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.

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

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

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

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.

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:

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

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.

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