Spherical harmonic expansion of the intermolecular site-site potential

An analytic expression is given for the expansion of a site-site intermolecular potential , where u αβ is a function of the form r αβ -n , r αβ being the site-site distances, in terms of (generalized) spherical harmonics. Explicit expressions are obtained for the harmonic coefficients for the cases of linear, tetrahedral and octahedral molecules and when u αβ is the Lennard-Jones (12, 6) model. The convergence of this expansion is studied for molecules of these symmetries, and is found to be rapid in most cases provided that L*(= L/σ) is less than about 0·22, where L is the largest centre-to-site distance, and σ is the effective molecular diameter.