Gaussian overlap model

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

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

where $n=2$, $\Phi _{12}(r)$ is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon(\mathbf{u}_1,\mathbf{u}_2) } and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})} are angle dependent strength and range parameters, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{\mathbf{r}}} is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger proposed a stripped-down version of the model, known as the Gaussian core model. Note that as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n \rightarrow \infty} this potential becomes the penetrable sphere model.

Equation of state

Main article: Equations of state for the Gaussian overlap model

Virial coefficients

Main article: Gaussian overlap model: virial coefficients

Phase diagram

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

References

Related reading

• P. A. Monson and K. E. Gubbins "Equilibrium properties of the Gaussian overlap fluid. Monte Carlo simulation and thermodynamic perturbation theory" Journal of Physical Chemistry 87 pp. 2852-2858 (1983)
• Tomas Boublik "The gaussian overlap model again", Molecular Physics 67 pp. 1327-1336 (1989)
• Lindsey Ann Shall and S. A. Egorov "Structural and dynamical anomalies of a Gaussian core fluid: A mode-coupling theory study", Journal of Chemical Physics 132 184504 (2010)
• Peter Mausbach and Richard J. Sadus "Thermodynamic properties in the molecular dynamics ensemble applied to the Gaussian core model fluid", Journal of Chemical Physics 134 114515 (2011)
• Atsushi Ikeda and Kunimasa Miyazaki "Thermodynamic and structural properties of the high density Gaussian core model", Journal of Chemical Physics 135 024901 (2011)
• Atsushi Ikeda and Kunimasa Miyazaki "Slow dynamics of the high density Gaussian core model", Journal of Chemical Physics 135 054901 (2011)