Gaussian overlap model: Difference between revisions
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Carl McBride (talk | contribs) (Added mention of the Gauusian core model.) |
Carl McBride (talk | contribs) m (Rewording.) |
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:<math>\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]</math> | :<math>\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]</math> | ||
where <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. | where <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'''. | ||
==Equation of state== | ==Equation of state== | ||
:''Main article: [[Equations of state for the Gaussian overlap model]]'' | :''Main article: [[Equations of state for the Gaussian overlap model]]'' | ||
Revision as of 13:13, 29 September 2009
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^{2}}{\sigma ^{2}(\mathbf {u} _{1},\mathbf {u} _{2},{\hat {\mathbf {r} }})}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71bd768a9d8cc123b8f44c0d2b3e3a915f7b8771)
where is the intermolecular pair potential, and are angle dependent strength and range parameters, and 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.
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, Saija and Giaquinta [3].
References
- ↑ Bruce J. Berne and Philip Pechukas "Gaussian Model Potentials for Molecular Interactions" Journal of Chemical Physics 56 pp. 4213-4216 (1972)
- ↑ Frank H. Stillinger "Phase transitions in the Gaussian core system", Journal of Chemical Physics 65 pp. 3968-3974 (1976)
- ↑ Santi Prestipino, Franz Saija, and Paolo V. Giaquinta "Phase diagram of the Gaussian-core model", Physical Review E 71 050102 (2005)
Related reading