Angular Pair Potentials
The angular pair potentials are a combination of the regular pair potentials and a angular dependent term similar to MEAM:
$$ V=\frac{1}{2}\sum\phi_{ij}(r_{ij})+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk})) $$
With this approach it is possible to fit potentials such as this one here.
Or it can be used to consider non-bonded angular interactions as DL_POLY does for the three-body terms (see 'tbp' interaction, p. 174 in the manual). This can be achieved defining the $f_{ij} = 1$ between the pairs that will form 'triple-bonds' and with their cutoff controlling the central radius to account for angular bonded neighbours. Then, just choosing the $g$ function as an harmonic one.
Number of potential functions
To describe a system of $N$ atom types you need $N(N+2)$ potentials.
| # atom types | $\phi_{ij}$ | $f_{ij}$ | $g_i$ | Total # potentials |
|---|---|---|---|---|
| $N$ | $N(N+1)/2$ | $N(N+1)/2$ | $N$ | $N(N+2)$ |
| 1 | 1 | 1 | 1 | 3 |
| 2 | 3 | 3 | 2 | 8 |
| 3 | 6 | 6 | 3 | 15 |
| 4 | 10 | 10 | 4 | 24 |
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:
$\phi_{00}, \ldots, \phi_{0N}, \phi_{11}, \ldots, \phi_{1N}, \ldots, \phi_{NN}$
$f_{00}, \ldots, f_{0N}, f_{11}, \ldots, f_{1N}, \ldots, f_{NN}$
$g_0, \ldots, g_N$