# 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¶

tersoff_mini 1 element

Here, element is the chemical symbol of the element.