# The Tersoff-mini potential

## Potential form

• Restrictions: This potential has only been developed for single-element systems so far.
• The site potential can be written as

$$U_i = \frac{1}{2} \sum_{j \neq i} f_{\rm C}(r_{ij}) \left[ f_{\rm R}(r_{ij}) - b_{ij} f_{\rm A}(r_{ij}) \right].$$

• The function $f_{\rm C}$ is a cutoff function, which is 1 when $r_{ij}\lt R_{IJ}$ and 0 when $r_{ij}\gt S_{IJ}$ and takes the following form in the intermediate region:

$$f_{\rm C}(r_{ij}) = \frac{1}{2} \left[ 1 + \cos \left( \pi \frac{r_{ij} - R}{S - R} \right) \right].$$

• The repulsive function $f_{\rm R}$ and the attractive function $f_{\rm A}$ take the following forms:

$$f_{\rm R}(r_{ij}) = \frac{D_0}{S-1} \exp\left(\alpha r_0\sqrt{2S} \right) e^{-\alpha\sqrt{2S} r_{ij}};$$ $$f_{\rm A}(r_{ij}) = \frac{D_0S}{S-1} \exp\left(\alpha r_0\sqrt{2/S} \right) e^{-\alpha\sqrt{2/S} r_{ij}}.$$

• The bond-order function is

$$b_{ij} = \left(1 + \zeta^{n}_{ij}\right)^{-\frac{1}{2n}},$$ where $$\zeta_{ij} = \sum_{k\neq i, j} f_C(r_{ik}) g_{ijk};$$ $$g_{ijk} = \beta \left(h-\cos\theta_{ijk}\right)^2.$$

## Parameters

 Parameter Units $D_0$ eV $\alpha$ A$^{-1}$ $r_0$ A $S$ dimensionless $n$ dimensionless $\beta$ dimensionless $h$ dimensionless $R$ A $S$ A

## Potential file format

### Single-element systems

   tersoff_mini 1