Editing Gaussian overlap model
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 1: | Line 1: | ||
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: | 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> | :<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'''. | 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'''. Note that as <math>n \rightarrow \infty</math> | ||
this potential becomes the [[penetrable sphere model]]. | this potential becomes the [[penetrable sphere model]]. | ||
==Equation of state== | ==Equation of state== | ||
:''Main article: [[Equations of state for the Gaussian overlap model]]'' | |||
==Virial coefficients== | ==Virial coefficients== | ||
:''Main article: [[Gaussian overlap model: virial coefficients]]'' | |||
==Phase diagram== | ==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]]. | 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== | ==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> | <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> | ||
==References== | ==References== | ||
<references/> | <references/> | ||
| Line 23: | Line 21: | ||
*[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/10.1063/1.3559678 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/10.1063/1.3609277 Atsushi Ikeda and Kunimasa Miyazaki "Thermodynamic and structural properties of the high density Gaussian core model", Journal of Chemical Physics '''135''' 024901 (2011)] | ||
[[Category: Models | [[Category: Models]] | ||