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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) 