# Gaussian overlap model

The Gaussian overlap model was developed by Bruce J. Berne and Philip Pechukas [1] and is given by Eq. 3 in the aforementioned reference:

${\displaystyle \Phi _{12}(\mathbf {u} _{1},\mathbf {u} _{2},\mathbf {r} )=\epsilon (\mathbf {u} _{1},\mathbf {u} _{2})\exp \left[{\frac {-r}{\sigma (\mathbf {u} _{1},\mathbf {u} _{2},{\hat {\mathbf {r} }})}}\right]^{n}}$

where ${\displaystyle n=2}$, ${\displaystyle \Phi _{12}(r)}$ is the intermolecular pair potential, ${\displaystyle \epsilon (\mathbf {u} _{1},\mathbf {u} _{2})}$ and ${\displaystyle \sigma (\mathbf {u} _{1},\mathbf {u} _{2},{\hat {\mathbf {r} }})}$ are angle dependent strength and range parameters, and ${\displaystyle {\hat {\mathbf {r} }}}$ is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger [2] proposed a stripped-down version of the model, known as the Gaussian core model. For ${\displaystyle n=4}$ a Soft cluster crystal phase has been observed. For Note that as ${\displaystyle n\rightarrow \infty }$ this potential becomes the penetrable sphere model.

## Phase diagram

The phase diagram of the Gaussian-core model has been calculated by Prestipino et al.[5] while the solid-liquid phase equilibria has been calculated by Mausbach et al [6] using the GWTS algorithm.

[8].