The Tersoff potential

  The family of potentials developed by Tersoff [31], are based on the concept of bond order: the strength of a bond between two atoms is not constant, but depends on the local environment. This idea is similar to that of the ``glue model'' for metals, to use the coordination of an atom as the variable controlling the energy. In semiconductors, however, the focus is on bonds rather than atoms: that is where the electronic charge is sitting in covalent bonding.

At first sight, a Tersoff potential has the appearance of a pair potential:  

$$V={1\over 2}\sum_{ij} \phi_R (r_{ij}) + +{1\over 2}\sum_{ij} B_{ij} \phi_A (r_{ij}) +$$ (41)

where R and A mean ``repulsive'' and ``attractive''. However, it is not a pair potential because B_ij is not a constant. In fact, it is the bond order for the bond joining i and j, and it is a decreasing function of a ``coordination'' G_ij assigned to the bond:

B_ij = B(G_ij) .

G_ij is in turn defined as

$$G_{ij} = \sum_k f_c(r_{ik}) g(\theta_{jik}) f(r_{ij}-r_{ik})$$ (43)

where f_c(r), f(r) and $g(\theta)$ are suitable functions. The basic idea is that the bond ij is weakened by the presence of other bonds ik involving atom i. The amount of weakening is determined by where these other bonds are placed. Angular terms appear necessary to construct a realistic model.

This scheme works in a broader spectrum of situations than the Stillinger-Weber potential, however it is not exempt from problems. One of the biggest problems is perhaps that the fit is difficult: with 6 functions to fit and angular terms, finding a good parametrization is not an easy task.

These potentials have also been applied to hydrocarbons [32].