Editing Gaussian overlap model

The '''Gaussian overlap model''' was developed by Bruce J. Berne and Philip Pechukas <ref>[http://dx.doi.org/10.1063/1.1677837 Bruce J. Berne and Philip Pechukas "Gaussian Model Potentials for Molecular Interactions" Journal of Chemical Physics '''56''' pp. 4213-4216  (1972)]</ref> and is given by Eq. 3 in the aforementioned reference:

:<math>\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</math>

where <math>n=2</math>, <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math> \epsilon(\mathbf{u}_1,\mathbf{u}_2) </math> and <math>\sigma (\mathbf{u}_1,\mathbf{u}_2, \hat{\mathbf{r}})</math> are angle dependent strength and range parameters, and <math>\hat{\mathbf{r}}</math> is a unit vector. Not long after the introduction of the Gaussian overlap model Stillinger <ref>[http://dx.doi.org/10.1063/1.432891 Frank H. Stillinger "Phase transitions in the Gaussian core system", Journal of Chemical Physics '''65''' pp. 3968-3974 (1976)]</ref> proposed a stripped-down version of the  model, known as the '''Gaussian core model'''. For <math>n=4</math> a [[Soft cluster crystal phase]] has been observed. For Note that as <math>n \rightarrow \infty</math>
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.<ref>[http://dx.doi.org/10.1103/PhysRevE.71.050102 Santi Prestipino, Franz Saija, and Paolo V. Giaquinta "Phase diagram of the Gaussian-core model", Physical Review E '''71''' 050102 (2005)]</ref> while the solid-liquid phase equilibria has been calculated by Mausbach et al <ref>[http://dx.doi.org/10.1063/1.3256004 Peter Mausbach, Alauddin Ahmed, and Richard J. Sadus "Solid-liquid phase equilibria of the Gaussian core model fluid", Journal of Chemical Physics '''131''' 184507 (2009)]</ref> using the [[GWTS algorithm]].
==Shear viscosity==
<ref>[http://dx.doi.org/10.1063/1.3273083  Alauddin Ahmed, Peter Mausbach, and Richard J. Sadus "Strain-rate dependent shear viscosity of the Gaussian core model fluid", Journal of Chemical Physics '''131''' 224511 (2009)]</ref>
==Isotropic-nematic phase transition==
<ref>[http://dx.doi.org/10.1063/1.4981887 G. Rickayzen and D. M. Heyes "Isotropic-nematic phase transition of uniaxial variable softness prolate and oblate ellipsoids", Journal of Chemical Physics 146, 164505 (2017)]</ref>.
==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1021/j100238a030 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)]
*[http://dx.doi.org/10.1080/00268978900101841 Tomas Boublik "The gaussian overlap model again", Molecular Physics '''67''' pp. 1327-1336 (1989)]
*[http://dx.doi.org/10.1063/1.3429354 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)]
*[http://dx.doi.org/10.1063/1.3559678 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)] 
*[http://dx.doi.org/10.1063/1.3609277 Atsushi Ikeda and Kunimasa Miyazaki "Thermodynamic and structural properties of the high density Gaussian core model", Journal of Chemical Physics '''135''' 024901 (2011)]
*[http://dx.doi.org/10.1063/1.3615949 Atsushi Ikeda and Kunimasa Miyazaki "Slow dynamics of the high density Gaussian core model", Journal of Chemical Physics '''135''' 054901 (2011)]
*[https://doi.org/10.1063/1.5013644 Manoj Kumar Nandi and Sarika Maitra Bhattacharyya "Analysis of the anomalous mean-field like properties of Gaussian core model in terms of entropy", Journal of Chemical Physics '''148''' 034504 (2018)]

[[Category: Models]] 
[[Category: liquid crystals]]