The fivefold dependence of the pair functions, , for liquids of rigid, fully anisotropic molecules makes these equations excessively complex for numerical work (see Ref. 1).
The first and essential ingredient for their reduction is a spherical harmonic
expansion of the correlation functions,
where the orientations , the Euler angles with respect
to the axial line between molecular centers,
is a generalized spherical harmonic and .
Inversion of this expression provides the coefficients
Note that by setting , one has the coefficients
for linear molecules.
References
- F. Lado, E. Lomba and M. Lombardero "Integral equation algorithm for fluids of fully anisotropic molecules", Journal of Chemical Physics 103 pp. 481-484 (1995)