Tersoff mini-potential¶
The Tersoff-mini potential is described in [Fan2020]. It currently only applies to systems with a single atom type. One can use the GPUGA potential to fit this potential for new systems.
Potential form¶
The site potential can be written as
\[U_i = \frac{1}{2} \sum_{j \neq i} f_\mathrm{C}(r_{ij}) \left[ f_\mathrm{R}(r_{ij}) - b_{ij} f_\mathrm{A}(r_{ij}) \right].\]
The function \(f_\mathrm{C}\) is a cutoff function, which is 1 when \(r_{ij}<R_{IJ}\) and 0 when \(r_{ij}>S_{IJ}\) and takes the following form in the intermediate region:
\[f_\mathrm{C}(r_{ij}) = \frac{1}{2}
\left[
1 + \cos \left( \pi \frac{r_{ij} - R}{S - R} \right)
\right].\]
The repulsive function \(f_\mathrm{R}\) and the attractive function \(f_\mathrm{A}\) take the following forms:
\[\begin{split}f_\mathrm{R}(r_{ij}) &= \frac{D_0}{S-1} \exp\left(\alpha r_0\sqrt{2S} \right) e^{-\alpha\sqrt{2S} r_{ij}} \\
f_\mathrm{A}(r_{ij}) &= \frac{D_0S}{S-1} \exp\left(\alpha r_0\sqrt{2/S} \right) e^{-\alpha\sqrt{2/S} r_{ij}}.\end{split}\]
The bond-order function is
\[b_{ij} = \left(1 + \zeta^{n}_{ij}\right)^{-\frac{1}{2n}},\]
where
\[\begin{split}\zeta_{ij} &= \sum_{k\neq i, j} f_C(r_{ik}) g_{ijk} \\
g_{ijk} &= \beta \left(h-\cos\theta_{ijk}\right)^2.\end{split}\]
Parameters¶
Parameter |
Unit |
|---|---|
\(D_0\) |
eV |
\(\alpha\) |
Å\(^{-1}\) |
\(r_0\) |
Å |
\(S\) |
dimensionless |
\(n\) |
dimensionless |
\(\beta\) |
dimensionless |
\(h\) |
dimensionless |
\(R\) |
Å |
\(S\) |
Å |
File format¶
The potential file reads:
tersoff_mini 1 element
D alpha r0 S beta n h R S
Here, element is the chemical symbol of the element.