For very small values of the wavevector

We end this section with some remarks about the intramolecular correlation function. We Fouriertransform
Eq. (2.27), and next add
to each of its
elements, obtaining

Here is the density of -atoms at a distance