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interactions:tersoffmod

# modified Tersoff Potential

The modified Tersoff potential1) is available when potfit is compiled with the tersoffmod flag, which also implies the apot flag for analytic potentials.

## Basic Theory

The total potential energy is defined as

$$E_{\text{total}}= \frac{1}{2}\sum_{i,j}f_c(r_{ij})\left(A_{ij}e^{-\lambda_{ij}r_{ij}}+b_{ij}B_{ij} e^{-\mu_{ij}r_{ij}}\right)$$

where

$$b_{ij} = \left(1+\zeta_{ij}^{\eta}\right)^{-\delta},$$

$$\zeta_{ij} = \sum_{k\neq i,j}f_c(r_{ik})g(\theta_{ijk})\exp[\alpha(r_{ij}-r_{ik})^\beta]$$

and

$$g(\theta_{ijk}) = c_1 + g_o(\theta)g_a(\theta)$$

$$g_o(\theta) = \frac{c_2(h-\cos\theta)^2}{c_3+(h-\cos\theta)^2}$$

$$g_a(\theta) = 1 + c_4\exp[-c_5(h-\cos\theta)^2].$$

The cutoff function $f_c$ is given as

$$f_c(r_{ij}) = \begin{cases} 1 & r_{ij} \le R_1 \\ \frac{1}{2} + \frac{9}{16}\cos\left(\frac{\pi(r_{ij}-R_1)}{R_2-R_1}\right)-\frac{1}{16} \cos\left(\frac{3\pi(r_{ij}-R_1)}{R_2-R_1}\right) & R_1 < r_{ij} < R_2 \\ 0 & R_2 \le r_{ij} \end{cases}.$$

### Analytic functions

To defined a modified Tersoff potential in potfit, there is the special tersoff_mod_pot function which requires 16 parameters.

## Number of potential functions

While basically systems with more than one atom type can be described using modified Tersoff potentials, this is completely untested. A system containing $N$ atom types requires $N(N+1)/2$ potential functions.

# atom types tersoff_mod_pot
$N$ $N(N-1)/2$
1 1
2 3
3 6
4 10

## Order of potential functions

The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.

The order of the potentials in the potential file for $N$ atom types is:

$\Phi_{00}, \ldots, \Phi_{0N}, \Phi_{11}, \ldots, \Phi_{1N}, \ldots, \Phi_{NN}$

### IMD output

An analytic IMD potential which can be used with the tersoffmod2 option of IMD is written to *.imd.tersoffmod.pot. This file, however, may not be used as a potential file for IMD. Instead, its contents need to be copied INTO the IMD parameter file.

### LAMMPS output

The potential can also be written in LAMMPS format. The name of the output file is *.lammps.tersoffmod.

1)
T. Kumagai et al., Comp. Mat. Sci. 39, 457 (2007)