Intermolecular pair potential

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[edit] Axially symmetric molecules

In general, the intermolecular pair potential for axially symmetric molecules, $Φ 12$ , is a function of five coordinates:

$\left. \Phi_{12} \right. = \Phi_{12}(r, \theta_1, \phi_1, \theta_2, \phi_2)$

The angles $θ i$ and $φ i$ 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 $ψ i$ do not influence the value of $Φ 12$ . A very powerful expansion of this pair potential is due to Pople (Ref. 1 Eq. 2.1):

$\left. \Phi_{12} \right. = 4\pi \sum_{L_1 L_2 m} L_1 L_2 m (r) Y_{L_1}^m (\theta_1, \phi_1) Y_{L_2}^m * (\theta_2, \phi_2)$ ,