Gaussian overlap model

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The Gaussian overlap model was developed by Bruce J. Berne and Philip Pechukas and is given by (Ref. 1 Eq. 3)

$\Phi_{12}(\mathbf{u}_1,\mathbf{u}_2,\mathbf{r}) = \epsilon(\mathbf{u}_1,\mathbf{u}_2) \exp \left[ \frac{-r^2}{\sigma^2 (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}}) } \right]$

where $Φ 12 (r)$ is the intermolecular pair potential, $\epsilon(\mathbf{u}_1,\mathbf{u}_2)$ and $\sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})$ are angle dependent strength and range parameters, and $\hat{\mathbf{r}}$ is a unit vector.