Intermolecular pair potential

The intermolecular pair potential is a widely used approximation. Real intermolecular interactions consist of two-body interactions, three-body interactions, four-body interactions etc. However, the calculation of even three-body interactions is computationally time consuming, and the calculation of only two-body interactions is frequent. Such "effective" pair potentials often include the higher order interactions implicitly.

Axially symmetric molecules

In general, the intermolecular pair potential for axially symmetric molecules, $\Phi _{12}$, is a function of five coordinates:

$\left.\Phi _{12}\right.=\Phi _{12}(r,\theta _{1},\phi _{1},\theta _{2},\phi _{2})$

The angles $\theta _{i}$ and $\phi _{i}$ can be considered to be polar angles, with the intermolecular vector, $r$, as the common polar axis. Since the molecules are axially symmetric, the angles $\psi _{i}$ do not influence the value of $\Phi _{12}$. A very powerful expansion of this pair potential is due to Pople (Ref. 1 Eq. 2.1):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.\Phi _{12}\right.=4\pi \sum _{L_{1}L_{2}m}L_{1}L_{2}m(r)Y_{L_{1}}^{m}(\theta _{1},\phi _{1})Y_{L_{2}}^{m}*(\theta _{2},\phi _{2})} ,

where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Y_{L}^{m}(\theta ,\phi )} are the spherical harmonics.

See also

• Idealised models

References

1. J. A. Pople "The Statistical Mechanics of Assemblies of Axially Symmetric Molecules. I. General Theory", Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 221 pp. 498-507 (1954)